Time-varying wavelet estimation and deconvolution by kurtosis maximization

Mirko van der Baan

doi:10.1190/1.2831936

Time-varying wavelet estimation and deconvolution by kurtosis maximization

Geophysics ◽

10.1190/1.2831936 ◽

2008 ◽

Vol 73 (2) ◽

pp. V11-V18 ◽

Cited By ~ 100

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.

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Nonstationary phase estimation using regularized local kurtosis maximization

Geophysics ◽

10.1190/1.3213533 ◽

2009 ◽

Vol 74 (6) ◽

pp. A75-A80 ◽

Cited By ~ 44

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.

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Phase decomposition

Interpretation ◽

10.1190/int-2015-0150.1 ◽

2016 ◽

Vol 4 (3) ◽

pp. SN1-SN10 ◽

Cited By ~ 15

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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A critique of seismic deconvolution methods

Geophysics ◽

10.1190/1.1441627 ◽

1984 ◽

Vol 49 (12) ◽

pp. 2109-2116 ◽

Cited By ~ 15

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.

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