Linear Radon transform

(a) Linear events in the CMP gather and (b) their slant-stack transforms. Theoretically, an event with linear moveout in the time-offset domain can be mapped to a point with the slant-stack transform, and a hyperbolic event, such as a primary or a multiple event, can be mapped to an ellipse in the τ-p domain (Treitel et al, 1982).

The Radon transform is a widely mathematical technique in seismic data processing and image analysis. Three types of Radon transforms used in seismic data processing: the slant-stack or τ-p (or linear Radon transform) transform; the hyperbolic Radon transform; and the parabolic Radon transform. Events with linear moveout in the time-offset domain are mapped to a point with the slant-stack transform as we can see here.

For many modern seismic applications, like multiple-elimination in the (τ-p)-domain, it is important to find a fast, digital Radon transform for sampled seismic data. Over the last twenty years, in seismic as well as other disciplines, attention has

been given to this problem. Mersereau and Oppenheim (1974) introduced a non-Cartesian grid in the 2-D Fourier plane, called the concentric squares grid. Recently, Averbuch et al. (2003) have proposed a discrete Radon transform that is rapidly computible and invertible by means of FFTs. Its basis is the concentric squares grid, which they call the pseudo-polar grid. In this appendix, we take advantage of the idea of the concentric squares grid, or the pseudo-polar grid, as introduced by these authors, to transform data to the 2-D Fourier space. For most seismic applications, it is sufficient to transform data to a triangle subdomain of the concentric squares grid. Therefore, we choose to call the transform the triangle-Fourier transform.

Multiple suppression by predictive deconvolution builds on the periodicity of multiples. However, on time-distance gathers, like common shot gathers, common midpoint gathers, and common receiver gathers, multiples are not periodic in time for non-zero offsets. Taner (1980) first recognized that multiples in layered media

are periodic along radial traces (fixed p). The time separation is different from one radial trace to another. Therefore, a predictive deconvolution operator can be designed from the autocorrelogram of eace p-trace and applied to attenuate multiples in the (τ,p)-domain, in which the primary and subsequent multipes are ellipses.

Other Images in Appendix D

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.