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.

RESOLUTION COMPARISON OF MINIMUM‐PHASE AND ZERO‐PHASE SIGNALS

Geophysics ◽  
1974 ◽  
Vol 39 (6) ◽  
pp. 826-833 ◽  
Author(s):  
M. Schoenberger
Keyword(s):  
Input Signal ◽  
Amplitude Spectrum ◽  
Synthetic Seismograms ◽  
Minimum Phase ◽  
Seismic Section ◽  
Intuitive Appeal ◽  
Amplitude Spectra ◽  
Seismic Sections ◽  
Zero Phase

Despite their intuitive appeal, minimum‐phase wavelets are not the shortest wavelets achievable on a seismic section. For several amplitude spectra typical of processed seismic sections, both minimum‐phase and zero‐phase wavelets are presented. In each case, several measures of length reveal that the zero‐phase wavelet is shorter than the minimum‐phase wavelet corresponding to the same amplitude spectrum. Furthermore, the zero‐phase wavelet has smaller side lobes than the corresponding minimum‐phase wavelet. Synthetic seismograms were generated using both the zero‐phase and minimum‐phase signals as inputs. In each case, the seismogram generated with the zero‐phase input signal had better resolution. This relation is demonstrated quantitatively and is also visually obvious on the seismograms. In addition to comparing the wavelets’ resolution capabilities, the accuracies permitted in estimating reflection times were compared. The zero‐phase wavelets resulted in more accurate estimates of both reflection times and spacings.

LEAST‐SQUARES INVERSE FILTERING AND WAVELET DECONVOLUTION

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1369-1383 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Seismic Data ◽  
Broad Band ◽  
Detailed Comparison ◽  
Inverse Filtering ◽  
Borehole Data ◽  
Seismic Wavelet ◽  
Phase Property ◽  
Seismic Sections ◽  
Phase Spectra ◽  
Zero Phase

Detailed comparison between borehole data and seismic data has taught that, in general, conventional seismic inverse filtering is not effective enough to produce desirable deconvolution results, i.e., seismic sections with broad‐band zero‐phase wavelets. Application of conventional seismic reverse filters has the advantage that very little information is needed from the user. However, as is shown in this paper, the phase spectra of these filters may be seriously in error, even if the seismic wavelet has the minimum‐phase property. In wavelet deconvolution the phase spectrum of the filter is correct, provided a good estimate of the seismic wavelet is available. In this paper, wavelet deconvolution is compared with Wiener filtering. The main conclusions are illustrated by examples.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

Complex seismic trace analysis of thin beds

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 344-352 ◽  
Author(s):  
James D. Robertson ◽  
Henry H. Nogami
Keyword(s):  
Instantaneous Frequency ◽  
Trace Analysis ◽  
Frequency Tuning ◽  
Seismic Energy ◽  
High Amplitude ◽  
Opposite Polarity ◽  
Peak Period ◽  
Seismic Wavelet ◽  
Porous Sandstone ◽  
Seismic Sections

Displays of complex trace attributes can help to define thin beds in seismic sections. If the wavelet in a section is zero phase, low impedance strata whose thicknesses are of the order of half the peak‐to‐peak period of the dominant seismic energy show up as anomalously high‐amplitude zones on instantaneous amplitude sections. These anomalies result from the well‐known amplitude tuning effect which occurs when reflection coefficients of opposite polarity a half period apart are convolved with a seismic wavelet. As the layers thin to a quarter period of the dominant seismic energy, thinning is revealed by an anomalous increase in instantaneous frequency. This behavior results from the less well‐known but equally important phenomenon of frequency tuning by beds which thin laterally. Instantaneous frequency reaches an anomalously high value when bed thickness is about a quarter period and remains high as the bed continues to thin. In this paper, complex trace analysis is applied to a synthetic model of a wedge and to a set of broadband field data acquired to delineate thin lenses of porous sandstone. The two case studies illustrate that sets of attribute displays can be used to verify the presence and dimensions of thin beds when definition of the beds is not obvious on conventional seismic sections.

Instantaneous frequency and amplitude at the envelope peak of a constant‐phase wavelet

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1058-1060 ◽  
Author(s):  
A. E. Barnes
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Amplitude Spectrum ◽  
Propagation Time ◽  
Ricker Wavelet ◽  
Spectral Frequency ◽  
Zero Phase

Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).

Energy distribution in wavelets and implications on resolving power

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Ralph W. Knapp
Keyword(s):  
Phase Shift ◽  
Energy Distribution ◽  
Total Energy ◽  
Minimum Energy ◽  
Amplitude Spectrum ◽  
Resolving Power ◽  
Amplitude Envelope ◽  
Quadrature Phase ◽  
Partial Energy ◽  
Zero Phase

The suite of a wavelet is defined as being all wavelets that share a common amplitude spectrum and total energy but differ in phase spectra. Within a suite there are also classes of wavelets. A wavelet class has a common amplitude envelope and energy distribution. As such, it includes all wavelets that differ by only a constant‐angle phase shift. Of all wavelets within suite, the zero‐phase wavelet has the minimum energy envelope width; its energy is confined to minimum time dispersion. Therefore, the zero‐phase wavelet has maximum resolving power within the suite. Because a zero‐phase wavelet shares its amplitude envelope with a class of wavelets that differ by only a constant phase shift, all wavelets of the class also have maximum resolving power within the suite. The most familiar of these is the quadrature‐phase wavelet (90‐degree phase shift). Use of the complex trace results in an evaluation of the total energy, both potential and kinetic, of the wavelet signal. Assuming the wavelet signal is the output of a velocity geophone, partial energy represents only kinetic energy. Total energy better represents wavelet energy propagating through the earth. Use of partial energy (real signal only) applies a bias that favors the zero‐phase wavelets with respect to others of its class despite identical energy distribution. This bias is corrected when the wavelet envelope is used in the evaluation rather than wavelet trace amplitude. On a wiggle‐trace seismic section (amplitude display) a zero‐phase wavelet maintains a detectability advantage in the presence of noise because of a slightly greater amplitude; however, the advantage is lost in complex trace sections (energy displays) because both reflection strength and instantaneous frequency are independent of a constant phase shift in the wavelet. These sections are identical whether the wavelet is zero‐phase, quadrature‐phase or any other constant phase value, i.e., a wavelet within the zero‐phase class. (This does not imply that reflection strength sections should replace wiggle trace ones, only that they have advantages in the solution of some problems.)

Euclid and the art of wavelet estimation, Part II: Robust algorithm and field‐data examples

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1939-1946 ◽  
Author(s):  
Eike Rietsch
Keyword(s):  
Field Data ◽  
Synthetic Data ◽  
Noise Resistance ◽  
Zero Eigenvalue ◽  
Seismic Line ◽  
Robust Algorithm ◽  
Seismic Wavelet ◽  
Time Zones ◽  
The Common ◽  
Common Signal

In this second part of a two‐part work, a more robust algorithm is derived and used for the estimation of the seismic wavelet as the common signal of two or more seismic traces. It is based on the properties of the eigenvectors with zero eigenvalue of a matrix derived in the first part, whose elements are the samples of the autocorrelation functions and crosscorrelation functions of these seismic traces for a number of lags. The noise resistance of this algorithm is illustrated by means of a synthetic‐data example and then demonstrated on field data. In one field‐data example, the so‐called Euclid wavelet is compared with one derived deterministically by means of an impedance log. The other example relates three quite different Euclid wavelets determined in three different time zones on a seismic line to one another by showing that their differences can be explained by absorption.

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