Multidimensional seismic data processing: Difference between revisions

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== Data acquisition ==

[[File:Offset VSP.jpg|thumb|Offset VSP]]

There are a number of data acquisition techniques used to generate seismic profiles, all of which involve measuring acoustic waves by means of a source and receivers. These techniques may be further classified into various categories,<ref>{{Cite encyclopedia|title = Vertical Seismic Profiling | encyclopedia = Encyclopedia of Solid Earth Geophysics|last = Rector|first = James|publisher = Springer|year = 2010|isbn = 978-90-481-8702-7|___location = |pages = 430–433|last2 = Mangriotis|first2 = M. D.}}</ref> depending on the configuration and type of sources and receivers used. For example, zero-offset vertical seismic profiling (ZVSP), walk-away VSP etc.

The source (which is typically on the surface) produces a wave travelling downwards. The receivers are positioned in an appropriate configuration at known depths. For example, in case of [[Vertical seismic profile|vertical seismic profiling]], the receivers are aligned vertically, spaced approximately 15 meters apart. The vertical travel time of the wave to each of the receivers is measured and each such measurement is referred to as a “check-shot” record. Multiple sources may be added or a single source may be moved along predetermined paths, generating seismic waves periodically in order to sample different points in the sub-surface. The result is a series of check-shot records, where each check-shot is typically a two or three-dimensional array representing a spatial dimension (the source-receiver offset) and a temporal dimension (the vertical travel time).

== Data processing ==

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The ''τ-p'' transform is a special case of the [[Radon transform]], and is simpler to apply than the Fourier transform. It allows one to study different wave modes as a function of their slowness values, <math>

p

</math>.<ref>{{Cite journal|url = http://www.crewes.org/ForOurSponsors/ResearchReports/1995/1995-11.pdf|title = Seismic reconstruction using a 3D tau-p transform|last = Donati|first = Maria|date = 1995|journal = CREWES Research Report|doi = |pmid = |access-date = |volume = 7}}</ref> Application of this transform involves summing (stacking) all traces in a record along a slope (slant), which results in a single trace (called the ''p'' value, slowness or the ray parameter). It transforms the input data from the space-time ___domain to intercept time-slowness ___domain.

<math>

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</math>

The ''τ-p'' transform converts seismic records into a ___domain where all these events are separated. Simply put, each point in the ''τ-p'' ___domain is the sum of all the points in the ''x-t'' plane lying across a straight line with a slope ''p'' and intercept ''τ''.<ref>{{cite journal|last1=McMechan|first1=G. A.|last2=Clayton|first2=R. W.|last3=Mooney|first3=W. D.|title=Application of Wave Field Continuation to the Inversion of Refraction Data|journal=Journal of Geophysical Research|date=10 February 1982|volume=87|doi=10.1029/JB087iB02p00927 | pages=927–935|url=https://authors.library.caltech.edu/34941/1/McMechan1982.pdf}}</ref> That also means a point in the ''x-t'' ___domain transforms into a line in the ''τ-p'' ___domain, hyperbolae transform into ellipses and so on. Similar to the Fourier transform, a signal in the ''τ-p'' ___domain can also be transformed back into the ''x-t'' ___domain.

=== Deconvolution ===

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During data acquisition, various effects have to be accounted for, such as near-surface structure around the source, noise, wavefront divergence and reverbations. It has to be ensured that a change in the seismic trace reflects a change in the geology and not one of the effects mentioned above. Deconvolution negates these effects to an extent and thus increases the resolution of the seismic data.

Seismic data, or a [[seismogram]], may be considered as a convolution of the source wavelet, the reflectivity and noise.<ref>{{cite journal|last1=Arya|first1=V|title=Deconvolution of Seismic Data - An Overview|journal=IEEE Transactions on Geoscience Electronics|date=April 1984|volume=16|issue=2|pages=95–98|doi=10.1109/TGE.1978.294570|doi-access=free}}</ref> Its deconvolution is usually implemented as a convolution with an inverse filter. Various well-known deconvolution techniques already exist for one dimension, such as predictive deconvolution, [[Kalman filter]]ing and deterministic deconvolution. In multiple dimensions, however, the deconvolution process is iterative due to the difficulty of defining an inverse operator. The output data sample may be represented as:

<math>