Multidimensional seismic data processing: Difference between revisions

Revision as of 08:15, 13 November 2015

Revision as of 06:27, 14 November 2015

Line 1:

'''Multidimensional seismic data processing''' forms a major component of [[Vertical seismic profile | seismic profiling]], a technique used in geophysical exploration. The technique itself has various applications, including mapping ocean floors, determining the structure of sediments, mapping [[subsurface currents]] and [[hydrocarbon exploration]]. Since geophysical data obtained in such techniques is a function of both space and time, [[multidimensional signal processing]] techniques may be better suited for processing such data.

== Data acquisition ==

Line 11:

=== Multichannel filtering ===

{{see also | Multidimensional Filter Design}}

Multichannel filters may be applied to each individual record or to the final seismic profile. This may be done to separate different types of waves and to improve the signal-to-noise ratio. There are two well-know methods of designing velocity filters for seismic data processing applications.<ref>{{cite journal|last1=Tatham|first1=R|last2=Mangriotis|first2=M|title=Multidimensional Filtering of Seismic Data|journal=Proceedings of the IEEE|date=Oct 1984|volume=72|issue=10|pages=1357-13691357–1369|doi=10.1109/PROC.1984.13023}}</ref>

==== Two-dimensional Fourier transform design ====

Line 47:

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=95-9895–98|doi=10.1109/TGE.1978.294570}}</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 | Kalman filtering]]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>

Line 87:

if <math>n \rightarrow \infty</math> and <math>|1 - \lambda R(\underline{k},\omega)| < 1</math>

Note that the output is the same as the output of an inverse filter. An inverse filter does not actually have to be realized and the iterative procedure can be easily implemented on a computer.<ref>{{cite book|last1=Mersereau|first1=Russell|last2=Dudgeon|first2=Dan|title=Multidimensional Digital Signal Processing|publisher=Prentice-Hall|pages=350-352350–352}}</ref>

=== Stacking ===

Line 117:

</math>

For implementation, an all-pass filter is used to approximate the ideal filter described above. It must allow propagation in the region <math>|\alpha \omega_2 | > |\omega_1 | </math> (called the propagating region) and attenuate waves in the region <math>|\alpha \omega_2 | < |\omega_1 | </math> (called the evanescent region). The ideal frequency response is shown in the figure below.<ref>{{cite book|last1=Mersereau|first1=Russell|last2=Dudgeon|first2=Dan|title=Multidimensional Digital Signal Processing|publisher=Prentice-Hall|pages=359-363359–363}}</ref>

[[File:Filter response for Seismic Migration.jpg|thumb|center|Filter response for Seismic Migration]]