Optimum Inverse Filters Which Shorten the Spacing of Velocity Logs

Foster, M. R.; Hicks, W. G.; Nipper, J. T.

doi:10.1190/1.1439017

Cited by 12 publications

(6 citation statements)

References 5 publications

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“…G, having especially desirable properties. 4. The optimum F filter is derived with GI constrained to be the filters determined in step 3.…”

Section: Ilztroductionmentioning

confidence: 99%

“…For this purpose the term--S(t -27) would be regarded as a ghost and Lindsey's requirement of a known relationship between ghost and signal would be met. We will instead view I(t) as a distorted signal in the presence of noise and design an optimum finite memory inverse (Foster, Hicks, and Nipper 1962) to the distortion filter given in (18). This inverse filter is the F filter in Figure I.…”

Section: I77mentioning

confidence: 99%

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Design of Sub‐optimum Filter Systems for Multi‐trace Seismic Data Processing*

Foster

Sengbush

Watson

1964

Geophysical Prospecting

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Using optimum filter theory as a starting point, we describe a method for the design of practical multi-trace seismic data processing systems. We assume the inputs to be the superposition of signal, coherent noise, and incoherent noise. The signal and coherent noise moveouts are described statistically by their probability densities. Our approach is to split the system into two stages. The first stage achieves optimum noise suppression but distorts the signal. The signal distortion is reduced in the second stage by an optimum finite memory inverse filter.The system that is obtained using our method of design depends upon the form of the probability density functions. We show two examples, ghost suppression and velocity filtering.In ghost suppression we choose a model with moveouts known exactly, which corresponds to delta functions for the probability densities.In velocity filtering the signal and coherent noise moveouts are equally probable within non-overlapping ranges.The resulting system in each case is both simple and effective. In ghost suppression a simple shift and subtract cancels the coherent noise. The signal distortion is reduced by an inverse filter. The velocity filter system consists of differentiated moving averages applied to each trace, followed by a go' phase shift and a low pass filter. DESIGN OF SUB-OPTIMUM FILTER SYSTEMS FOR MULTI-TRACE SEISMIC DATA PROCESSING I. IlztroductionThe use of Wiener optimum filter theory in multi-trace seismic data processing was proposed by Robinson (1954) and applied by Burg (1962). In this theory economic constraints are not imposed and the resulting filters are costly to construct and apply. Our purpose is to describe a method which goes beyond the optimum theory, producing practical filters whose performance is excellent. We begin by selecting a basic system which is optimum for high noise levels. For actual data this system effectively suppresses the noise but badly distorts the signal. We then apply an inverse filter to reduce the signal distortion.

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“…G, having especially desirable properties. 4. The optimum F filter is derived with GI constrained to be the filters determined in step 3.…”

Section: Ilztroductionmentioning

confidence: 99%

Section: I77mentioning

confidence: 99%

Design of Sub‐optimum Filter Systems for Multi‐trace Seismic Data Processing*

Foster

Sengbush

Watson

1964

Geophysical Prospecting

Self Cite

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“…Optimum least-squares filters have been used for a wide variety of applications in the mineral exploration industry. Rice (rg6z), Backus et al (rg64), Schneider et al (rg64), and Schneider et al (1965) have used such filters for processing seismic exploration data; Robinson (Ig63), Burg (rg64), and Claerbout (1964) have proposed their use for array data from teleseismic sources ; and Foster et al (1962) and George et al (1964) have made applications to well logs. A statement of the normal equations that has gained wide recognition was made by Levinson (1947).…”

Section: Introductionmentioning

confidence: 99%

Use of Expected Error in the Design of Least‐squares Optimum Filters*

Wiggins

1967

Geophysical Prospecting

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The design of least‐squares optimum filters is based upon minimizing a suitably defined error criterion. The expected value of this error is easily computable after the coefficients of the filter have been determined. When a particular filtering problem is specified, there are several parameters which are specifically not included in the optimization procedure. However, the magnitude of the expected error may be quite sensitive to these parameters. The examination of the relative values of the expected error for variations of these unspecified parameters may lead to a better definition of the filter problem. The parameters which are left unspecified by the general least‐square filter definition include: 1. The addition of white noise to the signal autocorrelation to stabilize the filter behavior. 2. The specification of the shape of the desired output of the filter. 3. The specification of the lag between the desired output and the input. Examples are given showing the relationship between these parameters and the value of the expected error.

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“…This is an approximation since h (t) must be designed to extract the primary events from a signal in the presence of noise, and hence a perfect inverse operator or exact inverse is not required (Foster et al, 1962). It follows that.…”

Section: I Imentioning

confidence: 99%

“…The procedure for finding the optimum Inverse fi1ter was outlined by Foster et al (1962). The problem was formulated in the manner indicated by the flow chart in Figure 5.…”

mentioning

confidence: 99%

Studies of the Effect of Depth of Focus on Seismic Pulses: Estimation Procedure for Focal-Depth Determination of Seismic Disturbances

Merdler¹

1964

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A new data processing technique is suggested to estimate the delay time between initially uptraveling energy which is reflected once at the earth's surface and initially downtraveiing energy on earthquake seismograms. The method uses optimum inverse filter together with a criterion that measures the simplicity of a seismic signal convolved with an inverse filter. The inverse filters are designed to extract primary energy in the presence of surface reflected energy and random noise on the basis of a least-mean-square error criterion. Filter design Is dependent on the delay time between primaries and surface reflected events, their amplitude ratio and noise to signal power ratio. The simplicity criterion was devised on the assumption that a maximum in the concentration of normalized seismic signal energy above a minimum level indicates which filter was most correctly designed. This is visualized as an expression of the hypothesis that the primary seismogram is generated by a few large discontinuities, rather than by many minor boundaries.The technique was applied to band-limited synthetic signals that contained several primary-secondary pairs in the presence of random noise. Of 27 synthetic signals which were analyzed, the procedure successfully selected the correct delay time in 22 cases,

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Optimum Inverse Filters Which Shorten the Spacing of Velocity Logs

Cited by 12 publications

References 5 publications

Design of Sub‐optimum Filter Systems for Multi‐trace Seismic Data Processing*

Design of Sub‐optimum Filter Systems for Multi‐trace Seismic Data Processing*

Use of Expected Error in the Design of Least‐squares Optimum Filters*

Studies of the Effect of Depth of Focus on Seismic Pulses: Estimation Procedure for Focal-Depth Determination of Seismic Disturbances

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