The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so-called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.
[1]
E. Robinson,et al.
Recursive solution to the multichannel filtering problem
,
1965
.
[2]
E. Robinson,et al.
SEISMIC WAVE PROPAGATION IN LAYERED MEDIA IN TERMS OF COMMUNICATION THEORY
,
1966
.
[3]
Jon F. Claerbout,et al.
The error in least-squares inverse filtering
,
1964
.
[4]
R. J. Watson,et al.
DESIGN OF SUB‐OPTIMUM FILTER SYSTEMS FOR MULTI‐TRACE SEISMIC DATA PROCESSING*
,
1964
.
[5]
P. C. Wuenschel.
SEISMOGRAM SYNTHESIS INCLUDING MULTIPLES AND TRANSMISSION COEFFICIENTS
,
1960
.
[6]
N. Levinson.
The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction
,
1946
.
[7]
E. Robinson,et al.
The Design of High-Resolution Digital Filters
,
1966
.
[8]
Ken Larner,et al.
A new data-processing technique for the elimination of ghost arrivals on reflection seismograms
,
1964
.