Amplitude spectrum of the two impulses

(a) The amplitude spectrum of the two impulses and (b) the amplitude spectrum of a signal. Notice that we have truncated the amplitude spectrum in (b) to see the small-scale features.

The difficulty with the Fourier transform in this example is that cosine wave signals are well localized in the Fourier domain, whereas impulses are spread over all the frequencies. In other words, we need to sum all frequencies so that constructive and destructive interferences can allow us to reconstruct simple signals such as impulses. As we discussed earlier in this chapter, the criterion for selecting cosine and sine functions as the basis of the functions of the Fourier representation is that cosine and sine functions are a set of simple functions which can be used to describe complex functions. There are exceptions to this statement: representing an impulse by combining an infinite number of cosine and sine functions is not an effective way of representing such a simple signal.

In general, if a signal contains sudden changes (e.g., discontinuities), the high frequencies relative to these changes are detected by the Fourier transform, but their contributions are spread all over the Fourier domain because the modulating function exp(i ω t) is not limited in a specific interval. The Fourier analysis is therefore more efficient in the study of signals that do not suffer sudden variations with time (or, if the sudden variations exit, they must exist at all times); i.e., they must be stationary signals.

Other Images in Chapter 4

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.