A photomicrograph of a sandstone

A photomicrograph of a sandstone showing very fine laminations of dark-brown humic organic matter.

Let us begin our description of the continuous-medium assumption by recalling the definition of continuous material. A material is considered continuous if it completely fills the space it occupies, leaving no pores or empty spaces, and if its properties can be described by continuous functions.

Like all substances, rock formations are made of atoms. They contain gaps or empty spaces. This feature is especially true for sedimentary rocks, which comprise most petroleum reservoirs. We will disregard the atom scale (microscopic scale) of rock formations and envision them without gaps or empty spaces. Furthermore, we will assume that mathematical functions (force, stress, displacement, and strain) which enter into wave propagation theory are continuous as well as the derivatives of these functions, if they enter. There is one exception to the continuous medium assumption: the physical properties of rock formations. The mathematical functions describing these properties can contain a finite number of surfaces separating regions of continuity. In other words, rock formations can be said to consist of piecewise-continuous regions, separated by interfaces, where the medium parameters are discontinuous.

The assumption of a continuous medium permits us not only to define stress, displacement, and strain at the particle scale (macroscopic scale) instead of at the microscopic scale but also to use the laws of continuous mechanics to study seismic wave propagation and seismic data.

Two additional assumptions often made about the nature of rock formations are that they are linearly elastic and isotropic. Elastic rock formations can return to their initial equilibrium after deformation and, for linearly elastic media, the force-displacement relationship at any point is linear. These assumptions are valid when forces, resulting displacements, and gradients of displacements are small. The word {\it isotropic} means that the physical properties of rock formations are identical in all directions. It should be clearly understood that the isotropic assumption is completely independent of homogeneous and heterogeneous assumption.

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.