Kirchhoff image propagation

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 126-134 ◽  
Author(s):  
Frank Adler
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Computation Time ◽  
Velocity Model ◽  
Image Point ◽  
Computationally Efficient ◽  
Initial Image ◽  
Migration Velocity Analysis ◽  
The Matrix ◽  
First Order Approximation

Seismic imaging processes are, in general, formulated under the assumption of a correct macrovelocity model. However, seismic subsurface images are very sensitive to the accuracy of the macrovelocity model. This paper investigates how the output of Kirchhoff inversion/migration changes for perturbations of a given 3‐D laterally inhomogeneous macrovelocity model. The displacement of a reflector image point from a perturbation of the given velocity model is determined in a first‐order approximation by the corresponding traveltime and slowness perturbations as well as the matrix. of the Beylkin determinant. The required traveltime derivatives can be calculated with ray perturbation theory. Using this result, a new, computationally efficient Kirchhoff inversion/migration technique is developed to predict in parallel a series of subsurface images for perturbations of a given macrovelocity model during a single inversion/migration process applied to the unmigrated seismic data. These images are constructed by superposition of the seismic data at predicted image point locations which lie on surfaces that expand from the initial image point as a function of the velocity perturbation. Because of the analogy to Huygens wavefronts in wave propagation, the technique is called Kirchhoff image propagation. A 2‐D implementation of Kirchhoff image propagation requires about 1.2 times the computation time of a single migration to calculate a set of propagated images. The propagated images provide good approximations to remigrated images and are applied to migration velocity analysis.

Automatic velocity analysis by differential semblance optimization

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1184-1191 ◽  
Author(s):  
W. A. Mulder ◽  
A. P. E. ten Kroode
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Cost Functional ◽  
Adjoint State ◽  
First Order Approximation ◽  
The Time Domain ◽  
The Cost ◽  
Adjoint State Method

We present a method for automatic velocity analysis of seismic data based on differential semblance optimization (DSO). The data are mapped for each offset from the time domain to the depth domain by a Born migration scheme using ray tracing with the efficient wavefront construction method. The DSO cost functional is evaluated by taking differences of the migration images for neighboring offsets. The gradient of this functional with respect to the underlying velocity model is obtained by a first‐order approximation of the adjoint‐state method, leading to an optimal complexity: the cost of evaluating the gradient is about the same as that of evaluating the functional. The method has been applied to a marine line. Multiples turned out to be a problem, but were handled effectively by incorporating a multiple filter inside the DSO cost functional.

True‐amplitude weight functions in 3D limited‐aperture migration revisited

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1025-1036 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Weight Function ◽  
Order Approximation ◽  
Velocity Model ◽  
Seismic Signal ◽  
Weight Functions ◽  
Image Point ◽  
Depth Migration ◽  
Amplitude Distortion ◽  
Pulse Distortion ◽  
Paraxial Ray

The true‐amplitude weight function in 3D limited‐aperture migration is obtained by extending its formula at an actual reflection point to any arbitrary subsurface point. This implies that the recorded seismic signal is a delta impulse. When the weight function is used in depth migration, it results in an amplitude distortion depending on the vertical distance from the target reflector. This distortion exists even if the correct velocity model is used. If the image point lies at a depth shallower than the half‐offset, the distortion cannot be ignored, even for a spatial wavelet having a short length. Using paraxial ray theory, I find a formula for the true‐amplitude weight function causing no amplitude distortion, under the condition that the earth's surface is smoothly curved. However, the formula is reflector dependent. As a result, amplitude distortion, in parallel with pulse distortion, is an intrinsic effect in depth migration, and true‐amplitude migration without amplitude distortion is possible only when the position of the target reflector is known. If this is the case, true‐amplitude migration without amplitude distortion can be realized by filtering the output of a simple unweighted diffraction stack with the weight function presented here. Also, using Taylor expansions with respect to the vertical, I derive an alternative formula for the true‐amplitude weight function that causes no amplitude distortion. Starting from this formula, I show that the previously published reflector‐independent true‐amplitude weight function is a zero‐order approximation to the one given here.

Case Study: Improving the quality of the seismic reflection image for a Fujian mineral exploration data set with offset-domain common-image gathers

Geophysics ◽  
2021 ◽  
pp. 1-45
Author(s):  
Guofeng Liu ◽  
Xiaohong Meng ◽  
Johanes Gedo Sea
Keyword(s):  
Wave Equation ◽  
Image Quality ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Mineral Exploration ◽  
Velocity Model ◽  
Image Point ◽  
Single Shot ◽  
Data Set ◽  
Depth Migration

Seismic reflection is a proven and effective method commonly used during the exploration of deep mineral deposits in Fujian, China. In seismic data processing, rugged depth migration based on wave-equation migration can play a key role in handling surface fluctuations and complex underground structures. Because wave-equation migration in the shot domain cannot output offset-domain common-image gathers in a straightforward way, the use of traditional tools for updating the velocity model and improving image quality can be quite challenging. To overcome this problem, we employed the attribute migration method. This worked by sorting the migrated stack results for every single-shot gather into the offset gathers. The value of the offset that corresponded to each image point was obtained from the ratio of the original migration results to the offset-modulated shot-data migration results. A Gaussian function was proposed to map every image point to a certain range of offsets. This helped improve the signal-to-noise ratio, which was especially important in handing low quality seismic data obtained during mineral exploration. Residual velocity analysis was applied to these gathers to update the velocity model and improve image quality. The offset-domain common-image gathers were also used directly for real mineral exploration seismic data with rugged depth migration. After several iterations of migration and updating the velocity, the proposed procedure achieved an image quality better than the one obtained with the initial velocity model. The results can help with the interpretation of thrust faults and deep deposit exploration.

Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D37-D41 ◽  
Author(s):  
Yves Rogister ◽  
Michael A. Slawinski
Keyword(s):  
Ray Tracing ◽  
Order Approximation ◽  
Anisotropy Parameter ◽  
Field Measurements ◽  
Velocity Model ◽  
Western Canada ◽  
First Order ◽  
Approximation Linear ◽  
The Difference ◽  
First Order Approximation

We study wave propagation in anisotropic inhomogeneous media. Specifically, we formulate and analytically solve the ray-tracing equations for the factorized model with wavefront velocity increasing linearly with depth and depending elliptically on direction. We obtain explicit expressions for traveltime, wavefront (phase) angle, and ray (group) velocity and angle, and study these seismological quantities for a model that successfully describes field measurements in the Western Canada Basin. By considering numerical examples, we also show that the difference between the wavefront and ray velocities depends only slightly on the anisotropy parameter, whereas the difference between the wavefront and ray angles is, in a first-order approximation, linear in the anisotropy parameter.

ADVANCES IN 3-D SEISMIC DATA PROCESSING TECHNIQUES

1992 ◽  
Vol 32 (1) ◽  
pp. 276
Author(s):  
T.J. Allen ◽  
P. Whiting
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Three Dimensional ◽  
Velocity Model ◽  
Migration Velocity ◽  
Seismic Data Processing ◽  
Data Set ◽  
Migration Velocity Analysis ◽  
Processing Techniques ◽  
Made In

Several recent advances made in 3-D seismic data processing are discussed in this paper.Development of a time-variant FK dip-moveout algorithm allows application of the correct three-dimensional operator. Coupled with a high-dip one-pass 3-D migration algorithm, this provides improved resolution and response at all azimuths. The use of dilation operators extends the capability of the process to include an economical and accurate (within well-defined limits) 3-D depth migration.Accuracy of the migration velocity model may be improved by the use of migration velocity analysis: of the two approaches considered, the data-subsetting technique gives more reliable and interpretable results.Conflicts in recording azimuth and bin dimensions of overlapping 3-D surveys may be resolved by the use of a 3-D interpolation algorithm applied post 3-D stack and which allows the combined surveys to be 3-D migrated as one data set.

scholarly journals Algorithm for estimating error of symbolic simplification

2021 ◽  
Vol 336 ◽  
pp. 06023
Author(s):  
Zdenek Kolka ◽  
Viera Biolkova ◽  
Josef Dobes ◽  
Martin Horak
Keyword(s):  
Order Approximation ◽  
Approximation Error ◽  
Exact Formula ◽  
Symbolic Analysis ◽  
Matrix Size ◽  
System Parameters ◽  
First Order ◽  
The Matrix ◽  
First Order Approximation ◽  
Approximate Result

The paper deals with an improved algorithm for estimating errors during approximate symbolic analysis. A linear system can be solved symbolically. However, the size of the resulting formula grows exponentially with the matrix size. The approximate symbolic analysis omits insignificant terms of the exact formula to decrease its size, which, on the other hand, limits the validity of the approximate result. The proposed algorithm estimates, in a computationally feasible way, the approximation error over a region of system parameters. This makes it possible to maintain the validity of the results even if the tolerances of the system parameters are defined. The method is based on the first-order approximation of error functions. The algorithm is demonstrated using the SNAP symbolic analyzer, which has been developed by the authors.

Application of the migration velocity analysis to a long-offset seismic data in the Ulleung basin, offshore Korea

2020 ◽  
Author(s):  
Woohyun Son ◽  
Byoung-Yeop Kim
Keyword(s):  
Seismic Data ◽  
Velocity Structure ◽  
Velocity Model ◽  
Ulleung Basin ◽  
Velocity Analysis ◽  
Time Processing ◽  
Depth Processing ◽  
Migration Velocity Analysis ◽  
Long Offset ◽  
Marine Seismic

<p>In order to obtain subsurface velocity for field seismic data, a time processing based on semblance velocity analysis has been performed so far. However, since the results of the time processing do not provide velocity information in the depth domain, it is difficult to know the exact subsurface velocity. In this study, to generate accurate velocity, the depth processing using the migration velocity analysis (MVA), which generates more reasonable subsurface velocity structure than the result from the time processing, is applied to the field marine seismic data obtained from Ulleung basin (offshore Korea). A marine seismic source is generated by air-gun (2,289 cu. in.). The long-offset (5.7 km) multichannel seismic (MCS) data were recorded by 456 receivers. The source and receiver spacings are 25 m and 12.5 m, respectively. The seismic survey line is about 168 L-km. The MVA workflow is composed of building a starting velocity model, sorting data to common offset gathers, Kirchhoff prestack depth migration (PSDM), sorting to common reflection point (CRP) gathers, picking residual moveout (RMO), and updating the velocity model. We repeatedly applied the MVA workflow until the remarkable events in the CRP gather were flat. From the results, we could confirm that the depth processing using MVA is successfully applied to field dataset and generates reasonable velocity structure in depth.</p>

scholarly journals Pre-stack 3-D Tau migration and velocity analysis: application to 3-D seismic data from offshore Abu Dhabi, United Arab Emirates

GeoArabia ◽  
2006 ◽  
Vol 11 (3) ◽  
pp. 43-60
Author(s):  
Tariq Alkhalifah ◽  
Saif Al Sharif ◽  
Kamal Belaid
Keyword(s):  
United Arab Emirates ◽  
Seismic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Abu Dhabi ◽  
Velocity Analysis ◽  
Low Velocity ◽  
Data Set ◽  
Velocity Anomaly ◽  
Migration Velocity Analysis

ABSTRACT A pre-stack 3-D Tau migration was applied to a 3-D seismic data set acquired in offshore Abu Dhabi, United Arab Emirates. The velocity model was built through an initial series of 2-D Tau migration velocity analysis, and supplemented by 3-D subset migration. A 3-D Tau migration velocity analysis was used for the final two updates of the model. The final interval velocity model provided low residuals in the common-image gathers from different offsets and was consistent with velocities from four wells located in the region. This velocity model included the main known features of the region including a low-velocity zone and a major fault. A final 3-D pre-stack Tau migration was applied using the velocity model and a relatively moderate aperture. This migration imaged the region including part of the critical poor data quality region, which includes the reservoir as well as reflections from the fault. Based on the derived velocity model, we concluded that the major cause for the poor image is the presence of a shallow high-velocity anomaly separated by a fault from a low-velocity anomaly.

3D common-reflection-point-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S161-S167 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Synthetic Data ◽  
Computation Time ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Spatial Coordinates

Three-dimensional prestack depth migration and depth residual picking in common-image gathers (CIGs) are the most time-consuming parts of 3D migration velocity analysis. Most migration-based velocity analysis algorithms need spatial coordinates of reflection points and CIG depth residuals at different offsets (or angles) to provide updated velocity information. We propose a new algorithm that can analyze 3D velocity quickly and accurately. Spatial coordinates and orientations of reflection points are provided by a 3D prestack parsimonious depth migration; the migration involves only the time samples picked from the salient reflection events on one 3D common-offset volume. Ray tracing from the reflection points to the surface provides a common-reflection-point (CRP) gather for each reflection point. Predicted (nonhyperbolic) moveouts for local velocity perturbations, based on maximizing the stacked amplitude, give the estimated velocity updates for each CRP gather. Then the velocity update for each voxel in the velocity model is obtained by averaging over all predicted velocity updates for that voxel. Prior model constraints may be used to stabilize velocity updating. Compared with other migration velocity analyses, the traveltime picking is limited to only one common-offset volume (and needs to be done only once); there is no need for intensive 3D prestack depth migration. Hence, the computation time is orders of magnitude less than other migration-based velocity analyses. A 3D synthetic data test shows the algorithm works effectively and efficiently.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation
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