Convolution of the waveLet corresponding to the

Multichannel Time Series Analysis with Digital Computer Programs

http://ieeexplore.ieee.org/iel6/8369/26351/01171185.pdf

A direct (noniterative) method is presented to determine an acoustic layered medium from the seismogram due to a time-limited plane wave incident from the lower halfspace. It is shown that one side of the autocorrelation of the seismogram due to an impulsive source at depth is the seismogram due to an impulsive source on the surface. This transforms the problem to the acoustic reflections problem as solved by Kunetz. Both the deep source time function and the layering can be determined from a surface seismogram.

Synthesis of a Layered Medium from its Acoustic Transmission Response

Least-squares inverse filters have found widespread use in the deconvolution of seismograms. The least-squares prediction filter with unit prediction distance is equivalent within a scale factor to the least-squares, zero-lag inverse filter. The use of least-squares prediction filters with prediction distances greater than unity leads to the method of predictive deconvolution which represents a more generalized approach to this subject.The predictive technique allows one to control the length of the desired output wavelet, and hence to specify the desired degree of resolution. Events which are periodic within given repetition ranges can be attenuated selectively. The method is thus effective in the suppression of rather complex reverberation patterns.

Predictive deconvolution: theory and practice

(1969). Multichannel Time Series Analysis with Digital Computer Programs. Technometrics: Vol. 11, No. 2, pp. 408-409.

Multichannel Time Series Analysis With Digital Computer Programs

The problem of a normally incident plane P wave propagating in a system of horizontally layered homogeneous perfectly elastic plates is reformulated in terms of concepts drawn from communication theory (z transform). This formulation leads to a degree of insight that would otherwise be difficult to achieve. One of the most interesting properties of the model used is the fact that a layered medium bounded by a perfect reflector at depth is representable as a dispersive, all-pass system with positive phase lag.

Seismic wave propagation in layered media in terms of communication theory

/pdf/computer-programs-for-time-and-space-adaptive-deconvolution-zuykz8fi4i.pdf

Convolution of the waveLet corresponding to the

Citations

Multichannel Time Series Analysis with Digital Computer Programs

References

Synthesis of a Layered Medium from its Acoustic Transmission Response

Predictive deconvolution: theory and practice

Multichannel Time Series Analysis With Digital Computer Programs

Seismic wave propagation in layered media in terms of communication theory

Computer programs for time and space adaptive deconvolution of single channel marine seismic reflection data

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