Typical stress-strain relation for a solid material

Typical stress-strain relation for a solid material.

As discussed earlier in this chapter, we are essentially considering small deformations so that we can use a linear relationship between stress and strain.

For small deformations, it is an experimentally observed fact that the strain in a deformed body is linearly proportional to the applied stress (generalized Hooke's law). In this case, the deformation is characterized as linearly elastic. As increasing deformations are imposed, the relationship between strain and stress becomes increasingly nonlinear, but the body still returns to its original state when the stress is removed (In an elastic body, stress depends only on the strain, and vice versa). In this case, the deformation is characterized as nonlinear elastic. If, however, the strain is increased past a certain limit, typically in the range 10^-4 to 10^-3 for relatively rigid materials, the deformation is no longer elastic. Beyond this elastic limit, the medium deforms permanently (plastic deformation) and ultimately fractures (materials are no longer elastic). Ordinarily, the plastic deformation region is not of interest in the study of petroleum seismology. For small deformations, we will limit our discussion to linear elasticity.

For a given point, x, at time t, the generalized Hooke's law states that the stress is linearly proportional to the strain:

τ = c e

The constants of proportionality, contained in c, are known as elastic moduli or stiffness constants. They define the elastic properties of a medium---more particularly, its resistance to deformation. These constants constitute a four-rank tensor which is known as the stiffness tensor. Notice that the elastic moduli here are assumed to be independent of time t. This is the case because we have assumed that the materials under consideration in this chapter are elastic. Anelastic materials will be discussed in Chapter 12.

Other Images in Chapter 2

An example of the sailing path of a marine vessel in a towed-streamer survey

Images - Chapter 8 An example of the sailing path of a marine vessel in a towed-streamer survey. Note that the time for turning from one sailing line to another is about nine hours for vessels carrying streamers that are 10 km long. The dotted line indicates the turning legs of the sailing path.

This figure illustrates a typical sailing path of a 3D survey; the vessel travels back and forth, shooting and collecting data along many parallel lines, resulting in seismic data generated along lines 25 to 50 meters apart. Note that it takes about nine hours to turn from one sailing line to another for a vessel carrying 10-km-long streamers. Today, data are recorded even when the vessel is turning.

A shot diagram

Images - Chapter 7 A display of source and receiver distribution of a 2D seismic line in the so-called shot diagram. The rows corresponding to common-shot gathers and columns to common-receiver gathers. The diagonal is the zero-offset section, and all the other lines parallel to the diagonal are common-offset gathers (also known as common-offset sections). The lines perpendicular to the diagonal are the CMP gathers.

Another illustration of towed streamer acquisition

Images - Chapter 7 Another illustration of towed streamer acquisition

Interference noise

Images - Chapter 7 An illustration of interference noise in seismic data before and after. This figure shows the stack of seismic interference noise contaminated shots from another line in the Gulf of Mexico. Interference noise is clearly visible. Attenuation of seismic interference noise can be achieved by the use f-x prediction filters. Courtesy of Western Geco.

Other examples of structural traps

Images - Chapter 1 Structural traps. (A) Tilted fault blocks in an extensional regime. The seals are overlying mudstones and cross-fault juxtaposition against mudstones. (B) Rollover anticline on thrust. Petroleum accumulations may occur on both the hanging wall and the footwall. The hanging wall accumulation is dependent on a subthrust fault seal, whereas at least part of the hanging wall trap is likely to be a simple, four-way, dip-closed structure. (C) Lateral seal of a trap against a salt diapir and compactional drape trap over the diapir crest. (D) Diapiric mudstone associated trap with lateral seal against mud wall. Diapiric mud associated traps share many common features with that of salt. In this diagram, the diapiric mud wall developed at the core of a compressional fold. (E) Compactional drape over a basement block commonly creates enormous low-relief traps. (F) Gravity-generated trapping commonly occurs in deltaic sequences. Sediment loading causes gravity-driven failure and produces convex-down (listric) faults. The hanging wall of the fault rotates, creating space for sediment accumulation adjacent to the fault planes. The marker beds (grey) illustrate the form of the structure that has many favourable sites for petroleum accumulation. Adapted from Gluyas JG and Swarbrick RE (2003) Petroleum Geoscience. Oxford: Blackwell Science.