Earth Impulse Response Research Articles

WAVELET DECONVOLUTION USING A SOURCE SCALING LAW*

AbstractWe present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source‐receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase.We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non‐minimum‐phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.

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

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.

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

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 band-pass 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.

A NEW APPROACH TO VIBROSEIS DECONVOLUTION*

AbstractA method is proposed to obviate the shortcomings of conventional deconvolution approaches applied to vibroseis data. The vibroseis wavelet reduces the time domain resolution of the earth's impulse response by restricting its passband. The spectrum of the wavelet is assumed to be a “low quefrency”phenomenon, and hence it can be estimated by low cut cepstral filtering. The wavelet's amplitude spectrum can then be removed by spectral division. By using an approach which is consistent with the principle of maximum entropy, the undetermined portions of the seismogram's Fourier transform can be filled in by autoregressive prediction. The process of initially deconvolving in a restricted passband reduces the enhancement of noise contaminated parts of the spectrum, and the spectral extension scheme increases the time domain resolution of the process.