A critique of seismic deconvolution methods

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2109-2116 ◽  
Author(s):  
Andrejs Jurkevics ◽  
Ralphe Wiggins
Keyword(s):  
Pulse Compression ◽  
Adaptive Methods ◽  
Substantial Improvement ◽  
Wiener Filtering ◽  
Minimum Entropy ◽  
Seismic Wavelet ◽  
Predictive Deconvolution ◽  
Phase Condition ◽  
Signal Distortions ◽  
Zero Phase

Different seismic pulse compression methods are evaluated. These include several algorithms for computing prediction error filters: Wiener filtering, Burg’s method, the [Formula: see text] norm criterion, Kalman filtering, and two time‐adaptive methods. Algorithms which do not assume a minimum‐phase condition for the seismic wavelet include minimum entropy, homomorphic, and zero‐phase deconvolution. The sensitivity of these algorithms is examined for various earth reflectivity functions, source waveforms, and signal distortions. The results indicate that standard Wiener predictive deconvolution is robust under a wide variety of input conditions. However, a substantial improvement in pulse compression can be obtained by the Burg algorithm under conditions of short data segments and by minimum entropy deconvolution for seismograms consisting of mixed‐phase wavelets combined with sparse reflectivity series.

Time-varying wavelet estimation and deconvolution by kurtosis maximization

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. V11-V18 ◽  
Author(s):  
Mirko van der Baan
Keyword(s):  
Field Measurements ◽  
Phase Changes ◽  
Data Driven ◽  
Wiener Filtering ◽  
Time Varying ◽  
Seismic Wavelet ◽  
Phase Rotation ◽  
Physical Laws ◽  
Kurtosis Maximization ◽  
Zero Phase

Phase mismatches sometimes occur between final processed sections and zero-phase synthetics based on well logs, despite best efforts for controlled-phase acquisition and processing. The latter are often based on deterministic corrections derived from field measurements and physical laws. A statistical analysis of the data can reveal whether a time-varying nonzero phase is present. This assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied. Kurtosis maximization by constant phase rotation is a statistical method that can reveal the phase of a seismic wavelet. It is robust enough to detect time-varying phase changes. Phase-only corrections can then be applied by means of a time-varying phase rotation. Alternatively, amplitude and phase deconvolution can be achieved using time-varying Wiener filtering. Time-varying wavelet extraction and deconvolution can also be used as a data-driven alternative to amplitude-only inverse-[Formula: see text] deconvolution.

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. V37-V46 ◽  
Author(s):  
Mirko van der Baan ◽  
Dinh-Tuan Pham
Keyword(s):  
Blind Deconvolution ◽  
General Purpose ◽  
Sufficient Accuracy ◽  
Wiener Filtering ◽  
Challenging Problem ◽  
Limited Data ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Principal Frequency ◽  
Band Limited

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

Predictive deconvolution and the zero‐phase source

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 379-397 ◽  
Author(s):  
Bruce Gibson ◽  
Ken Larner
Keyword(s):  
White Noise ◽  
Field Data ◽  
Synthetic Data ◽  
Phase Correction ◽  
Phase Spectrum ◽  
Signal Spectrum ◽  
Minimum Phase ◽  
Predictive Deconvolution ◽  
Different Levels ◽  
Zero Phase

Predictive deconvolution is commonly applied to seismic data generated with a Vibroseisr® source. Unfortunately, when this process invokes a minimum‐phase assumption, the phase of the resulting trace will not be correct. Nonetheless, spiking deconvolution is an attractive process because it restores attenuated higher frequencies, thus increasing resolution. For detailed stratigraphic analyses, however, it is desirable that the phase of the data be treated properly as well. The most common solution is to apply a phase‐shifting filter that corrects for errors attributable to a zero‐phase source. The phase correction is given by the minimum‐phase spectrum of the correlated Vibroseis wavelet. Because no minimum‐phase spectrum truly exists for this bandlimited wavelet, white noise is added to its amplitude spectrum in order to design the phase‐correction filter. Different levels of white noise, however, produce markedly different results when field data sections are filtered. A simple argument suggests that the amount of white noise used should match that added in designing the (minimum‐phase) spiking deconvolution operator. This choice, however, also produces inconsistent results; field data again show that the phase treatment is sensitive to the amount of added white noise. Synthetic data tests show that the standard phase‐correction procedure breaks down when earth attenuation is severe. Deterministically reducing the earth‐filter effects before deconvolution improved the resulting phase treatment for the synthetic data. After application of the inverse attenuation filter to the field data, however, phase differences again remain for different levels of added white noise. These inconsistencies are attributable to the phase action of spiking deconvolution. This action is dependent upon the shape of the signal spectrum as well as the spectral shape and level of contaminating noise. Thus, in practice the proper treatment of phase in data-dependent processing requires extensive knowledge of the spectral characteristics of both signal and noise. With such knowledge, one could apply deterministic techniques that either eliminate the need for statistical deconvolution or condition the data so as to satisfy better the statistical model assumed in data‐dependent processing.

Sensitivity of the dispersion correction to Q error

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 288-290 ◽  
Author(s):  
Richard E. Duren ◽  
E. Clark Trantham
Keyword(s):  
Amplitude Spectrum ◽  
Careful Attention ◽  
Dispersion Correction ◽  
Event Time ◽  
Seismic Wavelet ◽  
Reflection Time ◽  
Seismic Image ◽  
Time Zones ◽  
Seismic Sections ◽  
Zero Phase

A controlled‐phase acquisition and processing methodology for our company has been described by Trantham (1994). He pointed out that it is careful attention to wavelet phase that leads to improved well ties and a more geologically accurate seismic image. In addition, we prefer zero‐phase wavelets on our seismic sections. For a given amplitude spectrum they have the simplest shape and the highest peak; further, the peak occurs at the reflection time of the event. This alignment is important since the seismic wavelet generally broadens with increasing depth with a zero‐phase wavelet remaining symmetrical about the event time. Our experience has been that a true zero‐phase section can be tied over the entire length of a synthetic trace without having to slide the synthetic trace to tie different time zones.

Could the processed seismic wavelet be simpler than we think?

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 681-690 ◽  
Author(s):  
N. S. Neidell
Keyword(s):  
Unit Circle ◽  
Frequency Distribution ◽  
Amplitude Spectrum ◽  
Root Structure ◽  
Symmetric Form ◽  
Central Frequency ◽  
Seismic Wavelet ◽  
Phase Property ◽  
Short Piece ◽  
Zero Phase

J. P. Lindsey, (1988) in a clearly written short piece, opens an old question which concerns the analytic properties of seismic wavelets. This well conceived study concludes that most of the roots of a seismic wavelet as expressed by its z transform representation lie on or are very near the unit circle. The present discussion does not seek to characterize the form of all seismic wavelets, but only many if not most of those which have been processed with deconvolutions or “inversion” type operators to have reduced length, broadened bandwidth, and some desirable phase property. For such wavelets, despite the diversity by which they are obtained, remarkably simple operations having very few parameters can be extremely effective. As a case in point, constant‐phase rotations appear to carry such wavelets to zero‐phase symmetric form to a very good approximation. I start with empirical attributes which appear to characterize most processed seismic wavelets. Such wavelets tend to be of 40–100 ms duration with a smooth and unimodal amplitude spectrum of “peak” or “central” frequency between 15 and 30 Hz. The amplitude spectrum itself is further largely concentrated at frequencies between 5 and 55 Hz. A z transform root structure having essentially all of its roots only on the unit circle and on the real axis seems able to characterize all of the observed attributes rather well. This structure will be termed the band‐limiting root approximation (BLRA) and describes the attributes I seek to explain which are not as readily understood from alternative descriptions of the wavelets. Since the class of wavelets we address is obtained by a variety of means, and because the differences in character are at best subtle according to interpretive criteria, my justification is heuristic. The BLRA wavelet structure can be represented with remarkably few parameters (typically fewer than five). Of these few parameters, two relate to the frequency distribution. Such a formalism should be exceptionally useful for designing seismic techniques which seek to extract interpretive information based on properties of the wavelet.

Nonstationary phase estimation using regularized local kurtosis maximization

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. A75-A80 ◽  
Author(s):  
Mirko van der Baan ◽  
Sergey Fomel
Keyword(s):  
Statistical Estimation ◽  
Phase Estimation ◽  
Time Varying ◽  
Seismic Wavelet ◽  
Optimization Framework ◽  
Phase Rotation ◽  
Seismic Sections ◽  
The Stability ◽  
Kurtosis Maximization ◽  
Zero Phase

Phase mismatches sometimes occur between final processed seismic sections and zero-phase synthetics based on well logs — despite best efforts for controlled-phase acquisition and processing. Statistical estimation of the phase of a seismic wavelet is feasible using kurtosis maximization by constant-phase rotation, even if the phase is nonstationary. We cast the phase-estimation problem into an optimization framework to improve the stability of an earlier method based on a piecewise-stationarity assumption. After estimation, we achieve space-and-time-varying zero-phasing by phase rotation.

Ghosting and marine signature deconvolution: A prerequisite for detailed seismic interpretation

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1468-1485 ◽  
Author(s):  
Dushan B. Jovanovich ◽  
Roger D. Sumner ◽  
Sharon L. Akins‐Easterlin
Keyword(s):  
Gulf Coast ◽  
Seismic Line ◽  
Near Surface ◽  
Seismic Wavelet ◽  
Phase Errors ◽  
Air Gun ◽  
Statistical Hypotheses ◽  
Seismic Sections ◽  
Sonic Logs ◽  
Zero Phase

Detailed lithologic interpretation of seismic sections and/or pseudo‐sonic logs generated from seismic data requires that the seismic trace can be modeled as a reflection series convolved with a zero‐phase broadband wavelet. Ghosting and marine signature deconvolution processing is a prerequisite for assuring that the seismic wavelet on a marine CDP section will be zero phase. A deterministic approach to deconvolution is centered around the concept of abandoning the purely statistical method of wavelet estimation and actually measuring the seismic wavelet. A proper signature recording for marine data is, therefore, a crucial component of deterministic deconvolution. Another important element in the deterministic deconvolution sequence is the application of a deghosting filter to remove near‐surface reflections. Proper application of a deghosting filter significantly improves the correlation between log synthetics and the seismic trace. It has been found that statistical deconvolution schemes, because of the number of statistical hypotheses required to produce a deconvolution filter, produce residual wavelets that are highly variable in character and whose average phases cover the entire phase spectrum, modulo 2π. Examples of a Gulf Coast marine line which was shot with Aquapulse™, air gun, and Maxipulse™ sources by the RV Hollis Hedberg are presented to demonstrate the differences between statistical and deterministic deconvolution processing sequences. It will be shown, using sonic logs from wells adjacent to the seismic line, that the deterministic deconvolution sections for all three sources are close to zero phase while the statistical deconvolution sections have residual average phase errors between 180 and 270 degrees. The deterministic deconvolution sections have a high degree of correlation among themselves and to the wells adjacent to the line, while the statistical deconvolution sections correlate poorly to each other and to the wells. Synthetic seismograms and their impedance logs, and the seismic sections and their corresponding pseudo‐sonic logs, are used to demonstrate how deconvolution influences lithologic interpretation. ™Western Geophysics Co.

A matched‐filter approach to impedance estimation

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 484-495 ◽  
Author(s):  
James L. Simmons ◽  
Milo M. Backus
Keyword(s):  
Thin Layer ◽  
Layer Thickness ◽  
Basis Functions ◽  
Time Range ◽  
Earth Model ◽  
Average Thickness ◽  
Minimum Entropy ◽  
Data Set ◽  
Seismic Wavelet ◽  
Simple Interface

Stacked seismic data are modeled as a superposition of simple‐interface and thin layer reflections. This parameterization permits a parsimonious blocky model of the impedance. The method is an alternative to the classical least‐mean‐squared‐error approach and is similar in spirit to minimum‐entropy deconvolution and sparse‐spike inversion, although much different, and simpler, in implementation. A specified number of events on a seismic trace are modeled (inverted) independently. The selected set of basis functions used to represent the data includes a simple interface and a suite of high and low impedance layers covering a range of layer thickness. The simple interface basis function is the seismic wavelet, which is presumed to be known. Each event is classified using a normalized zero‐lag crosscorrelation of the basis functions with the seismic trace. Modeled events are prevented from overlapping, thereby ensuring a sparse earth model. Real data results show that a portion of a shallow‐marine data set can be well modeled in the context of a sparse earth model. A maximum of 30 simple‐interface and thin‐layer reflections (per trace) model 65 stacked traces over the time range of 0.8–1.9 s. We use a time and space invariant, statistically derived, autoregressive, seismic wavelet estimate. Wavelet polarity is chosen such that the inversion correctly models the fluid anomaly signals as low impedance layers. For wavelet A, we make the common assumption of white reflectivity and achieve a data misfit that is 7.8 dB down. For wavelet B, we assume a blue reflectivity that has a 3 dB/octave increase with frequency and achieve an improved fit to the data. Wavelet B also produces a more accurate estimate of the layer thickness of a known gas reservoir (10–12 ms average thickness) than does wavelet A (15–17 ms average thickness). Our results are competitive with other approaches to impedance estimation and are obtained in a much simpler fashion.

Phase decomposition

2016 ◽  
Vol 4 (3) ◽  
pp. SN1-SN10 ◽  
Author(s):  
John Castagna ◽  
Arnold Oyem ◽  
Oleg Portniaguine ◽  
Understanding Aikulola
Keyword(s):  
Phase Changes ◽  
Thin Layers ◽  
Rock Properties ◽  
Bright Spot ◽  
Phase Decomposition ◽  
Phase Component ◽  
Zero Crossings ◽  
Seismic Wavelet ◽  
Component Amplitude ◽  
Zero Phase

Any seismic trace can be decomposed into a 2D function of amplitude versus time and phase. We call this process phase decomposition, and the amplitude variation with time for a specific seismic phase is referred to as a phase component. For seismically thin layers, phase components are particularly useful in simplifying seismic interpretation. Subtle lateral impedance variations occurring within thin layers can be greatly amplified in their seismic expression when specific phase components are isolated. For example, the phase component corresponding to the phase of the seismic wavelet could indicate isolated interfaces or any other time symmetrical variation of reflection coefficients. Assuming a zero-phase wavelet, flat spots and unresolved water contacts may show directly on the zero-phase component. Similarly, thin beds and impedance ramps will show up on components that are 90° out of phase with the wavelet. In the case of bright spots caused by hydrocarbons in thin reservoirs because these occur when the reservoir is of an anomalously low impedance, it is safe to assume that the brightening caused by hydrocarbons occurs on the component [Formula: see text] out of phase with the wavelet. Amplitudes of other phase components associated with bright reflection events, resulting perhaps from differing impedances above and below the reservoir, thus obscure the hydrocarbon signal. Assuming a zero-phase wavelet, bright-spot interpretation is thus greatly simplified on the [Formula: see text] phase component. Amplitude maps for the Teal South Field reveal that the lateral distribution of amplitudes is greatly different for the original seismic data and the [Formula: see text] phase component, exhibiting very different prospectivity and apparent areal distribution of reservoirs. As the impedance changes laterally, the interference pattern for composite seismic events also changes. Thus, waveform peaks, troughs, and zero crossings, may not be reliable indicators of formation top locations. As the waveform phase changes laterally due to lateral rock properties variations, the position of a formation top on the waveform also changes. By picking horizons on distinct phase components, this ambiguity is reduced, and more consistent horizon picking is enabled.

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