Source wavelet and its angular spectrum from plan‐wave seismograms

Geophysics ◽  
1990 ◽  
Vol 55 (8) ◽  
pp. 1026-1035 ◽  
Author(s):  
Philip M. Carrion ◽  
Selma dos S. Sacramento ◽  
Reynam da C. Pestana
Keyword(s):  
Plane Wave ◽  
Rate Of Convergence ◽  
Radiation Pattern ◽  
Numerical Algorithm ◽  
Angular Spectrum ◽  
Reverse Time ◽  
Vertical Derivative ◽  
Seismic Experiment ◽  
Recorded Data ◽  
Time Extrapolation

In a typical seismic experiment (land or marine), the generated source wavelet is either unknown, or known only approximately. In order to solve many geophysical problems, an accurate wavelet estimation is crucial. This paper demonstrates a fast numerical algorithm which allows not only estimating the source wavelet but also its angular spectrum (radiation pattern) from plane‐wave decomposed seismograms. Surprisingly, literature on this subject is virtually missing, although a nonuniform angular spectrum of the generated wavelet can substantially affect the recorded data. The technique presented here is based on the downward continuation (DC) and reverse‐time extrapolation (RTE) of the recorded data (both pressure and its vertical derivative). The proposed method is iterative: The rate of convergence does not depend on phase characteristics of the generated wavelet. We demonstrate that both the wavelet signature and its angular spectrum can be estimated accurately from plane‐wave seismograms. We also illustrate the technique on a variety of wavelets with different amplitude/phase characteristics.

3-D elastic prestack, reverse‐time depth migration

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Differences ◽  
Synthetic Data ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Depth Migration ◽  
Full Wave ◽  
Source Data ◽  
Recorded Data ◽  
Time Extrapolation

By combining and extending previous algorithms for 2-D prestack elastic migration and 3-D prestack acoustic migration, a full 3-D elastic prestack depth migration algorithm is developed. Reverse‐time extrapolation of the recorded data is by 3-D elastic finite differences; computation of the image time for each point in the 3-D volume is by 3-D acoustic finite differences. The algorithm operates on three‐component, vector‐wavefield common‐source data and produces three‐component vector reflectivity distributions. Converted P‐to‐S reflections are automatically imaged with the primary P‐wave reflections. There are no dip restrictions as the full wave equation is used. The algorithm is illustrated by application to synthetic data from three models; a flat reflector, a dipping truncated wedge overlying a flat reflector, and the classical French double dome and fault model.

Estimation of wavelet and source radiation pattern by reverse time extrapolation

1989 ◽  
Author(s):  
Philip M. Carrion ◽  
Selma dos S. Sacramento ◽  
Reynam da C. Pestana
Keyword(s):  
Radiation Pattern ◽  
Reverse Time ◽  
Source Radiation ◽  
Time Extrapolation

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S33-S46 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Rongrong Wang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Sampling Method ◽  
Singular Spectrum Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Tests ◽  
Time Migration

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

Fast plane-wave reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S549-S556 ◽  
Author(s):  
Xiongwen Wang ◽  
Xu Ji ◽  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Time Delay ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Time Domain ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Source ◽  
Computation Cost ◽  
Time Migration

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

Near-Borehole Imaging Using Full-Waveform Sonic Data

2021 ◽  
Author(s):  
Hala Alqatari ◽  
Thierry-Laurent Tonellot ◽  
Mohammed Mubarak
Keyword(s):  
Seismic Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Waveform ◽  
Time Migration ◽  
Imaging Results ◽  
High Resolution Images ◽  
Recorded Data ◽  
The Impact ◽  
Processing Steps

Abstract This work presents a full waveform sonic (FWS) dataset processing to generate high-resolution images of the near-borehole area. The dataset was acquired in a nearly horizontal well over a distance of 5400 feet. Multiple formation boundaries can be identified on the final image and tracked at up to 200 feet deep, along the wellbore's trajectory. We first present a new preprocessing sequence to prepare the sonic data for imaging. This sequence leverages denoising algorithms used in conventional surface seismic data processing to remove unwanted components of the recorded data that could harm the imaging results. We then apply a reverse time migration algorithm to the data at different processing stages to assess the impact of the main processing steps on the final image.

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

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