Brittle Structures

June 04, 2020    Comment   

Brittle Structures

If you look at the photographs of rock outcrops, you’ll notice thin dark lines that cross the rock faces. These lines represent traces of natural cracks along which the rock broke and separated into two pieces during brittle deformation.  Geologists refer to such natural cracks as joints (figure above a, b). Rock bodies do not slide past each other on joints. Since joints are roughly planar structures, we define their orientation by their strike and dip, as described in (Describing the Orientation of Geologic Structures).

Joints develop in response to tensile stress in brittle rock: a rock splits open because it has been pulled slightly apart. Joints may form for a variety of geologic reasons. For example, some joints form when a rock cools and shrinks because the process makes one part of a rock pull away from the adjacent part. Others develop when rock formerly at depth undergoes a decrease in pressure as overlying rock erodes away, and thus changes shape slightly. Still others form when rock layers bend.

Geotechnical engineers, people who study the geologic setting of construction sites, pay close attention to jointing when recommending where to put roads, dams, and buildings. Water flows much more easily through joints than it does through solid rock, so it would be a bad investment to situate a water reservoir over rock containing lots of joints the water would leak down into the joints. Also, building a road on a steep cliff composed of jointed rock could be risky, for joint-bounded blocks separate easily from bedrock, and the cliff might collapse.

If groundwater or hydrothermal fluids seep through cracks in rocks, minerals such as quartz or calcite may precipitate out of the groundwater and fill the crack. A mineral-filled crack is called a vein. Veins may look like white stripes cutting across a body of rock (figure above c). Some veins contain small quantities of valuable metals, such as gold.

After the San Francisco earthquake of 1906, geologists found a rupture that had torn through the land surface near the city. Where this rupture crossed orchards, it offset rows of trees, and where it crossed a fence, it broke the fence in two; the western side of the fence moved northward by about 2 m. The rupture represents the trace of the San Andreas Fault. As we have seen, a fault is a fracture on which sliding occurs, and slip events, or faulting, can generate earthquakes. Faults, like joints, are planar structures, so we can represent their orientation by strike and dip.

Faults have formed throughout Earth history. Some are currently active in that sliding has been occurring on them in recent geologic time, but most are inactive, meaning that sliding on them ceased long ago. Some faults, such as the San Andreas, intersect the ground surface and thus displace the ground when they move. Others accommodate the sliding of rocks in the crust at depth and remain invisible at the surface unless they are later exposed by erosion.

Fault Classification

Not all faults result in the same kind of crustal deformation some accommodate horizontal shear, some accommodate shortening, and some accommodate stretching. It’s important for geologists to distinguish among different kinds of faults in order to interpret their tectonic significance. Fault classification focuses on two characteristics of faults: (1) the dip of the fault surface (seeDescribing the Orientation of Geologic Structures) the dip can be vertical, horizontal, or any angle in between; and (2) the shear sense across the fault by shear sense, we mean the direction that material on one side of the fault moved relative to the material on the other side. With this concept in mind, let’s consider the principal kinds of faults.

The different categories of faults.

• Strike-Slip Faults: A strike-slip fault is a fault on which the slip direction is parallel to a strike line, a horizontal line on the fault surface (seeDescribing the Orientation of Geologic Structures). This means that the block on one side of the fault slips sideways, relative to the block on the other side, and there is no up-or-down motion. Most strike-slip faults have a steep to vertical dip. Geologists distinguish between two types of strike-slip faults based on the shear sense as viewed when you are facing the fault and looking across it. If the block on the far side slipped to your left, the fault is a left-lateral strike-slip fault, and if the block slipped to the right, the fault is a right-lateral strike-slip fault (figure above a). The faults that occur at transform plate boundaries are strike-slip faults.
• Dip-Slip Faults: On a dip-slip fault, movement is parallel to the dip line, a line parallel to the slope of the fault surface  (seeDescribing the Orientation of Geologic Structures), so the hanging-wall block, meaning the material above the fault surface, slides up or down relative to the footwall block, the material below the fault surface (figure above b). If the hanging-wall block slides up, the fault is a reverse fault; a reverse fault with a gentle dip is also known as thrust fault. Reverse faults accommodate shortening of the crust, as happens during continental collision. If the hanging-wall block slides down, the fault is a normal fault. Normal faults accommodate stretching of the Earth’s crust, as happens during rifting.
• Oblique-Slip Faults: On an oblique-slip fault, sliding occurs diagonally on the fault plane. In effect, an oblique-slip fault is a combination of a strike-slip and a dip-slip fault (figure above c).

Recognizing Faults

Recognizing fault displacement in the field.

How do you recognize a fault when you see one? The most obvious criterion is the occurrence of displacement, meaning the movement across a fault plane. Displacement offsets the layers in rocks, so that layers on one side of a fault are not continuous with layers on the other side (figure above a, b).

Faults may also leave their mark on the landscape. Those that intersect the ground surface while they are active can displace natural landscape features such as stream valleys or glacial moraines (figure above c), and human-made features such as highways, fences, or rows of trees in orchards. Displacement on a dip-slip or oblique-slip fault will make a step on the ground surface; this step is called a fault scarp (figure above a). And because faults tend to break up and weaken rock, the “fault trace” (the line of intersection between the fault and the ground surface) preferentially erodes to become a linear valley.

Faulting under brittle conditions may crush or break rock. If this shattered rock consists of visible angular fragments, then it is called fault breccia (figure above b), but if it consists of a fine powder, then it is called fault gouge. Some fault surfaces are polished and grooved by the movement on the fault. Polished fault surfaces are called slickensides, and linear grooves on fault surfaces are slip lineations or fault striations (figure above c). We specify the orientation of a slip lineation by giving its plunge and bearing (seeDescribing the Orientation of Geologic Structures).

Features of exposed fault surfaces.

Describing the Orientation of Geologic Structures

Specifying the orientation of planar and linear structures.

When discussing geologic structures, it’s important to be able to communicate information about their orientation. For example, does a fault exposed in an outcrop at the edge of town continue beneath the nuclear power plant 3 km to the north, or does it go beneath the hospital 2 km to the east? If we knew the fault’s orientation, we might be able to answer this question. To describe the orientation of a geologic structure, geologists picture the structure as a simple geometric shape, then specify the angles that the shape makes with respect to a horizontal plane (a flat surface parallel to sea level), a vertical plane (a flat surface perpendicular to sea level), and the north direction (a line of longitude).

Let’s start by considering planar structures such as faults, beds, and joints. We call these structures planar because they resemble a geometric plane. A planar structure’s orientation can be specified by its strike and dip. The strike is the angle between an imaginary horizontal line  (the strike line) on the plane and the direction to true north (figure above a, b). We measure the strike with a special type of compass (figure above c). The dip is the angle of the plane's slope more precisely, it is the angle between a horizontal plane

and the dip line (an imaginary line parallel to the steepest slope on the structure), as measured in a vertical plane perpendicular to the strike. We measure the dip angle with a clinometer, a type of protractor. A horizontal plane has a dip of 0°, and a vertical plane has a dip of 90°. We represent strike and dip on a geologic map using the symbol shown in figure above b.

A linear structure resembles a geometric line rather than a plane; examples of linear structures include scratches or grooves on a rock surface. Geologists specify the orientation of a line by giving its plunge and bearing (figure above d). The plunge is the angle between a line and horizontal in the vertical plane that contains the line. A horizontal line has a plunge of 0°, and a vertical line has a plunge of 90°. The bearing is the compass heading of the line, meaning the angle between the projection of the line on the horizontal plane and the direction to true north.

Credits: Stephen Marshak (Essentials of Geology)

Folds and Foliations

June 04, 2020    Comment   

Folds and Foliations

Geometry of Folds Imagine a carpet lying ?At on the ?Oor. Push on one end of the carpet, and it'll wrinkle or contort into a series of wavelike curves. Stresses evolved throughout mountain constructing can similarly warp or bend bedding and foliation (or other planar features) in rock. The end result a curve in the shape of a rock layer is called a fold.

Geometric traits of folds.

Not all folds look the same some look like arches, some look like troughs, and some have other shapes. To describe these shapes, we must first label the parts of a fold (figure above a). The hinge refers to a line along which the curvature is greatest, and the limbs are the sides of the fold that display less curvature. The axial surface is an imaginary plane that contains the hinges of successive layers and effectively divides the fold into two halves. With these terms in hand, we distinguish among the following:

• Anticlines, synclines, and monoclines: Folds that have an arch-like shape in which the limbs dip away from the hinge are called anticlines (figure above a), whereas folds with a trough-like shape in which the limbs dip toward the hinge are called synclines (figure above b). A monocline has the shape of a carpet draped over a stair step (figure above c).
• Non-plunging and plunging folds: If the hinge is horizontal, the fold is called a non-plunging fold, but if the hinge is tilted, the fold is called a plunging fold (figure above d).
• Domes and basins: A fold with the shape of an overturned bowl is called a dome, whereas a fold shaped like an upright bowl is called a basin (figure above e, f). Domes and basins both display circular outcrop patterns that look like bull’s-eyes the oldest layer occurs in the centre of a dome, whereas the youngest layer is located in the centre of a basin.

Using these terms, now see if you can identify the various folds shown in figure above a–e.

Formation of Folds

Fold improvement in flexural-slip and passive go with the flow-folding.

Folds develop in two principal ways (figure above a, b). During formation of flexural-slip folds, a stack of layers bends, and slip occurs between the layers. The same phenomenon happens when you bend a deck of cards to accommodate the change in shape, the cards slide with respect to each other. Passive-flow folds form when the rock, overall, is so soft that it behaves like weak plastic and slowly flows; these folds develop simply because different parts of the rock body flow at different rates.

Folding is caused by several special strategies, as illustrated by the following move sections.

Why do folds form? Some layers wrinkle up, or buckle, in response to end-on compression (figure above a–d). Others form where shear stress gradually shifts one part of a layer up and over another part. Still others develop where rock layers move up and over step-like bends in a fault and must curve to conform with the fault’s shape. Finally, some folds form when new slip on a fault causes a block of basement to move up so that the overlying sedimentary layers must warp.

Tectonic Foliation in Rocks

In an undeformed sandstone, the grains of quartz are roughly spherical, and in an undeformed shale, clay flakes press  together into the plane of bedding so that shales tend to split parallel to the bedding. During ductile deformation, however, internal changes take place in a rock that gradually modify the original shape and arrangement of grains. For example, quartz grains may transform into cigar shapes, elongate ribbons, or tiny pancakes, and clay flakes may recrystallize or reorient so that they lie at an angle to the bedding. Overall, deformation can produce inequant grains and can cause them to align parallel to each other. We refer to layering developed by the alignment of grains in response to deformation as tectonic foliation.

The development of tectonic foliation in rock.

We introduced foliation, which include slaty cleavage, schistosity, and gneissic layering, at the same time as discussing the outcomes of metamorphism. Here we add to the story with the aid of noting that such foliation bureaucracy in reaction to ?Attening and shearing in ductilely deforming rocks in other phrases, foliation indicates that the rock has advanced a stress below metamorphic situations (discern above a, b).

Credits: Stephen Marshak (Essentials of Geology)

Structural geology and tectonics

May 27, 2020    Comment   

Structural geology and tectonics

The word shape is derived from the Latinword struere, to construct, and lets say:

"A geologic shape is a geometrical con?Guration of rocks, and structural geology deals with the geometry, distribution and formation of systems".

It should be added that structural geology only deals with structures created during rock deformation, not with primary structures formed by sedimentary or magmatic processes. However, deformation structures can form through the modification of primary structures, such as folding of bedding in a sedimentary rock.

The closely related word tectonics comes from the Greek word tektos, and both structural geology and tectonics relate to the building and resulting structure of the Earth’s lithosphere, and to the motions that change and shape the outer parts of our planet. We could say that tectonics is more closely connected to the underlying processes that cause structures to form:

"Tectonics is attached with outside and frequently local methods that generate a feature set of structures in a place or a location".

By external we mean external to the rock volume that we study. External processes or causes are in many cases plate motions, but can also be such things as forceful intrusion of magma, gravity-driven salt or mud diapirs, flowing glaciers and meteor impacts. Each of these “causes” can create characteristic structures that define a tectonic style, and the related tectonics can be given special names. Plate tectonics is the large-scale part of tectonics that directly involves the movement and interaction of lithospheric plates. Within the realm of plate tectonics, expressions such as subduction tectonics, collision tectonics and rift tectonics are applied for more specific purposes.

Glaciotectonics is the deformation of sediments and bedrock (generally sedimentary rocks) at the toe of an advancing ice sheet. In this case it is the pushing of the ice that creates the deformation, particularly where the base of the glacier is cold (frozen to the substrate).

Salt tectonics deals with the deformation caused by the (mostly) vertical movement of salt through its overburden. Both glaciotectonics and salt tectonics are primarily driven by gravity, although salt tectonics can also be closely related to plate tectonics. For example, tectonic strain can create fractures that enable salt to gravitationally penetrate its cover. The term gravity tectonics is generally restricted to the downward sliding of large portions of rocks and sediments, notably of continental margin deposits resting onweak salt or overpressured shale layers. Raft tectonics is a type of gravity tectonics occurring in such environments. Smaller landslides and their structures are also considered examples of gravity tectonics by some, while others regard such surficial processes as non-tectonic. Typical nontectonic deformation is the simple compaction of sediments and sedimentary rocks due to loading by younger sedimentary strata.

Neotectonics is concerned with recent and ongoing crustal motions and the contemporaneous stress field. Neotectonic structures are the surface expression of faults in the form of fault scarps, and important data sets stem from seismic information from earthquakes and changes in elevation of regions detected by repeated satellite measurements.

At smaller scales, microtectonics describes microscale deformation and deformation structures visible under the microscope.

Structural geology typically pertains to the observation, description and interpretation of structures that can be mapped in the field. How do we recognize deformation or strain in a rock? “Strained” means that something primary or preexisting has been geometrically modified, be it cross stratification, pebble shape, a primary magmatic texture or a preexisting deformation structure. Hence strain can be defined as a change in length or shape, and recognizing strain and deformation structures actually requires solid knowledge of undeformed rocks and their primary structures.

Being able to apprehend tectonic deformation depends on our know-how of number one systems.

The ensuing deformation shape additionally depends at the initial fabric and its texture and shape. Deforming sandstone, clay, limestone or granite effects in signi?Cantly distinctive systems due to the fact they reply otherwise. Furthermore, there is often a close dating among tectonics and the formation of rocks and their number one structures. Sedimentologists enjoy this as they observe variations in thickness and grain length inside the striking wall (down-thrown aspect) of syndepositional faults. This is illustrated in Fig. 1, where the sluggish rotation and subsidence of the down-faulted block offers space for thicker strata near the fault than farther away, resulting in wedge formed strata and regularly steeper dips down phase. There is likewise a facies variation, with the coarsest-grained deposits forming near the fault, which may be attributed to the fault-induced topography visible in Fig. 1.

Another close relationship between tectonics and rock forming processes is shown in Figure 2, where forceful rising and perhaps inflating of magma deforms the outer and oldest part of the pluton and its country rock. Forceful intrusion of magma into the crust is characterized by deformation near the margin of the pluton, manifested by folding and shearing of the layers in Figure 2. Ellipses in this figure illustrate the shape of enclaves (inclusions), and it is clear that they become more and more elongated as we approach the margin of the pluton. Hence, the outer part of the pluton has been flattened during a forceful intrusion history.

Metamorphic growth of minerals before, all through, and after deformation may offer important records about the pressure?Temperature situations all through deformation, and might incorporate textures and systems re?Ecting kinematics and deformation history. Hence, sedimentary, magmatic and metamorphic strategies may additionally all be closely associated with the structural geology of a locality or region.

These examples relate to strain, but structural geologists, especially those dealing with brittle structures of the upper crust, are also concerned with stress. Stress is a somewhat diffuse and abstract concept to most of us, since it is invisible. Nevertheless, there will be no strain without a stress field that exceeds the rock’s resistance against deformation. We can create a stress by applying a force on a surface, but at a point in the lithosphere stress is felt from all directions, and a full description of such a state of stress considers stress from all directions and is therefore three-dimensional. There is always a relationship between stress and strain, and while it may be easy to establish from controlled laboratory experiments it may be difficult to extract from naturally formed deformation structures.

Structural geology covers deformation structures shaped at or near the Earth?S floor, within the cool, upper part of the crustwhere rocks have a propensity to fracture, in the warmer, decrease crust wherein the deformation tends to be ductile, and intheunderlying mantle.It embraces systems at the size of loads of kilometers down to micro- or atomic-scale systems, structures that shape nearly instantly, and systems that form over tens of thousands and thousands of years.

A big number of subdisciplines, procedures and strategies consequently exist in the ?Eld of structural geology. The oil exploration geologist may be thinking about entice-forming structures fashioned during rifting or salt tectonics, at the same time as the manufacturing geologist worries about subseismic sealing faults (faults that prevent ?Uid ?Ow in porous reservoirs). The engineering geologist may don't forget fracture orientations and densities in relation to a tunnel project, at the same time as the college professor makes use of structural mapping, bodily modeling or pc modeling to apprehend mountain-building tactics. The techniques and processes are many, however they serve to recognize the structural or tectonic improvement of a vicinity or to expect the structural sample in an area. In most instances structural geology is founded on statistics and observations that ought to be analyzed and interpreted. Structural analysis is therefore an important a part of the ?Eld of structural geology.

Structural data are analyzed in ways that lead to a tectonic model for an area. By tectonic model we mean a model that explains the structural observations and puts them into context with respect to a larger-scale process, such as rifting or salt movements. For example, if we map out a series of normal faults indicating E–W extension in an orogenic belt, we have to look for a model that can explain this extension. This could be a rift model, or it could be extensional collapse during the orogeny, or gravity-driven collapse after the orogeny. Age relations between structures and additional information (radiometric dating, evidence for magmatism, relative age relations and more) would be important to select a model that best fits the data. It may be that several models can explain a given data set, and we should always look for and critically evaluate alternative models. In general, a simple model is more attractive than a complicated one.

Structural information units

Planet Earth represents an incredibly complex physical system, and the structures that result from natural deformation reflect this fact through their multitude of expressions and histories. There is thus a need to simplify and identify the one or few most important factors that describe or lead to the recognition of deformation structures that can be seen or mapped in naturally deformed rocks. Field observations of deformed rocks and their structures represent the most direct and important source of information on how rocks deform, and objective observations and careful descriptions of naturally deformed rocks are the key to understanding natural deformation. Indirect observations of geologic structures by means of various remote sensing methods, including satellite data and seismic surveying, are becoming increasingly important in our mapping and description of structures and tectonic deformation. Experiments performed in the laboratory give us valuable knowledge of how various physical conditions, including stress field, boundary condition, temperature or the physical properties of the deforming material, relate to deformation. Numerical models, where rock deformation is simulated on a computer, are also useful as they allow us to control the various parameters and properties that influence deformation.

Experiments and numerical models no longer best assist us understand how external and internal physical situations control or are expecting the deformation structures that form, however additionally deliver information on how deformation structures evolve, i.E. They provide insights into the deformation records. In assessment, certainly deformed rocks constitute cease-effects of herbal deformation histories, and the history may be dif?Cult to study out of the rocks themselves. Numerical and experimental models permit one to control rock homes and boundary conditions and explore their effect on deformation and deformation history. Nevertheless, any deformed rock includes a few information about the history of deformation. The challenge is to understand what to look for and to interpret this facts. Numerical and experimental work aids in completing this project, collectively with goal and accurate ?Eld observations.

Numerical, experimental and remotely acquired information units are crucial, however should continually be based on ?Eld observations.

It is tough to overemphasize the importance of conventional ?Eld observations of deformed rocks and their structures. Rocks contain greater records than we can ever be capable of extract from them, and the achievement of any physical or numerical version is predicated on the accuracy of remark of rock structures within the ?Eld. Direct contact with rocks and structures which have no longer been ?Ltered or interpreted via humans or computers is beneficial.

Unfortunately, our capacity to make goal observations is limited. What we've got found out and visible within the past strongly in?Uences our visible impressions of deformed rocks. Any student of deformed rocks need to therefore teach himself or herself to be objective. Only then can we count on to discover the surprising and make new interpretations that can make contributions to our information of the structural development of a area and to the ?Eld of structural geology in trendy. Many structures are ignored until the day that a person factors out their lifestyles and meaning, upon which they all of a sudden appear ?Everywhere?. Shear bands in strongly deformed ductile rocks (mylonites). They were either neglected or taken into consideration as cleavage till the late 1970s, once they were well described and interpreted. Since then, they have been defined from almost each important shear region or mylonite zone inside the world.

Traditional ?Eldwork involves the use of simple gear consisting of a hammer, measuring tool, topomaps, a hand lens and a compass, and the facts amassed are especially structural orientations and samples for skinny segment research. This type of information series is still crucial, and is aided by using modern-day international positioning machine (GPS) gadgets and excessive-decision aerial and satellite tv for pc pictures. More superior and distinct work can also contain the usage of a portable laser-scanning unit, where pulses of laser mild strike the surface of the Earth and the time of return is recorded. This information can be used to build an in depth topographic or geometrical model of the outcrop, onto which one or extra high-resolution ?Eld photographs may be draped. An instance of the sort of version is shown in Figure 3, even though the gain of in reality shifting around in the model can not be validated by way of a ?At photograph. Geologic observations such as the orientation of layering or fold axes can then be made on a pc.

In many cases, the most vital manner of recording ?Eld statistics is via use of cautious ?Eld sketches, aided by way of photos, orientation measurements and different measurements that can be associated with the cartoon. Sketching additionally forces the ?Eld geologist to look at features and info which can in any other case be left out. At the equal time, sketches can be made to be able to emphasize relevant statistics and forget about beside the point details. Field sketching is, in large part, a be counted of exercise.

Satellite images, such as those shown in Figure 4a, c, are now available at increasingly high resolutions and are a valuable tool for the mapping of map-scale structures. An increasing amount of such data is available on the World Wide Web, and may be combined with digital elevation data to create three-dimensional models. Orthorectified aerial photos (orthophotos) may give more or other details (Figure 4b), with resolutions down to a few tens of centimetres in some cases. Both ductile structures, such as folds and foliations, and brittle faults and fractures are mappable from satellite images and aerial photos.

In the field of neotectonics, InSAR (Interferometric Synthetic Aperture Radar) is a useful remote sensing technique that uses radar satellite images. Beams of radar waves are constantly sent toward the Earth, and an image is generated based on the returned information. The intensity of the reflected information reflects the composition of the ground, but the phase of the wave as it hits and becomes reflected is also recorded. Comparing phases enables us to monitor millimetre-scale changes in elevation and geometry of the surface, which may reflect active tectonic movements related to earthquakes. In addition, accurate digital elevation models (see next section) and topographic maps can be constructed from this type of data.

GPS records in popular are an crucial source of records that may be retrieved from GPS satellites to measure plate actions (Figure 5). Such information also can be amassed on the floor by using stationary GPS devices with right down to millimetre-scale accuracy.

DEM, GIS and Google Earth

Conventional paper maps are still useful for many field mapping purposes, but rugged laptops, tablets and handheld devices now allow for direct digitizing of structural features on digital maps and images and are becoming more and more important. Field data in digital form can be combined with elevation data and other data by means of a Geographical Information System (GIS). By means of GIS we can combine field observations, various geologic maps, aerial photos, satellite images, gravity data, magnetic data, typically together with a digital elevation model, and perform a variety of mathematical and statistical calculations. A digital elevation model (DEM) is a digital representation of the topography or shape of a surface, typically the surface of the Earth, but a DEM can be made for any geologic surface or interface that can be mapped in three dimensions. Surfaces mapped from cubes of seismic data are now routinely presented as DEMs and can easily be analyzed in terms of geometry and orientations.

Inexpensive or unfastened get admission to to geographic information exists, and this kind of statistics was revolutionized with the aid of the improvement of Google Earth within the ?Rst decade of this century. The particular information to be had from Google Earth and related sources of virtual facts have taken the mapping of faults, lithologic contacts, foliations and more to a new stage, both in terms of ef?Ciency and accuracy.

Seismic information

In the mapping of subsurface structures, seismic data are invaluable and since the 1960s have revolutionized our understanding of fault and fold geometry. Some seismic data are collected for purely academic purposes, but the vast majority of seismic data acquisition is motivated by exploration for petroleum and gas. Most seismic data are thus from rift basins and continental margins.

Fig. 6. Seismic 2-D line from the Santos Basin offshore Brazil, illustrating how important structural aspects of the subsurface geology can be imaged by means of seismic exploration. Note that the vertical scale is in seconds.

Acquisition of seismic data is, by its nature, a special type of remote sensing (acoustic), although always treated separately in the geo-community. Marine seismic reflection data (Figure 6) are collected by boat, where a sound source (air gun) generates sound waves that penetrate the crustal layers under the sea bottom. Microphones can also be put on the sea floor. This method is more cumbersome, but enables both seismic S- and P-waves to be recorded (S-waves do not travel through water). Seismic information can also be collected onshore, putting the sound source and microphones (geophones) on the ground. The onshore sound source would usually be an explosive device or a vibrating truck, but even a sledgehammer or specially designed gun can be used for very shallow and local targets.

The sound waves are re?Ected from layer limitations in which there may be an growth in acoustic impedance, i.E. Wherein there's an abrupt exchange in density and/or the velocity with which sound waves journey within the rock. A lengthy line of microphones, onshore referred to as geophones and offshore referred to as hydrophones, file the re?Ected sound signals and the time they seem at the surface. These records are amassed in digital shape and processed by computers to generate a seismic photograph of the underground.

Seismic information can be processed in a number of ways, depending on the focus of the study. Standard reflection seismic lines are displayed with two-way travel time as the vertical axis. Depth conversion is therefore necessary to create an ordinary geologic profile from those data. Depth conversion is done using a velocity model that depends on the lithology (sound moves faster in sandstone than in shale, and yet faster in limestone) and burial depth (lithification leads to increased velocity). In general it is the interpretation that is depth converted. However, the seismic data themselves can also be depth migrated, in which case the vertical axis of the seismic sections is depth, not time. This provides more realistic displays of faults and layers, and takes into accountlateralchangesinrockvelocitythatmaycausevisual or geometrical challenges to the interpreter when dealing with a time-migrated section. The accuracy of the depthmigrated data does however rely on the velocity model

Deep seismic lines can be accrued wherein the power emitted is suf?Ciently high to penetrate deep parts of the crust and even the upper mantle. Such traces are useful for exploring the massive-scale shape of the lithosphere. While broadly spaced deep seismic traces and local seismic lines

are called two-dimensional (2-D) seismic data, more and more commercial (petroleum company) data are collected as a three-dimensional (3-D) cube where line spacing is close enough (c. 25m) that the data can be processed in three dimensions, and where sections through the cube can be made in any direction. The lines parallel to the direction of collection are sometimes called inlines, those orthogonal to inlines are referred to as crosslines, while other vertical lines are random lines. Horizontal sections are called time slices, and can be useful during fault interpretation.

Three-dimensional seismic data provide unique opportunities for 3-D mapping of faults and folds in the subsurface. However, seismic data are restricted by seismic resolution, which means that one can only distinguish layers that are a certain distance apart (typically around 5–10m), and only faults with a certain minimum offset can be imaged and interpreted. The quality and resolution of 3-D data are generally better than those of 2-D lines because the reflected energy is restored more precisely through 3-D migration. The seismic resolution of high-quality 3-D data depends on depth, acoustic impedance of the layer interfaces, data collection method and noise,but would typically be at around 15–20m for identification of fault throw.

Sophisticated methods of data analysis and visualization at the moment are to be had for 3-D seismic information units, beneficial for identifying faults and different systems which are underground. Petroleum exploration and exploitation typically rely on seismic three-D statistics units interpreted on computers by geophysicists and structural geologists. The interpretation makes it feasible to generate structural contour maps and geologic pass-sections that can be analyzed structurally in diverse methods, e.G. Through structural healing.

Three-D seismic statistics shape the inspiration of our structural knowledge of hydrocarbon ?Elds.

Other styles of seismic records also are of interest to structural geologists, particularly seismic data from earthquakes. This data offers us important facts approximately present day fault motions and tectonic regime, which in simple terms manner whether or not a place is undergoing shortening, extension or strike-slip deformation.

Offshore collection of seismic information is achieved by using a vessel that travels at about 5 knots whilst towing arrays of air guns and streamers containing hydrophones some meters beneath the floor of the water. The tail buoy enables the crew find the stop of the streamers. The air guns are activated periodically, which include each 25m (approximately each 10 seconds), and the ensuing sound wave that travels into the Earth is re?Ected back via the underlying rock layers to hydrophones at the streamer and then relayed to the recording vessel for in addition processing.

The few sound traces shown at the ?Gure suggest how the sound waves are each refracted across and re?Ected from the interfaces between the water and Layer 1, between Layer 1 and a pair of, and between Layer 2 and three. Re?Ection happens if there is an increase within the product among speed and density from one layer to the next. Such interfaces are referred to as re?Ectors. Re?Ectors from a seismic line image the top stratigraphy of the North Sea Basin (right). Note the upper, horizontal sea mattress re?Ector, horizontal Quaternary re?Ectors and dipping Tertiary layers. Unconformities like this one usually suggest a tectonic occasion. Note that maximum seismic sections have seconds (two-manner time) as vertical scale.

Credits: Haakon Fossen (Structural Geology)

Structural analysis

May 26, 2020    Comment   

Structural analysis

Many structural tactics span thousands to hundreds of thousands of years, and maximum structural data describe the ?Nal made of a protracted deformation history. The history itself can simplest be found out via careful evaluation of the data. When searching at a fold, it could not be apparent whether it shaped by way of layer parallel shortening, shearing or passive bending. The identical factor applies to a fault. What part of the fault fashioned ?Rst? Did it form with the aid of linking of person segments, or did it grow from a unmarried factor outward, and in that case, become this factor inside the vital part of the prevailing fault floor? It won't usually be smooth to reply such questions, but the technique need to constantly be to analyze the ?Eld records and examine with experimental and/or numerical models.

The analysis of the geometry of structures is referred to as geometric analysis. This includes the shape, geographic orientation, size and geometric relation between the main (first-order) structure and related smaller-scale (second-order) structures. The last point emphasizes the fact that most structures are composite and appear in certain structural associations at various scales. Hence, various methods are needed to measure and describe structures and structural associations.

Geometric evaluation is the conventional descriptive approach to structural geology that most secondary structural geologic analytical strategies construct on.

Fig. 2. Listric normal fault showing very irregular curvature in the sections perpendicular to the slip direction. These irregularities can be thought of as large grooves or corrugations along which the hanging wall can slide.

Shape is the spatial description of open or closed surfaces such as folded layer interfaces or fault surfaces. The shape of folded layers may give information about the fold-forming process or the mechanical properties of the folded layer, while fault curvature may have implications for hanging-wall deformation (Figure 1) or could give information about the slip direction (Figure 2).

Orientations of linear and planar structures are perhaps the most common type of structural data. Shapes and geometric features may be described by mathematical functions, for instance by use of vector functions. In most cases, however, natural surfaces are too irregular to be described accurately by simple vector functions, or it may be impossible to map faults or folded layers to the extent required for mathematical description. Nevertheless, it may be necessary to make geometric interpretations of partly exposed structures. Our data will always be incomplete at some level, and our minds tend to search for geometric models when analyzing geologic information. For example, when the Alps were mapped in great detail early in the twentieth century, their major fold structures were generally considered to be cylindrical, which means that fold axes were considered to be straight lines. This model made it possible to project folds onto cross-sections, and impressive sections or geometric models were created. At a later stage it became clear that the folds were in fact non-cylindrical, with curved hinge lines, requiring modification of earlier models.

Fig 3, Synthetic structural data sets showing different degree of homogeneity. (a) Synthetic homogeneous set of strike and dip measurements. (b) Systematic variation in layer orientation measurements. (c) Homogeneous subareas due to kink or chevron folding. (d, e) Systematic fracture systems. Note how the systematics is reflected in the stereonets.

Fig. 4. Lineation data from subareas defined in the previous figure. The plots show the variations within each subarea, portrayed by means of poles, rose diagrams, and an arrow indicating the average orientation. The number of data within each subarea is indicated by “n”.

In geometric analysis it is very useful to represent orientation data (e.g. Fig. 3 and 4) by means of stereographic projection. Stereographic projection is used to show or interpret both the orientation and geometry of structures. The method is quick and efficient, and the most widely used tool for presenting and interpreting spatial data. In general, geometry may be presented in the form of maps, profiles, stereographic projections, rose diagrams or threedimensional models based on observations made in the field, from geophysical data, satellite information or laser scanning equipment. Any serious structural geologist needs to be familiar with the stereographic projection method.

Strain and kinematic evaluation

Geometric description and analysis may form the basis for strain quantification or strain analysis. Such quantification is useful in many contexts, e.g. in the restoration of geologic sections through deformed regions. Strain analysis commonly involves finite strain analysis, which concerns changes in shape from the initial state to the very end result of the deformation. Structural geologists are also concerned with the deformation history, which can be explored by incremental strain analysis. In this case only a portion of the deformation history is considered, and a sequence of increments describes the deformation history.

By definition, strain applies to ductile deformation, i.e. deformation where originally continuous structures such as bedding or dikes remain continuous after the deformation. Ductile deformation occurs when rocks flow (without fracture) under the influence of stress. The opposite, brittle deformation, occurs when rocks break or fracture. However, modern geologists do not restrict the use of strain to ductile deformation. In cases where fractures occur in a high number and on a scale that is significantly smaller than the discontinuity each of them causes, the discontinuities are overlooked and the term brittle strain is used. It is a simplification that allows us to perform strain analysis on brittle structures such as fault populations.

Fig. 5. Abrasive marks (slickenlines) on fault slip surfaces give local kinematic information. Seismically active fault in the Gulf of Corinth.

Fig. 6. An example of how geometric analysis can lead to a kinematic model, in this case of sense of movement on a fault. (a) A fault where stratigraphy cannot be correlated across the fault. (b, c) Relative movement can be determined if layer rotation can be observed close to the fault. The geometry shown in (b) supports a normal fault movement, while (c) illustrates the geometry expected along a reverse fault.

Geometric description also forms the foundation of kinematic analysis, which concern show rock particles have moved during deformation (the Greek word kinema means movement). Striations on fault surfaces (Figure 5) and deflection of layering along faults and in shear zones are among the structures that are useful in kinematic analysis.

To illustrate the relationship between kinematic evaluation and geometric evaluation, keep in mind the fault depicted in Figure 6a. We can not correlate the layers from one aspect to the other, and we do not realize whether or not this is a normal or opposite fault. However, if we ?Nd a de?Ection of the layering along the fault, we will use that geometry to interpret the experience of motion at the fault. Figure 6 b, c indicates the one-of-a-kind geometries that we would count on for everyday and reverse movements. In other words, a ?Eld based totally kinematic evaluation is based on geometric analysis.

Dynamics is the study of forces that cause motion of particles (kinematics). Forces acting on a body generate stress, and if the level of stress becomes high enough, rocks start to move. Hence dynamics in the context of structural geology is about the interplay between stress and kinematics. When some particles start to move relative to other particles we get deformation, and we may be able to see changes in shape and the formation of new structures.

Dynamic analysis explores the stresses or forces that purpose systems to form and stress to accumulate.

In maximum instances dynamic analysis seeks to reconstruct the orientation and magnitude of the pressure ?Eld via studying a hard and fast of structures, typically faults and fractures. Returning to the example proven in Fig. 6, it maybe assumed that a sturdy force or pressure acted in the vertical path in case (b), and within the horizontal course in case (c). In exercise, the exact orientations of forces and pressure axes are dif?Cult or impossible to estimate from a unmarried fault structure, but may be predicted for populations of faults forming in a uniform strain ?Eld.

Applying stress to syrup gives a different result than stressing a cold chocolate bar: the syrup will flow, while the chocolate bar will break. We are still dealing with dynamic analyses, but the part of dynamics related to the flow of rocks is referred to as rheologic analysis. Similarly, the study of how rocks (or sugar) break or fracture is the field of mechanical analysis. In general, rocks flow when they are warm enough, which usually means when they are buried deep enough.“Deep enough” means little more than surface temperatures for salt, around 300 C for a quartz-rich rock, perhaps closer to 550 C for a feldspathic rock, and even more for olivine-rich rocks. Pressure also plays an important role, as does water content and strain rate. It is important to realize that different rocks behave differently under any given conditions, but also that the same rock reacts differently to stress under different physical conditions. Rheological testing is done in the laboratory in order to understand how different rocks flow in the lithosphere.

Fig 7. Scanning electron microphotograph of a millimeter-skinny region of grain deformation (deformation band) in the Entrada Sandstone close to Goblin Valley State Park, Utah.

Tectonic evaluation includes dynamic, kinematic and geometric evaluation at the dimensions of a basin or orogenic belt. This kind of evaluation may also consequently contain extra elements of sedimentology, paleontology, petrology, geophysics and different subdisciplines of geoscience. Structural geologists worried in tectonic analysis are once in a while known as tectonicists. On the opposite quit of the size range, some structural geologists analyze the systems and textures that may most effective be studied thru the microscope. This is the study of the way deformation takes place among and within person mineral grains and is referred to as microstructural evaluation or microtectonics. Both the optical microscope and the scanning electron microscope (SEM) (Fig. 7.) are beneficial equipment in microstructural analysis.

Credits: Haakon Fossen (Structural Geology)

Stereographic projection

May 26, 2020    Comment   

Stereographic projection

Stereographic projection is about representing planar and linear features in a two-dimensional diagram. The orientation of a plane is represented by imagining the plane to pass through the centre of a sphere (Fig. 1a). The line of intersection between the plane and the sphere will then represent a circle, and this circle is formally known as a great circle. Except for the field of crystallography, where upper-hemisphere projection is used, geologists use the lower part of the hemisphere for stereographic projections, as shown in Fig. 1b. We would like to project the plane onto the horizontal plane that runs through the centre of the sphere. Hence, this plane will be our projection plane, and it will intersect the sphere along a horizontal circle called the primitive circle.

To perform the projection we connect points on the lower half of our great circle to the topmost point of the sphere or the zenith (red lines in Fig. 1c). A circleshaped projection (part of a circle) then occurs on our horizontal projection plane, and this projection is a stereographic projection of the plane. If the plane is horizontal it will coincide with the primitive circle, and if vertical it will be represented by a straight line. Stereographic projections of planes are formally called cyclographic traces, but are almost always referred to as great circles because of their close connection with great circles as defined above.

Once we understand how the stereographic projection of a plane is finished it also will become obvious how lines are projected, because a line is only a subset of a plane. Lines for that reason mission as points, even as planes assignment as super circles. A exceptional circle (as any circle) can be considered to include factors, each of which represents a line withinthe plane. Hence, a line contained in a plane, inclusive of a slickenline or mineral lineation, will therefore seem as a factor on the amazing circle corresponding to that plane.

In Fig. 2 we have additionally projected the road this is normal to a given plane, represented by way of the pole to the aircraft. The projection is determined by means of orienting the line thru the middle and connecting its intersection with the decrease hemisphere with the zenith (pink line in Fig. 2a). The intersection of this (red) line with the projection plane is the pole to the aircraft. Hence, planes may be represented in two approaches, as notable circle projections and as poles. Note that horizontal strains plot along the primitive circle (completely horizontal poles are represented by means of opposite symbols) and vertical lines plot in the centre.

For stereographic projections to be practical, we have to establish a grid of known surfaces for reference. We have already equipped the primitive circle with geographical directions (north, south, east and west), and we can compare the sphere with a globe with longitudes and latitudes. In three dimensions this is illustrated in Fig. 3, looking from the south pole toward the north pole: longitudes and latitudes are the lines of intersection between great circles (the original meaning) and so-called small circles. If we now project the small and great circles onto the horizontal projection plane, typically for every 2 and 10 degree interval, we will get what is called a stereographic net or stereonet.

The longitudes are planes that intersect in a common line (the N–S line), and thus appear as great circles in the stereonet. The projections of the latitudes, which are not planes but cones coaxial with the N–S line, are usually referred to as small circles (also their projections onto the stereonet). The net that emerges from the particular projection described above is called the Wulff net.

Fig. 5. The equal area projection. A plane is projected onto the projection aircraft, which in this case has been made tangential to the decrease pole of the sphere. The projection is illustrated in 3-D (a) and alongside a seasoned?Le thru C and A (b).

Fig. 6. Two hundred and fifty quartz c-axes measured at the U-level and plotted inside the stereonet. An asymmetrical pattern with recognize to the foliation (trending E?W in the plot), consisting of the only shown here, indicates the sense of shear.

The Wulff net makes it possible to work with angular relations (it preserves angles between planes across the net), which can be useful in some cases, for instance for crystallographic purposes. However, for most structural purposes it is more useful to preserve area, so that the densities of projections in one part of the plot can be directly compared to those of another. The method of plotting is the same, but because the projection is not stereographic but equal area (Fig. 4), the positions of planes and lines in the plot become somewhat different. The net is called a Schmidt net or simply an equal area net (Fig. 5 shows the equal area projection). Multiple data plotted in an equal area net can be contoured with respect to density, which can be useful when evaluating concentrations of structural data around certain geographic directions. Contouring is typically done for crystallographic axes such as quartz c-axes (Fig. 6), and the contour values exhibit the number of points as the percentage within a given 1% area of the stereonet. Contouring is easily done by means of one of the many computer programs available for personal computers.

Plotting planes

Planes can be represented in a stereonet in two different ways: by means of great circles or poles (Fig 2). Fig. 5 gives a demonstration of how to plot both by hand, and we will start with a great circle representation.

Fig. 7. Plotting the plane N 030 E, 30 NE in the stereonet (equal area projection).

A aircraft placing 030 (or N 30 E) and dipping 30 to the SE is plotted as an instance. Tracing paper is located over a pre-made internet (an equal vicinity internet was chosen), and the facilities are attached by way of a thumb tack. The primitive circle and north (N) are marked on the transparent overlay. We then mark off the strike price of our plane, that's 030 (Fig. 7a), and then rotate the overlay so that this mark happens above the N direction of the underlying stereo plot (Fig. 7b). For our instance, this includes rotating the overlay 30 anticlockwise. We then count the dip fee from the primitive circle inwards, and hint the superb circle that it falls on (Fig. 7b). When N on the tracing paper is circled returned to its unique orientation (Fig. 7c) we have a splendid circle that represents our aircraft. The shallower its dip, the nearer it comes to the primitive circle, which itself represents a horizontal aircraft.

The technique is pretty similar if we need to devise poles. All we do otherwise is to matter the dip from the middle of the plot inside the course opposite to that of the dip, which in our example is to the left. When performed efficaciously, there can be ninety between the tremendous circle and the pole of the same aircraft (see Fig. 7b). The pole for this reason falls on the other aspect of the diagram from that of the corresponding superb circle. Poles are commonly favored in structural analyses that involve big amounts of orientation information, and specially if grouping of structural orientations is an problem (which commonly is the case).

Plotting strains

Fig. Eight. Plotting the line plunging 40 tiers toward N 030 E inside the stereonet (equal location projection).

Plotting a line orientation is similar (but distinctive) to plotting a aircraft orientation. For instance, a line plunging 40 ranges closer to 030 (NE) is considered. As for the plane, we mark off the trend (030) (Fig. 8a), rotate the overlay both 30 levels anticlockwise, as for the plane (Fig. 8b), or until it reaches the E course (a clockwise rotation of 60 stages for our instance). Now remember the plunge fee along the directly line towards the middle, beginning at the primitive circle, and mark off the pole (Fig. 8b). Back-rotate the overlay, and the assignment is completed (Fig. 8c).

Pitch (rake)

Fig. 9. A constructed, however realistic, state of affairs wherein diverse structural factors in a deformed rock series are represented in stereonets. Plotting bedding orientations exhibits the b-axis (local orientation of the hinge line). The attitude between the fracture sets can be observed by way of counting levels alongside the super circle that ?Ts both statistics units. Fault facts are plotted one after the other, showing the fault aircraft as a amazing circle and lineations as dots on that exquisite circle.

When doing fault analyses it's far useful to plot each the slip plane and its lineation(s) in the equal plot. In this example the lineation will lie at the first-rate circle that is representing the slip plane. The attitude among the horizontal direction and the lineation is referred to as the rake or pitch, and is plotted by using rotating the extraordinary circle of the plane to a N?S orientation after which counting the wide variety of ranges from the horizontal (N or S), i.E. The pitch cost measured within the ?Eld (Fig. 9). Users of the proper hand rule will always degree the pitch clockwise from the strike value, in order that the attitude might be up to 180 ranges . The proper-hand rule has been used in Fig. Nine. Others degree the acute attitude and count from the ideal strike course, wherein case the pitch will not exceed ninety levels.

Fitting a plane to traces

If or greater strains are known to lie in a not unusual plane, the aircraft is observed by plotting the traces in a internet. The lines are then turned around until they fall on a commonplace incredible circle, which represents the aircraft we are seeking out.

Line of intersection

The line of intersection among two planes is possibly most easily seen by means of plotting the awesome circles of the 2 planes, in which case the road of intersection is represented by the point wherein the 2 first rate circles go. When plotting poles to planes, the road of intersection is the pole to the excellent circle that ?Ts (includes) the two poles.

Angle among planes and lines

The angle between two planes is found by plotting the planes as poles and then rotating the tracing paper until the two points fall on a great circle. The angle between the planes is then found by counting the degrees between the two points on the great circle (Fig. 9, where the angle of two sets of fractures is considered). The angle between two lines is found in a similar manner, where the two lines are fitted to a great circle (the plane containing both lines) and the distance between them (in degrees) represents the angle (Fig. 9, lineations).

Orientation from apparent dips

Finding the orientation of a planar structure from observations of apparent dips can sometimes be useful. If two or more apparent dips are measured on two arbitrarily oriented planes, and each of those two planes is represented by a great circle and a point representing the apparent dip (measured at the outcrop), then the great circle that best fits the points represents the plane we want to find. An inverse problem would be to determine apparent dips of a known planar fabric or structure as exposed on selected surfaces. We then plot the planar fabric as a great circle, and the apparent dip will be defined by the point of intersection between the planar fabric and the surface of interest.

Rotation of planes and contours

Rotation of planar and linear structures may be done via shifting them along a amazing circle, the pole of which represents the rotation axis. Rotation about a horizontal axis is simple: simply rotate the tracing paper so that the rotation axis falls along the N?S path, and then rotate poles via counting levels along the small circles.

Rotating alongside an inclined axis is a chunk greater bulky. It involves rotating the whole lot so that the axis of rotation will become horizontal, then appearing the rotation as above, and ?Nally, again-rotating so that the axis of rotation achieves its authentic orientation.

Rose diagram

Fig. 10. The plots display the versions within every subarea, portrayed via poles, rose diagrams, and an arrow indicating the common orientation. The number of records within every subarea is indicated with the aid of ?N?.

Sometimes best the strike issue of planes is measurable or of interest, wherein case the facts may be represented inside the form of a rose diagram. A rose diagram is the predominant circle subdivided into sectors, wherein the quantity of measurements recorded inside every sector is represented by using the length of the respective petal. This is a visually attractive manner of representing the orientation of fractures and lineaments as they appear at the surface of the Earth, and can also be used to symbolize the trend distribution of linear structures (Fig. 10).

Plotting programs

All of these operations and more may be achieved extra quick with the aid of stereographic plotting applications, inclusive of the one generously made available to the structural community with the aid of Richard Allmendinger (1998). However, expertise the underlying standards is the important thing to success when the use of such packages. Several plotting packages additionally have statistical add-ons which are quite beneficial.

Credits: Haakon Fossen (Structural Geology)

What is deformation?

May 26, 2020    Comment   

What is deformation?

The term deformation is, like several other structural geology terms, used in different ways by different people and under different circumstances. In most cases, particularly in the field, the term refers to the distortion (strain) that is expressed in a (deformed) rock. This is also what the word literally means: a change in form or shape. However, rock masses can be translated or rotated as rigid units during deformation, without any internal change in shape. For instance, fault blocks can move during deformation without accumulating any internal distortion. Many structural geologists want to include such rigid displacements in the term deformation, and we refer to them as rigid body deformation, as opposed to non-rigid body deformation (strain or distortion).

Deformation is the transformation from an initial to a ?Nal geometry through inflexible frame translation, rigid body rotation, stress (distortion) and/or extent trade.

It is useful to think of a rock or rock unit in terms of a continuum of particles. Deformation relates the positions of particles before and after the deformation history, and the positions of points before and after deformation can be connected with vectors. These vectors are called displacement vectors, and a field of such vectors is referred to as the displacement field. Displacement vectors, such as those displayed in the central column of Fig. 1, do not tell us how the particles moved during the deformation history they merely link the undeformed and deformed states. The actual path that each particle follows during the deformation history is referred to as a particle path, and for the deformations shown in Fig. 1 the paths are shown in the right column (green arrows). When specifically referring to the progressive changes that take place during deformation, terms such as deformation history or progressive deformation should be used.

Components of deformation

The displacement ?Eld may be decomposed into various additives, depending on the reason of the decomposition. The conventional manner of decomposing it is with the aid of setting apart rigid body deformation inside the form of inflexible translation and rotation from trade in form and volume. In Fig. 2 the interpretation aspect is proven in (b), the rotation element in (c) and the relaxation (the strain) in (d). Let us have a better observe those expressions.

Translation

Fig. Three. The Jotun Nappe in the Scandinavian Caledonides seems to were transported more than three hundred km to the southeast, primarily based on recuperation and the orientation of lineations. The displacement vectors are indicated, but the quantity of rigid rotation across the vertical axis is unknown. The amount of strain is usually concentrated to the base.

Translation moves each particle in the rock in the equal direction and the same distance, and its displacement ?Eld consists of parallel vectors of equal duration. Translations can be giant, as an example in which thrust nappes (detached slices of rocks) have been transported several tens or masses of kilometres. The Jotun Nappe (Fig. Three) is an example from the Scandinavian Caledonides. In this example maximum of the deformation is rigid translation. We do not know the precise orientation of this nappe previous to the onset of deformation, so we cannot estimate the inflexible rotation (see underneath), but ?Eld observations screen that the alternate in form, or pressure, is largely con?Ned to the lower elements. The total deformation consequently consists of a large translation element, an unknown but probable small inflexible rotation aspect and a stress element localised to the bottom of the nappe.

On a smaller scale, rock additives (mineral grains, layers or fault blocks) can be translated along slip planes or planar faults with none internal alternate in shape.

Rotation

Rotation is here taken to mean rigid rotation of the entire deformed rock volume that is being studied. It should not be confused with the rotation of the (imaginary) axes of the strain ellipse during progressive deformation. Rigid rotation involves a uniform physical rotation of a rock volume (such as a shear zone) relative to an external coordinate system.

Large-scale rotations of a major thrust nappe or whole tectonic plate generally occur about vertical axes. Fault blocks in extensional settings, however, may additionally rotate round horizontal axes, and small-scale rotations may additionally occur about any axis.

Strain

Strain or distortion is non-rigid deformation and relatively simple to define:

Any change in form, without or with trade in extent, is referred to as strain, and it implies that particles in a rock have changed positions relative to every different.

A rock volume can be transported (translated) and turned around rigidly in any manner and sequence, however we are able to by no means be able to inform just from searching on the rock itself. All we can see in the ?Eld or in samples is stress, and perhaps the manner that stress has accrued. Consider your lunch bag. You can deliver it to school or work, which includes lots of rotation and translation, however you cannot see this deformation at once. It might be that your lunch bag has been squeezed on your manner to high school ? You could inform by means of evaluating it with what it looked like before you left home. If a person else organized your lunch and placed it on your bag, you will use your expertise of ways a lunch bag should be shaped to estimate the strain (change in shape) worried.

The ultimate factor may be very applicable, due to the fact with very few exceptions, we've got no longer visible the deformed rock in its undeformed state. We then need to use our knowledge of what such rocks normally look like while unstrained. For example, if we ?Nd strained ooliths or discount spots in the rock, we may assume them to were round (round in cross-phase) within the undeformed state.

Volume change

Even if the shape of a rock volume is unchanged, it may have shrunk or expanded. We therefore have to add volume change (area change in two dimensions) for a complete description of deformation. Volume change, also referred to as dilation, is commonly considered to be a special type of strain, called volumetric strain. However, it is useful to keep this type of deformation separate if possible.

System of reference

For studies of deformation, a reference or coordinate device need to be selected. Standing on a dock looking a huge deliver entering or departing can provide the influence that the dock, no longer the ship, is transferring. Unconsciously, the reference system receives ?Xed to the ship, and the relaxation of the arena actions via translation relative to the ship. While that is captivating, it isn't always a completely useful desire of reference. Rock deformation should additionally be taken into consideration in the body of some reference coordinate system, and it must be chosen with care to maintain the level of complexity down.

We always want a reference frame while coping with displacements and kinematics.

It is frequently beneficial to orient the coordinate machine alongside critical geologic structures. This might be the base of a thrust nappe, a plate boundary or a nearby shear sector. In many cases we need to eliminate translation and inflexible rotation. In the case of shear zones we typically area two axes parallel to the shear zone with the 0.33 being perpendicular to the sector. If we're inquisitive about the deformation in the shear zone as a whole, the beginning may be ?Xed to the margin of the zone. If we're interested in what goes on round any given particle inside the sector we can ?Glue? The origin to a particle in the zone (nonetheless parallel/perpendicular to the shear quarter obstacles). In both cases translation and rigid rotation of the shear sector are eliminated, because the coordinate system rotates and interprets together with the shear quarter. There is nothing incorrect with a coordinate gadget that is oblique to the shear quarter boundaries, however visually and mathematically it makes matters greater complicated.

Deformation: indifferent from history

Deformation is the distinction between the deformed and undeformed states. It tells us not anything approximately what truely took place in the course of the deformation history.

A given stress might also have accrued in an in?Nite variety of ways.

Imagine a worn-out student (or professor for that rely) who falls asleep in a ship while ?Shing on the ocean or a lake. The pupil knows in which she or he changed into while falling asleep, and shortly ?Gures out the brand new vicinity while waking up,however the precise course that currents and winds have taken the boat is unknown. The scholar best knows the position of the boat before and after the nap, and may evaluate the stress (change in shape) of the boat (optimistically 0). One can map the deformation, but no longer the deformation history.

Let us also consider particle flow: Students walking from one lecture hall to another may follow infinitely many paths (the different paths may take longer or shorter time, but deformation itself does not involve time). All the lecturer knows, busy between classes, is that the students have moved from one lecture hall to the other. Their history is unknown to the lecturer (although he or she may have some theories based on cups of hot coffee etc.). In a similar way, rock particles may move along a variety of paths from the undeformed to the deformed state. One difference between rock particles and individual students is of course that students are free to move on an individual basis, while rock particles, such as mineral grains in a rock, are “glued” to one another in a solid continuum and cannot operate freely.

Homogeneous and heterogeneous deformation

Where the deformation applied to a rock volume is identical throughout that volume, the deformation is homogeneous. Rigid rotation and translation by definition are homogenous, so it is always strain and volume or area change that can be heterogeneous. Thus homogeneous deformation and homogeneous strain are equivalent expressions.

Fig. 4. Homogeneous deformations of a rock with brachiopods, reduction spots, ammonites and dikes. Two different deformations are shown (pure and simple shear). Note that the brachiopods that are differently oriented before deformation obtain different shapes.

For homogeneous deformation, originally straight and parallel lines will be straight and parallel also after the deformation, as demonstrated in Fig. 4. Further, the strain and volume/area change will be constant throughout the volume of rock under consideration. If not, then the deformation is heterogeneous (inhomogeneous). This means that two objects with identical initial shape and orientation will end up having identical shape and orientation after the deformation. Note, however, that the initial shape and orientation in general will differ from the final shape and orientation. If two objects have identical shapes but different orientations before deformation, then they will generally have different shapes after deformation even if the deformation is homogeneous. An example is the deformed brachiopods in Fig. 4. The difference reflects the strain imposed on the rock.

Homogeneous deformation: Straight traces remain instantly, parallel strains stay parallel, and identically shaped and oriented objects can also be identically formed and orientated after the deformation.

A circle will be converted into an ellipse during homogeneous deformation, where the ellipticity (ratio between the long and short axes of the ellipse) will depend on the type and intensity of the deformation. Mathematically, this is identical to saying that homogeneous deformation is a linear transformation. Homogeneous deformation can therefore be described by a set of first-order equations (three in three dimensions) or, more simply, by a transformation matrix referred to as the deformation matrix.

Fig. 5. A regular grid in undeformed and deformed state. The overall strain is heterogeneous, so that some of the straight lines have become curved. However, in a restricted portion of the grid, the strain is homogeneous. In this case the strain is also homogeneous at the scale of a grid cell.

Before searching at the deformation matrix, the point made in Fig. 5 must be emphasised:

A deformation that is homogeneous on one scale may be considered heterogeneous on a different scale.

Fig. 6. Discrete or discontinuous deformation can be approximated as continuous and even homogeneous in some cases. In this sense the concept of strain can also be applied to brittle deformation (brittle strain). The success of doing so depends on the scale of observation.

A conventional example is the increase in pressure normally seen from the margin toward the centre of a shear zone. The stress is heterogeneous on this scale, however can be subdivided into thinner factors or zones in which strain is about homogeneous. Another instance is shown in Fig. 6, in which a rock extent is penetrated by faults. On a huge scale, the deformation can be considered homogeneous because the discontinuities represented via the faults are relatively small. On a smaller scale, however, those discontinuities grow to be greater apparent, and the deformation need to be considered heterogeneous.

Credits: Haakon Fossen (Structural Geology)

Siccar Point - the world's most important geological site and the birthplace of modern geology

May 12, 2020    Comment   

Siccar Point - the world's most important geological site and the birthplace of modern geology

Siccar Point is world-famous as the most important unconformity described by James Hutton (1726-1797) in support of his world-changing ideas on the origin and age of the Earth.

James Hutton unconformity with annotations - Siccar Point

In 1788, James Hutton first discovered Siccar Point, and understood its significance. It is by far the most spectacular of several unconformities that he discovered in Scotland, and very important in helping Hutton to explain his ideas about the processes of the Earth.At Siccar Point, gently sloping strata of 370-million-year-oldFamennian LateDevonianOld RedSandstone and a basal layer of conglomerate overlie near vertical layers of 435-million-year-old lowerSilurianLlandovery Epoch greywacke, with an interval of around 65 million years.

Standing on the angular unconformity at Siccar Point (click to enlarge). Photo: Chris Rowan, 2009

As above, with annotations. Photo: Chris Rowan, 2009

Hutton used Siccar Point to demonstrate the cycle of deposition, folding, erosion and further deposition that the unconformity represents. He understood the implication of unconformities in the evidence that they provided for the enormity of geological time and the antiquity of planet Earth, in contrast to the biblical teaching of the creation of the Earth.

How the unconformity at Siccar Point formed.

At this range, it is easy to spot that the contact between the two units is sharp, but it is not completely flat. Furthermore, the lowest part of the overlying Old Red Sandstone contains fragments of rock that are considerably larger than sand; some are at least as large as your fist, and many of the fragments in this basal conglomerate are bits of the underlying Silurian greywacke. These are all signs that the greywackes were exposed at the surface, being eroded, for a considerable period of time before the Old Red Sandstone was laid down on top of them.

The irregular topography and basal conglomerate show that this is an erosional contact. Photo: Chris Rowan, 2009

The Siccar Point which is a rocky promontory in the county of Berwickshire on the east coast of Scotland.

Why perform strain analysis?

May 09, 2020    Comment   

Why perform strain analysis?

Why do we carry out stress analysis?. It can be critical to retrieve information approximately stress from deformed rocks. First of all, strain analysis gives us an opportunity to discover the kingdom of pressure in a rock and to map out stress versions in a sample, an outcrop or a place. Strain facts are crucial in the mapping and information of shear zones in orogenic belts. Strain measurements can also be used to estimate the quantity of offset across a shear sector. It is possible to extract vital facts from shear zones if stress is known.

In many instances it's far beneficial to know if the strain is planar or three dimensional. If planar, an vital criterion for section balancing is ful?Lled, be it across orogenic zones or extensional basins. The shape of the stress ellipsoid might also include statistics about how the deformation occurred. Oblate (pancake-shaped) pressure in an orogenic setting may, for instance, suggest ?Attening pressure related to gravity-driven fall apart in preference to conventional push-from-in the back of thrusting.

The orientation of the strain ellipsoid is likewise critical, particularly in terms of rock structures. In a shear quarter putting, it could inform us if the deformation was simple shear or not. Strain in folded layers helps us to apprehend fold-forming mechanism(s). Studies of deformed reduction spots in slates provide desirable estimates on how plenty shortening has occurred throughout the foliation in such rocks, and stress markers in sedimentary rocks can now and again permit for reconstruction of unique sedimentary thickness.

Strain in one measurement

Two elongated belemnites in Jurassic limestone inside the Swiss Alps. The exceptional approaches that the two belemnites have been stretched provide us some -dimensional records about the pressure ?Eld: the upper belemnite has experienced sinistral shear strain at the same time as the lower one has not and have to be close to the most stretching direction.

One-dimensional strain analyses are concerned with changes in length and therefore the simplest form of strain analysis we have. If we can reconstruct the original length of an object or linear structure we can also calculate the amount of stretching or shortening in that direction. Objects revealing the state of strain in a deformed rock are known as strain markers. Examples of strain markers indicating change in length are boudinaged dikes or layers, and minerals or linear fossils such as belemnites or graptolites that have been elongated, such as the stretched Swiss belemnites shown in Figure above. Or it could be a layer shortened by folding. It could even be a faulted reference horizon on a geologic or seismic profile. The horizon may be stretched by normal faults or shortened by reverse faults, and the overall strain is referred to as brittle strain. One-dimensional strain is revealed when the horizon, fossil, mineral or dike is restored to its pre-deformational state.

Strain in two dimensions

Reduction spots in Welsh slate. The light spots shaped as spherical volumes of bleached (chemically reduced) rock. Their new shapes are elliptical in move-section and oblate (pancake-formed) in 3 dimensions, re?Ecting the tectonic stress in these slates.

In two-dimensional strain analyses we look for sections that have objects of known initial shape or contain linear markers with a variety of orientations (Figure first). Strained reduction spots of the type shown in Figure above are perfect, because they tend to have spherical shapes where they are undeformed. There are also many other types of objects that can be used, such as sections through conglomerates, breccias, corals, reduction spots, oolites, vesicles, pillow lavas (Figure below), columnar basalt, plutons and so on. Two-dimensional strain can also be calculated from one-dimensional data that represent different directions in the same section. A typical example would be dikes with different orientations that show different amounts of extension.

Section through a deformed Ordovician pahoe-hoe lava. The elliptical shapes were originally more circular, and Hans Reusch, who made the sketch in the 1880s, understood that they had been flattened during deformation. The Rf/f, center-to-center, and Fry methods would all be worth trying in this case.

Strain extracted from sections is the maximum commonplace type of stress statistics, and sectional information may be combine to estimate the 3-dimensional pressure ellipsoid.

Changes in angles

Strain can be discovered if we recognise the unique perspective among sets of traces. The authentic angular family members between systems including dikes, foliations and bedding are sometimes discovered in both undeformed and deformed states, i.E. Inside and outside a deformation zone. We can then see how the strain has affected the angular relationships and use this statistics to estimate pressure. In different cases orthogonal strains of symmetry discovered in undeformed fossils which include trilobites, brachiopods and malicious program burrows (perspective with layering) may be used to decide the angular shear in some deformed sedimentary rocks. In widespread, all we need to recognize is the trade in attitude between sets of traces and that there is no stress partitioning due to contrasting mechanical homes of the items with recognize to the enclosing rock.

If the perspective changed into ninety degree in the undeformed state, the alternate in attitude is the local angular shear. The in the beginning orthogonal strains continue to be orthogonal after the deformation, then they should represent the primary strains and for that reason the orientation of the strain ellipsoid. Observations of variously oriented line units therefore deliver data about the stress ellipse or ellipsoid. All we need is a useful technique. Two of the maximum commonplace strategies used to ?Nd pressure from to start with orthogonal traces are known as the Wellman and Breddin strategies, and are supplied within the following sections.

The Wellman approach

Wellman?S approach includes creation of the stress ellipse through drawing parallelograms based on the orientation of in the beginning orthogonal pairs of lines. The deformation was produced on a laptop and is a homogeneous easy shear. However, the pressure ellipse itself tells us nothing approximately the degree of coaxiality: the same end result might have been attained via natural shear.

This method dates back to 1962 and is a geometric construction for finding strain in two dimensions (in a section). It is typically demonstrated on fossils with orthogonal lines of symmetry in the undeformed state. In Figure above a we use the hinge and symmetry lines of brachiopods. A line of reference must be drawn (with arbitrary orientation) and pairs of lines that were orthogonal in the unstrained state are identified. The reference line must have two defined endpoints, named A and B in Figure above b. A pair of lines is then drawn parallel to both the hinge line and symmetry line for each fossil, so that they intersect at the endpoints of the reference line. The other points of intersection are marked (numbered 1–6 in Figure above b, c). If the rock is unstrained, the lines will define rectangles. If there is a strain involved, they will define parallelograms. To find the strain ellipse, simply fit an ellipse to the numbered corners of the parallelograms (Figure above c). If no ellipse can be fitted to the corner points of the rectangles the strain is heterogeneous or, alternatively, the measurement or assumption of initial orthogonality is false. The challenge with this method is, of course, to find enough fossils or other features with initially orthogonal lines typically 6–10 are needed.

The Breddin graph

We have already stated that the angular shear depends on the orientation of the principal strains: the closer the deformed orthogonal lines are to the principal strains, the lower the angular shear. This fact is utilized in a method first published by Hans Breddin in 1956 in German (with some errors). It is based on the graph shown in Figure above, where the angular shear changes with orientation and strain magnitude R. Input are the angular shears and the orientations of the sheared line pairs with respect to the principal strains. These data are plotted in the so-called Breddin graph and the R-value (ellipticity of the strain ellipse) is found by inspection (Figure above). This method may work even for only one or two observations.

In many cases the orientation of the foremost axes is unknown. In such instances the statistics are plotted with recognize to an arbitrarily drawn reference line. The facts are then moved horizontally at the graph till they ?T one of the curves, and the orientations of the stress axes are then found at the intersections with the horizontal axis (Figure above). In this case a bigger number of records are wished for top results.

Elliptical objects and the Rf/f-approach

Objects with initial circular (in sections) or spherical (in three dimensions) geometry are relatively uncommon, but do occur. Reduction spots and ooliths perhaps form the most perfect spherical shapes in sedimentary rocks. When deformed homogeneously, they are transformed into ellipses and ellipsoids that reflect the local finite strain. Conglomerates are perhaps more common and contain clasts that reflect the finite strain. In contrast to oolites and reduction spots, few pebbles or cobbles in a conglomerate are spherical in the undeformed state. This will of course influence their shape in the deformed state and causes a challenge in strain analyses. However, the clasts tend to have their long axes in a spectrum of orientations in the undeformed state, in which case methods such as the Rf/f-method may be able to take the initial shape factor into account.

The Rf/f method illustrated. The ellipses have the equal ellipticity (Ri) earlier than the deformation starts. The Rf?F diagram to the proper suggests that Ri=2. A natural shear is then added with Rs=1.5 accompanied by way of a pure shear strain of Rs=three. The deformation matrices for those deformations are proven. Note the trade within the distribution of factors in the diagrams to the right. Rs inside the diagrams is the real pressure this is delivered. Modi?Ed from Ramsay and Huber (1983).

The Rf/f-method became ?Rst brought by John Ramsay in his well-known 1967 textbook and changed into later stepped forward. The technique is illustrated in Figure above. The markers are assumed to have approximately elliptical shapes within the deformed (and undeformed) nation, and that they must display a signi?Cant variant in orientations for the method to paintings.

The Rf/f-approach handles to begin with non-round markers, but the method calls for a signi?Cant version inside the orientations of their long axes.

The ellipticity (X/Y) in the undeformed (initial) state is called Ri. In our example (Figure above) Ri=2. After a strain Rs the markers exhibit new shapes. The new shapes are different and depend on the initial orientation of the elliptical markers. The new (final) ellipticity for each deformation marker is called Rf and the spectrum of Rf-values is plotted against their orientations, or more specifically against the angle f' between the long axis of the ellipse and a reference line (horizontal in Figure above). In our example we have applied two increments of pure shear to a series of ellipses with different orientations. All the ellipses have the same initial shape Ri=2, and they plot along a vertical line in the upper right diagram in Figure above. Ellipse 1 is oriented with its long axis along the minimum principal strain axis, and it is converted into an ellipse that shows less strain (lower Rf-value) than the true strain ellipse (Rs). Ellipse 7, on the other hand, is oriented with its long axis parallel to the long axis of the strain ellipse, and the two ellipticities are added. This leads to an ellipticity that is higher than Rs. When Rs=3, the true strain Rs is located somewhere between the shape represented by ellipses 1 and 7, as seen in Figure above (lower right diagram).

For Rs=1.5 we still have ellipses with the full spectrum of orientations ( 90 to 90 ; see middle diagram in Figure above), while for Rs=3 there is a much more limited spectrum of orientations (lower graph in Figure above). The scatter in orientation is called the fluctuation F. An important change happens when ellipse 1, which has its long axis along the Z-axis of the strain ellipsoid, passes the shape of a circle (Rs=Ri,) and starts to develop an ellipse whose long axis is parallel to X. This happens when Rs=2, and for larger strains the data points define a circular shape. Inside this shape is the strain Rs that we are interested in. But where exactly is Rs? A simple average of the maximum and minimum Rf-values would depend on the original distribution of orientations. Even if the initial distribution is random, the average R-value would be too high, as high values tend to be over represented (Figure above, lower graph).

To find Rs we have to treat the cases where Rs >Ri and Rs <Ri separately. In the latter case, which is represented by the middle graph in Figure above, we have the following expressions for the maximum and minimum value for Rf:

In both cases the orientation of the lengthy (X) axis of the stress ellipse is given through the location of the maximum Rf-values. Strain can also be located by way of ?Tting the information to pre-calculated curves for numerous values for Ri and Rs. In practice, such operations are most ef?Ciently carried out by way of computer programs.

The example shown in Figure above and discussed above is idealized in the sense that all the undeformed elliptical markers have identical ellipticity. What if this were not the case, i.e. some markers were more elliptical than others? Then the data would not have defined a nice curve but a cloud of points in the Rf/f-diagram. Maximum and minimum Rf-values could still be found and strain could be calculated using the equations above. The only change in the equation is that Ri now represents the maximum ellipticity present in the undeformed state.

Another worry that can stand up is that the preliminary markers may have had a limited variety of orientations. Ideally, the Rf/f-approach requires the elliptical gadgets to be extra or much less randomly oriented previous to deformation. Conglomerates, to which this method usually is applied, generally tend to have clasts with a preferred orientation. This may additionally result in an Rf?F plot wherein simplest part of the curve or cloud is represented. In this situation the maximum and minimal Rf-values may not be representative, and the formulas above may not provide the precise solution and have to get replaced through a laptop primarily based iterative retrodeformation technique wherein X is enter. However, many conglomerates have a few clasts with initially anomalous orientations that permit the use of Rf/f analysis.

Center-to-center technique

The center-to-center method. Straight lines are drawn between neighbouring object centers. The length of each line (d') and the angle (a') that they make with a reference line are plotted in the diagram. The data define a curve that has a maximum at X and a minimum at the Y-value of the strain ellipse, and where Rs= X/Y.

This approach, right here verified in Figure above, is based on the idea that round gadgets have a more or less statistically uniform distribution in our section(s). This means that the distances between neighboring particle facilities had been pretty consistent earlier than deformation. The debris should constitute sand grains in nicely-looked after sandstone, pebbles, ooids, dust crack facilities, pillow-lava or pahoe-hoe lava facilities, pluton centers or different objects which can be of similar size and in which the facilities are effortlessly de?Nable. If you are unsure about how carefully your phase complies with this criterion, attempt anyway. If the technique yields a fairly properly-de?Ned ellipse, then the approach works.

The technique itself is straightforward and is illustrated in Figure above: Measure the gap and route from the center of an ellipse to those of its neighbours. Repeat this for all ellipses and graph the gap d' among the facilities and the angles a' among the center tie strains and a reference line. A instantly line takes place if the phase is unstrained, even as a deformed section yields a curve with most (d' max) and minimal values (d' min). The ellipticity of the pressure ellipse is then given through the ratio: Rs =( d' max)/(d' min).

The Fry method

The Fry approach performed manually. (a) The centerpoints for the deformed items are transferred to a transparent overlay. A imperative factor (1 at the ?Gure) is de?Ned. (b) The obvious paper is then moved to another of the points (point 2) and the centerpoints are again transferred onto the paper (the overlay ought to now not be turned around). The method is repeated for all the points, and the result (c) is an image of the pressure ellipsoid (shape and orientation). Based on Ramsay and Huber (1983).

A quicker and visually more attractive method for finding two-dimensional strain was developed by Norman Fry at the end of the 1970s. This method, illustrated in Figure above, is based on the center-to-center method and is most easily dealt with using one of several available computer programs. It can be done manually by placing a tracing overlay with a coordinate origin and pair of reference axes on top of a sketch or picture of the section. The origin is placed on a particle center and the centers of all other particles (not just the neighbours) are marked on the tracing paper. The tracing paper is then moved, without rotating the paper with respect to the section, so that the origin covers a second particle center, and the centers of all other particles are again marked on the tracing paper. This procedure is repeated until the area of interest has been covered. For objects with a more or less uniform distribution the result will be a visual representation of the strain ellipse.The ellipse is the void area in the middle, defined by the point cloud around it (Figure above c).

The Fry technique, in addition to the opposite strategies supplied on this phase, outputs -dimensional stress. Three-dimensional pressure is determined via combining pressure estimates from or more sections via the deformed rock extent. If sections can be observed that each include two of the main stress axes, then two sections are suf?Cient. In different cases three or extra sections are wished, and the 3-dimensional pressure have to be calculated via use of a laptop.

Strain in three dimensions

Three-dimensional strain expressed as ellipses on exceptional sections through a conglomerate. The foliation (XY-plane) and the lineation (X-axis) are annotated. This instance became published in 1888, but what are actually routine strain techniques have been now not evolved until the Nineteen Sixties.

A complete strain analysis is three-dimensional. Three dimensional strain data are presented in the Flinn diagram or similar diagrams that describe the shape of the strain ellipsoid, also known as the strain geometry. In addition, the orientation of the principal strains can be presented by means of stereographic nets. Direct field observations of three-dimensional strain are rare. In almost all cases, analysis is based on two-dimensional strain observations from two or more sections at the same locality (Figure above). A well-known example of three-dimensional strain analysis from deformed conglomerates is presented in below heading.

In order to quantify ductile stress, be it in two or three dimensions, the following conditions want to be met:

The stress have to be homogeneous at the scale of observation, the mechanical homes of the gadgets have to have been just like those in their host rock all through the deformation, and we have to have a fairly correct understanding about the original shape of strain markers.

The stress have to be homogeneous at the scale of observation, the mechanical homes of the gadgets have to have been just like those in their host rock all through the deformation, and we have to have a fairly correct understanding about the original shape of strain markers.

The second point is an important one. For ductile rocks it means that the object and its surroundings must have had the same competence or viscosity. Otherwise the strain recorded by the object would be different from that of its surroundings. This effect is one of several types of strain partitioning, where the overall strain is distributed unevenly in terms of intensity and/or geometry in a rock volume. As an example, we mark a perfect circle on a piece of clay before flattening it between two walls. The circle transforms passively into an ellipse that reveals the two-dimensional strain if the deformation is homogeneous. If we embed a coloured sphere of the same clay, then it would again deform along with the rest of the clay, revealing the three-dimensional strain involved. However, if we put a stiff marble in the clay the result is quite different. The marble remains unstrained while the clay around it becomes more intensely and heterogeneously strained than in the previous case. In fact, it causes a more heterogeneous strain pattern to appear. Strain markers with the same mechanical properties as the surroundings are called passive strain markers because they deform passively along with their surroundings. Those that have anomalous mechanical properties respond differently than the surrounding medium to the overall deformation, and such markers are called active strain markers.

Strain acquired from deformed conglomerates, plotted in the Flinn diagram. Different pebble sorts show distinctive shapes and ?Nite traces. Polymict conglomerate of the Utslettefjell Formation, Stord, southwest Norway.

An example of data from active strain markers is shown in Figure above. These data were collected from a deformed polymictic conglomerate where three-dimensional strain has been estimated from different clast types in the same rock and at the same locality. Clearly, the different clast types have recorded different amounts of strain. Competent (stiff) granitic clasts are less strained than less competent greenstone clasts. This is seen using the fact that strain intensity generally increases with increasing distance from the origin in Flinn space. But there is another interesting thing to note from this figure: It seems that competent clasts plot higher in the Flinn diagram (Figure. above) than incompetent(“soft”) clasts, meaning that competent clasts take on a more prolate shape. Hence, not only strain intensity but also strain geometry may vary according to the mechanical properties of strain markers.

The way that the different markers behave depends on factors such as their mineralogy, preexisting fabric, grain size, water content and temperature-pressure conditions at the time of deformation. In the case of Figure above, the temperature-pressure regime is that of lower to middle greenschist facies. At higher temperatures, quartz-rich rocks are more likely to behave as “soft” objects, and the relative positions of clast types in Flinn space are expected to change.

The ultimate factor above also requires interest: the initial form of a deformed object actually in?Uences its postdeformational form. If we don't forget -dimensional items such as sections via oolitic rocks, sandstones or conglomerates, the Rf/f technique mentioned above can handle this sort of uncertainty. It is higher to degree up or extra sections through a deformed rock the usage of this technique than dig out an item and degree its three-dimensional shape. The unmarried object could have an unexpected preliminary shape (conglomerate clasts are seldom perfectly round or elliptical), however by way of combining severa measurements in numerous sections we get a statistical variation that could resolve or lessen this problem.

Three-dimensional strain is usually located by combining two-dimensional information from numerous in a different way orientated sections.

There are actually computer applications that can be used to extract 3-dimensional pressure from sectional records. If the sections each include two of the primary strain axes everything turns into easy, and most effective two are strictly wanted (although three could still be properly). Otherwise, strain facts from at the least 3 sections are required.

Quartz or quartzite conglomerates with a quartzite matrix are normally used for strain analyses. The greater similar the mineralogy and grain length of the matrix and the pebbles, the less deformation partitioning and the higher the pressure estimates. A conventional have a look at of deformed quartzite conglomerates is Jake Hossack?S have a look at of the Norwegian Bygdin conglomerate, posted in 1968. Hossack became lucky he observed natural sections alongside the fundamental planes of the strain ellipsoid at each locality. Putting the sectional facts collectively gave the three dimensional country of pressure (stress ellipsoid) for each locality. Hossack located that pressure geometry and intensity varies inside his ?Eld vicinity. He related the stress pattern to static ?Attening below the weight of the overlying Caledonian Jotun Nappe. Although info of his interpretation can be challenged, his work demonstrates how conglomerates can monitor a complicated strain sample that otherwise might had been impossible to map.

Hossack mentioned the following sources of error:

• Inaccuracy connected with data collection (sections not being perfectly parallel to the principal planes of strain and measuring errors).
• Variations in pebble composition.
• The pre-deformational shape and orientation of the pebbles.
• Viscosity contrasts between clasts and matrix.
• Volume changes related to the deformation (pressure solution).
• The possibility of multiple deformation events.

Credits: Haakon Fossen (Structural Geology)