Born approximation

A comparison of modeling results based on the Born approximation and those on an exact solution for a slab velocity of 2.2 km/s and for various slab thicknesses (PP0 is the primary reflection at the top of the slab, and PP1 is the primary reflection at the bottom of the slab).

This figure and the next two figures show comparisons of the Born solution and the exact solutions for different values of slab thickness and of slab velocities. We can see for the cases in which the wavelength of the signal propagating in the slab is much greater compared to the thickness of the slab (i.e., h << λ₁), and in which the relative perturbation is less that 0.36, the Born approximation solution is almost identical to the exact solution. However, as the thickness of the slab increases, we can see that the reflection at the bottom of the slab in the Born approximation solution starts departing from the exact solution, even when ΔK is quite small. We earlier alluded to the reason for the differences between the Born approximation solution and the exact solution, which is that the Born approximation solution propagates in the slab with the velocity of the background medium instead of the slab velocity. If the difference between the velocity of the background medium and the slab velocity is large, or the duration of propagation through the slab is long enough, then the arrival time of the reflection from the bottom of the slab cannot be accurately predicted by the Born approximation.

Notice that the arrival time of the reflection from the top of the slab in the Born approximation solution is not affected by the slab velocity or slab thickness. However, the amplitudes of this reflection are affected by the relative perturbation between the slab and the background medium, ΔK. We will see in the next figures that for ΔK = 0.55, the amplitude in the Born approximation solution can be quite inaccurate.

Notice also that the shape of the Born approximation solution for the case in which the slab thickness is 25 m and the slab velocity is 3.0 km/s appears quite different from that of the exact solution. The reason for this difference in shape is that the Born approximation, which assumes that the waves propagate in the slab with the background velocity, predicts two events with a small overlap between them, whereas in the exact solution, which is based on waves propagating with the actual velocity, the two events totally overlap due to the fast slab velocity.

Finally, we can also notice that for the cases in which ΔK = 0.55 and h ≥ 100 m, the internal multiple corresponding to two bounces in the slab is visible in the exact solution and not in the Born approximation, because the background medium is assumed to be homogeneous. The internal multiples are not predicted by the Born approximation if the medium is smooth; the homogeneous medium is an ideal example of a smooth medium.

Other Images in Chapter 11

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.