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.

Pulse distortion in depth migration

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1561-1569 ◽  
Author(s):  
Martin Tygel ◽  
Jörg Schleicher ◽  
Peter Hubral
Keyword(s):  
Velocity Model ◽  
Velocity Variation ◽  
Depth Migration ◽  
Kirchhoff Type ◽  
Reflection Angle ◽  
Pulse Distortion ◽  
Migration Theory ◽  
Original Time ◽  
The Relationship ◽  
Time Pulse

When migrating seismic primary reflections obtained from arbitrary source‐receiver configurations (e.g., common shot or constant offset) into depth, a pulse distortion occurs along the reflector. This distortion exists even if the migration was performed using the correct velocity model. Regardless of the migration algorithm, this distortion is a consequence of varying reflection angle, reflector dip, and/or velocity variation. The relationship between the original time pulse and the depth pulse after migration can be explained and quantified in terms of a prestack, Kirchhoff‐type, diffraction‐stack migration theory.

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.

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.

A case study for azimuthally anisotropic prestack depth imaging of an onshore Alaska prospect

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. B177-B186 ◽  
Author(s):  
Jinming Zhu ◽  
John Mathewson ◽  
Gail Liebelt
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Image Point ◽  
Depth Imaging ◽  
Depth Migration ◽  
Isotropic Media ◽  
Well Data ◽  
Reflection Tomography ◽  
Very High

In a study of the Sterling-Triangle area of Alaska, U.S.A., we initiated prestack depth migration (PSDM) to improve imaging on a prospect initially identified on a prestack time-migrated (PSTM) volume. Under the isotropic media assumption, the first few iterations of the reflection tomography had difficulty in converging to the proper velocity model. Upon further investigation, a very-high-velocity conglomerate layer was identified in the middle of the section across the whole survey area. We adopted the salt-flood practice, routine in depth-imaging salt provinces such as the Gulf of Mexico. The strategy was to focus on the shallow section above the conglomerate first, followed by a constant-velocity flood for picking the conglomerate base. The finalisotropic PSDM result showed that significant residual moveout differences existed on gathers along different azimuths. The net anisotropic effect on the isotropic PSDM was a degraded final PSDM volume. In the subsequent anisotropic PSDM work, azimuthally variant horizontal velocities were allowed in the model building. Common-image-point (CIP) gathers were created along different azimuths using sectored input gathers. Residuals picked on the sectored CIP gathers were used in joint tomography to invert different horizontal velocities. Incorporating significant well information, we built an anisotropic velocity model such that the azimuthal moveout on the butterfly gathers was essentially flat. The resulting anisotropic PSDM was consistent with well data and could be interpreted with much higher confidence.

Fresnel volume migration of multicomponent data

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. S121-S129 ◽  
Author(s):  
Stefan Lüth ◽  
Stefan Buske ◽  
Rüdiger Giese ◽  
Alexander Goertz
Keyword(s):  
Heterogeneous Media ◽  
Specular Reflection ◽  
Image Point ◽  
Polarization Angle ◽  
Depth Migration ◽  
Migration Operator ◽  
Measured Polarization ◽  
Paraxial Ray ◽  
Multicomponent Data ◽  
Homogeneous Media

If the aperture of a seismic reflection experiment is strongly limited, Kirchhoff migration suffers from strong artifacts attributable to incomplete summation. This can be overcome by restricting the migration operator to the region that physically contributes to a reflection event. Examples of such limited-aperture experiments include data acquisition in boreholes, tunnels, and mines. We present an extension to three-component (3C) Kirchhoff prestack depth migration, where the migration operator is restricted to the Fresnel volume of the specular reflected raypath. We use the measured polarization direction at a 3C receiver to determine points of specular reflection. In homogeneous media, the polarization angle of 3C data can be used directly to decide whether a certain image point belongs to the Fresnel volume of a specular reflection. In heterogeneous media, the Fresnel volume around an image point is approximated by means of paraxial ray tracing. The method is tested on a synthetic vertical seismic profiling experiment with strongly limited aperture. Migration artifacts and crosstalk effects from converted waves are strongly reduced compared with standard migration schemes. The method is successfully applied to seismic data acquired in a tunnel.

Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger
Keyword(s):  
Signal To Noise Ratio ◽  
Velocity Model ◽  
Point Of View ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Models ◽  
Time Domain Data ◽  
And Migration ◽  
Point To Point ◽  
Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

Rhyl Field: developing a new structural model by integrating basic geological principles with advanced seismic imaging in the Irish Sea

2016 ◽  
Vol 8 (1) ◽  
pp. 355-371 ◽  
Author(s):  
Gavin Ward ◽  
Dean Baker
Keyword(s):  
Structural Model ◽  
Seismic Imaging ◽  
Critical Factor ◽  
Integrated Approach ◽  
Velocity Model ◽  
Irish Sea ◽  
Depth Migration ◽  
Processing Power ◽  
And Migration ◽  
Automated Quality Control

AbstractA new model of compression in the Upper Triassic overlying the Rhyl Field has been developed for the Keys Basin, Irish Sea. This paper highlights the significance of the overburden velocity model in revealing the true structure of the field. The advent of 3D seismic and pre-stack depth migration has improved the interpreter's knowledge of complex velocity fields, such as shallow channels, salt bodies and volcanic intrusions. The huge leaps in processing power and migration algorithms have advanced the understanding of many anomalous features, but at a price: seismic imaging has always been a balance of quality against time and cost. As surveys get bigger and velocity analyses become more automated, quality control of the basic geological assumptions becomes an even more critical factor in the processing of seismic data and in the interpretation of structure. However, without knowledge of both regional and local geology, many features in the subsurface can be processed out of the seismic by relying too heavily on processing algorithms to image the structural model. Regrettably, without an integrated approach, this sometimes results in basic geological principles taking second place to technology and has contributed to hiding the structure of the Rhyl Field until recently.

Leading-order seismic imaging using curvelets

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. S231-S248 ◽  
Author(s):  
Huub Douma ◽  
Maarten V. de Hoop
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Angular Frequency ◽  
Leading Order ◽  
Numerical Examples ◽  
Depth Migration ◽  
Map Migration ◽  
Kirchhoff Depth Migration ◽  
Homogeneous Media ◽  
Spatial Support

Curvelets are plausible candidates for simultaneous compression of seismic data, their images, and the imaging operator itself. We show that with curvelets, the leading-order approximation (in angular frequency, horizontal wavenumber, and migrated location) to common-offset (CO) Kirchhoff depth migration becomes a simple transformation of coordinates of curvelets in the data, combined with amplitude scaling. This transformation is calculated using map migration, which employs the local slopes from the curvelet decomposition of the data. Because the data can be compressed using curvelets, the transformation needs to be calculated for relatively few curvelets only. Numerical examples for homogeneous media show that using the leading-order approximation only provides a good approximation to CO migration for moderate propagation times. As the traveltime increases and rays diverge beyond the spatial support of a curvelet; however, the leading-order approximation is no longer accurate enough. This shows the need for correction beyond leading order, even for homogeneous media.

Efficient velocity model building for prestack depth migration

1996 ◽  
Vol 15 (6) ◽  
pp. 751-753 ◽  
Author(s):  
Y. C. Kim ◽  
C. M. Samuelsen ◽  
T. A. Hauge
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Model Building
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