True‐amplitude seismic migration: A comparison of three approaches

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 929-936 ◽  
Author(s):  
Samuel H. Gray
Keyword(s):  
Elastic Parameter ◽  
Reflection Point ◽  
Seismic Migration ◽  
Amplitude Variation With Offset ◽  
Prestack Migration ◽  
Fundamental Limitations ◽  
Common Depth Point ◽  
Seismic Records ◽  
Migration Method ◽  
Angle Dependent Reflectivity

Knowledge of elastic parameter (compressional and shear velocities and density) contrasts within the earth can yield knowledge of lithology changes. Elastic parameter contrasts manifest themselves on seismic records as angle‐dependent reflectivity. Interpretation of angle‐dependent reflectivity, or amplitude variation with offset (AVO), on unmigrated records is often hindered by the effects of common‐depth‐point smear, incorrectly specified geometrical spreading loss, source/receiver directivity, as well as other factors. It is possible to correct some of these problems by analyzing common‐reflection‐point gathers after prestack migration, provided that the migration is capable of undoing all the amplitude distortions of wave propagation between the sources and the receivers. A migration method capable of undoing such distortions and thus producing angle‐dependent reflection coefficients at analysis points in a lossless, isotropic, elastic earth is called a “true‐amplitude migration.” The principles of true‐amplitude migration are simple enough to allow several methods to be considered as “true‐amplitude.” I consider three such migration methods in this paper: one associated with Berkhout, Wapenaar, and co‐workers at Delft University; one associated with Bleistein, Cohen, and co‐workers at Colorado School of Mines and, more recently, Hubral and co‐workers at Karlsruhe University; and a third introduced by Tarantola and developed internationally by many workers. These methods differ significantly in their derivations, as well as their implementation and applicability. However, they share some fundamental similarities, including some fundamental limitations. I present and compare summaries of the three methods from a unified perspective. The objective of this comparison is to point out the similarities of these methods, as well as their relative strengths and weaknesses.

NOISE ATTENUATION ON COMMON‐DEPTH‐POINT SEISMIC RECORDS BY A SEMIDETERMINISTIC APPROACH

Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 723-733 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Frequency Domain ◽  
Random Noise ◽  
Analytic Solutions ◽  
Harmonic Spectrum ◽  
Algebraic Equations ◽  
Coherent Noise ◽  
Common Depth Point ◽  
Seismic Records ◽  
Point Data ◽  
The Time Domain

A simple seismic record synthesis for common‐depth‐point data was examined for analytic representation in terms of its harmonic spectrum. This frequency‐domain investigation revealed that the primary‐reflection signal can be completely recovered in the absence of random noise, or it can be better recovered in the presence of random noise than normal stacking affords, especially, if the coherent‐noise‐to‐random‐noise ratio is high. The success of this technique is founded upon the principle that difference equations in the time domain become algebraic equations in the frequency domain. The technique is partially “probabilistic” because analytic solutions for the primary‐reflection signal are stacked for further attenuation of noise. The constituents of the seismic records, after static and normal‐moveout corrections, are: identical, coincident, primary‐reflection signal; identical, time‐shifted coherent noise; and random noise. The coherent‐noise time shifts must be determined for application of the semideterministic technique; methods are discussed in the Data Processing section.

Angle‐dependent reflectivity by means of prestack migration

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1223-1234 ◽  
Author(s):  
C. G. M. de Bruin ◽  
C. P. A. Wapenaar ◽  
A. J. Berkhout
Keyword(s):  
Reflection Coefficient ◽  
Wave Field ◽  
Grid Point ◽  
Depth Level ◽  
Wave Fields ◽  
Prestack Migration ◽  
Reflected Wave ◽  
Zero Offset ◽  
Source Wave ◽  
Angle Dependent Reflectivity

Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent reflectivity in the imaging we must not only add all frequency contributions but we should extend the imaging principle by adding along lines of constant angle in the wavenumber‐frequency domain. This procedure is carried out for each grid point. The resulting amplitude information provides a rigorous approach to amplitude‐versus‐offset related methods. The new imaging technique has been tested on media with horizontal layers. However, with our shot‐record oriented algorithm it is possible to handle any subsurface geometry. The first tests show excellent results up to high angles, both in the acoustic and in the elastic case. With angle‐dependent reflectivity information it becomes feasible to derive detailed velocity and density information in a subsequent stratigraphic inversion step.

Reducing 3-D acquisition footprint for 3-D DMO and 3-D prestack migration

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1177-1183 ◽  
Author(s):  
Anat Canning ◽  
Gerald H. F. Gardner
Keyword(s):  
Spatial Distribution ◽  
Velocity Analysis ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Prestack Migration ◽  
Avo Analysis ◽  
And Migration

The acquisition patterns of 3-D surveys often have a significant effect on the results of dip moveout (DMO) or prestack migration. When the spatial distribution of input traces is irregular, results from DMO and migration are contaminated by artifacts. In many cases, the footprint of the acquisition patterns can be seen on the migrated section and may result in incorrect interpretation. This phenomena also has a very significant effect on the feasibility of conducting amplitude variation with offset (AVO) analysis after 3-D prestack migration or after 3-D DMO, and also may affect velocity analysis. We propose a simple enhancement to migration and DMO programs that acts to minimize acquisition artifacts.

The vertical image projection method for migration stretch compensation

2021 ◽  
pp. 1-55
Author(s):  
Arash JafarGandomi
Keyword(s):  
Real Data ◽  
Amplitude Variation ◽  
Seismic Migration ◽  
Amplitude Variation With Offset ◽  
Amplitude Inversion ◽  
Image Projection ◽  
And Migration ◽  
Avo Attributes ◽  
Conditioning Approach ◽  
The Impact

True amplitude inversion is often carried out without taking into account migration distortions to the wavelet. Seismic migration leaves a dip-dependent effect on the wavelet that can cause significant inaccuracies in the inverted impedances obtained from conventional inversion approaches based on 1D vertical convolutional modelling. Neglecting this effect causes misleading inversion results and leakage of dipping noise and migration artifacts from higher frequency bands to the lower frequencies. I have observed that despite dip-dependency of this effect, low-dip and flat events may also suffer if they are contaminated with cross-cutting noise, steep migration artifacts, and smiles. In this paper I propose an efficient, effective and reversible data pre-conditioning approach that accounts for dip-dependency of the wavelet and is applied to migrated images prior to inversion. My proposed method consists of integrating data with respect to the total wavenumber followed by the differentiation with respect to the vertical wavenumber. This process is equivalent to applying a deterministic dip-consistent pre-conditioning that projects the data from the total wavenumber to the vertical wavenumber axis. This preconditioning can be applied to both pre- and post-stack data as well as to amplitude variation with offset (AVO) attributes such as intercept and gradient before inversion. The vertical image projection methodology that I propose here reduces the impact of migration artifacts such as cross-cutting noise and migration smiles and improves inverted impedances in both synthetic and real data examples. In particular I show that neglecting the proposed pre-conditioning leads to anomalously higher impedance values along the steeply dipping structures.

STATISTICALLY OPTIMAL STACKING OF SEISMIC DATA

Geophysics ◽  
1970 ◽  
Vol 35 (3) ◽  
pp. 436-446 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Mean Value ◽  
Seismic Model ◽  
Seismic Record ◽  
Signal To Noise ◽  
Statistical Procedures ◽  
Common Depth Point ◽  
Noise Energy ◽  
Seismic Records

A theory for weighting seismic records in the stacking process has been developed from a statistical seismic model. The model applies to common‐depth‐point seismic records which have been statically and dynamically corrected; the same model applies to an ordinary stacking procedure. The model stipulates for the signal and noise components, respectively, of a seismic record that (1) the signal is coincident with and similarly shaped to the signal on other records, and (2) the noise is statistically independent of that on any other record and of the signal and has zero mean value. In accord with the model, a seismic record is completely described for the purpose of weighting by its signal scale and its signal‐to‐noise energy ratio. Several statistical procedures for evaluating these parameters for seismic field data are presented. The most favorable procedure is demonstrated with both synthetic and field seismic records.

Migration before stack—Procedure and significance

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 204-212 ◽  
Author(s):  
Sudhir Jain ◽  
A. Easton Wren
Keyword(s):  
Common Source ◽  
Alternative Technique ◽  
High Frequencies ◽  
Prestack Migration ◽  
Common Depth Point ◽  
Reflection Time ◽  
Time Differential ◽  
Gain Recovery

Common‐depth‐point (CDP) stacking is based on the assumption that reflection points are coincident and situated midway between the respective source and receiver locations. If the reflector is structurally deformed, the reflection points move updip from the midpoint. As the structural dip increases, the reflection points for a CDP group of traces are farther removed from each other and normal stacking procedures [i.e., reflection apparent velocities for horizontal reflectors used for normal moveout (NMO) corrections] become increasingly inaccurate. Under such circumstances prestack migration is desirable, particularly when high frequencies are to be preserved. One published approach to prestack migration (Sattlegger and Stiller, 1973) involves the generation of substacks of adjacent traces followed by migration and summation of individual substacks. While adequate in many instances, cases exist where even substacks are degraded by the reflection time differential between component traces. This paper discusses an alternative technique to prestack migration without recourse to substacks. Common‐source traces, after gain recovery and static time corrections but before NMO corrections, are migrated using Kirchhoff summation. Aperture is computed for each sample according to specified maximum dips. Traces are simultaneously migrated and stacked, then output sequentially in sets of 12. The method is economical and provides enhanced reflection continuity and reliability in comparison to poststack migration. Moreover, the collapsing of diffractions is more effective.

Coupling in amplitude variation with offset and the Wiggins approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. N21-N33 ◽  
Author(s):  
Kristopher A. Innanen
Keyword(s):  
Wave Reflection ◽  
Elastic Parameter ◽  
P Wave ◽  
Converted Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
P Wave Velocity ◽  
Higher Order Corrections

Linear amplitude-variation-with-offset (AVO) approximations, which experience a reduction in accuracy as elastic parameter contrasts become large, may be adjusted with second- and higher-order corrections. Corrective terms can be expressed in many ways, but they only serve a meaningful purpose if they provide the same qualitative interpretability as did the linearization. Some aspects of nonlinear AVO can be understood, quantitatively and qualitatively, in terms of coupling — the interdependence of elastic parameter contrasts amongst themselves in their determination of reflection strengths. Coupling, for instance, explains the weak but nonnegligible dependence of the converted wave reflection coefficient on the lower half-space P-wave velocity. This fact can be exposed by expanding the solutions of the Zoeppritz equations in a particular hierarchy of series. Also explainable through this approach is the mathematical importance of what is sometimes referred to as the “Wiggins approximation,” under which [Formula: see text]. This special number is seen to coincide with a full decoupling of density contrasts from [Formula: see text] and [Formula: see text] contrasts at the second order. The decoupling persists across several variations of the nonlinear AVO approximations, including both expressions in terms of the relative changes [Formula: see text], [Formula: see text], and [Formula: see text], and expressions in terms of single-parameter reflectivities.

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