Showing papers on "Wavelet published in 1978"

On Maximum-Likelihood Detection and Estimation of Reflection Coefficients.

Abstract: : A procedure is developed for obtaining maximum-likelihood estimates of the reflection coefficient sequence from seismic data. The reflection coefficient sequence is modeled as an impulsive process, where the reflection amplitudes are uncorrelated and Gaussian distributed. The wavelet and all other parameters are assumed known. The results of this procedure are demonstrated for synthetic data. (Author)

Adaptive Deconvolution of Seismic Signals

Abstract: Seismic signals are often modeled as the convolution of a wavelet with the earth reflectivity function. Deconvolution, for the purpose of obtaining the reflectivity function, can be done using state space estimation methods. Such methods are hampered, however, by lack of precise modeling information. The deconvolution problem then becomes an adaptive estimation problem. In this paper the correct model is assumed to be one of a finite set of candidate models, and adaptive deconvolution is accomplished using estimation algorithms developed for this type of model uncertainty.

Possible instability in the burg maximum entropy method

Abstract: The maximum entropy method (MEM) suggested by Burg is claimed to give power spectral estimates with high resolution, especially for short records. However, we can produce examples for which Burg's algorithm gives unrealistic spectra. It is shown that the algorithm fails when applied to minimum phase wavelets. A new algorithm, one-sided Burg algorithm, is proposed to circumvent this difficulty. Both the new and original algorithms give reasonable spectral estimates when they are applied to stationary data.

Applications of short-time homomorphic signal analysis to seismic wavelet estimation

Abstract: The use of homomorphic systems to deconvolve seismic reflection and teleseismic data has been proposed and explored by a number of researchers with varying success. A careful study of the methods employed reveals a number of problems involving both the class of characteristic systems used and their numerical implementation. Furthermore, the analysis strategies used introduce deterministic constraints on the estimation of the seismic wavelet which may lead to serious problems in determining the earth impulse response. Several novel results are presented in this paper. A class of homomorphic systems matched to the bandpass nature of seismic signals is discussed and improved and more reliable implementation algorithms are developed. The concept of short-time wavelet estimation by homomorphic filtering is introduced. This technique takes into account the specific time-varying characteristics of seismic traces. Strategies for homomorphic wavelet estimation are proposed and illustrated. The recovery of the earth impulse response may then be accomplished by combining homomorphic wavelet estimation with parametric inverse filtering.

Self‐matching deconvolution in the frequency domain *

Abstract: In a previous paper the author showed how, by computing an inverse filter in the frequency domain, an automatic compromise could be made between the conflicting requirements to spike a wavelet and to keep the attendant noise amplification within bounds. This paper extends the technique to take account of errors in the estimated shape of the wavelet defined to the deconvolution process. The drastic effects which such errors can have if they are ignored are demonstrated. A novel form of filter–called the “self-matching filter”–is defined which allows the user to limit not only the noise amplification but also the sensitivity of the filter to random uncertainties in the estimated wavelet. This is achieved by whitening the spectrum only within automatically selected pass bands whilst suppressing other noise-dominated or uncertainly defined frequency components. Conventional Wiener filtering is shown to be a special case of this more general filter, namely one in which the wavelet uncertainty is completely ignored. The type of phase spectrum which the output pulse should be designed to possess (e.g. zero phase or minimum phase) is briefly discussed.

Recursive derivation of reflection coefficients from noisy seismic data

Abstract: We consider plane-wave motion at normal incidence in a horizontally layered system. The system is assumed lossless, and only the compressional waves are treated. A procedure is introduced for determining the reflection coefficients of the layered system when the observed seismic data may contain random noise. No deconvolution of the measured seismic data is required by the procedure when the input is a narrow wavelet.

Optimum mixed delay spiking filters

Abstract: Recent increased knowledge of mixed delay seismic source input wavelets requires extension of industry understanding of high-resolution digital spiking filters A close analysis of widely existing minimum delay deconvolution processes can be used to gain insights and estimates in mixed delay casesThis paper presents a time-domain method wherein a double application of standard (zero delay spiking) deconvolution processes yields understanding of the mixed delay nature of a wavelet given for spiking It is shown that such deconvolution of both a given mixed delay wavelet and the reversal of this given wavelet can be combined to estimate the complete variable delay suite of spiking filter performances for the given mixed delay waveletThe intuitive basis of the method lies in the observation that the reversal of a wavelet is equivalent to inversion of the zeros of the wavelet Z-transform in the complex plane Thus, (zero delay spiking) deconvolution of the wavelet emphasizes the minimum-phase portion of the wavelet while such deconvolution of the reversed wavelet emphasizes the maximum-phase portion of the original wavelet

Seismogram display and method

Abstract: A novel seismogram display and method for making same are provided wherein a portion of the areas under certain ones of the positive and negative wavelet lobes of each seismic trace is shaded. Each shaded area originates at or near a null point. The novel seismogram allows an interpreter to correlate both partially shaded lobes per wavelet, instead of one completely shaded, single lobe per wavelet. The invention therefore greatly simplifies and enhances the correlation and interpretation process.

The Phase Property of a Finite Realization of Random Noise and its Influence on Deconvolution

Abstract: A finite realization of a discrete random noise process may be considered as a one-sided energy signal. Its phase property can then be described by means of the center position. The samples of such a realization are the components of a random signal vector and the center position is therefore a random variable. A statistical analysis shows that the expected value of the center position equals half the time duration of the realization. This implies that the Z-transform of the realization may be expected to have an equal number of poles and zeros inside and outside the unit circle. The standard deviation from the expected value of the center position is shown to depend on the time duration of the realization and on the autocorrelation of the process. It follows that, for processes that can be described by the convolution of a white series and a disturbance wavelet, the center position is independent of the phase property of the wavelet. A conclusion based on these results is that the homomorphic technique of wavelet estimation through cepstrum stacking must give questionable outcomes. Another conclusion is that the super-position of a realization of random noise on a minimum phase wavelet will in general give a mixed phase resulting signal. It is pointed out that schemes for the derivation of deconvolution filters do not take account of this phenomenon.

Measurement of apparent velocity and azimuth of seismic signals recorded at an array

Abstract: A set of computer programs was written which enables one to determine automatically, the apparent velocity and azimuth of any portion of the seismic wave-train recorded at various seismic arrays. All that is required to use these programs is that the raw data be available on digital tape and that the user have access to any modern computer. The programs are written in Fortran IV and make use of the adaptive processing method whereby the arrival times of the wavefront at each sensor are accurately determined by cross-correlating the observed wavelet of interest with the corresponding wave on the beam trace. The new arrival times are then used to create a new and improved beam and the whole operation is repeated in an iterative manner until convergence takes place.

Deconvolution ofSeismic Data-AnOverview

Abstract: Itiscommonpractice tomodelaseismic trace asaconvo- lution ofthereflectivity function oftheearth andanenergy waveform referred toastheseismic wavelet. Theobjective ofdeconvolution isto extract thereflectivity function fromtheseismic trace. Wewill describe fourtechniques whichhavebeenandarebeing usedtoaccomplish this objective. Thesetechniques arepredictive deconvolution, homomorphic filtering, Kalmanfiltering, anddeterministic deconvolution. Inaddi- tion, weshall outline thephysical effects governing thebandwidth of theseismic datasuchasshooting geometry, recording filters, and absorption. I.INTRODUCTION IN SEISMIC exploration oftheearth's subsurface, anacous- ticenergy waveform-a seismic wavelet ingeophysical terms-is emitted andthenthereflections fromchanges inthe velocity ordensity, withdepth oftherockpackages inthe subsurface aredetected using pressure orvelocity sensitive de- tectors. Ifweassume, fornow,that theshape oftheseismic wavelet remains constant along itspropagation path, then the reflected signal will beasuperposition ofdelayed wavelets. Eachwavelet will bescaled according tothereflectivity iten- countered andalso tothedegree ofdivergence ithasunder- gone.Thuswecanrepresent theseismic recording (trace) S(t) (Fig. 1)by