Imaging and velocity estimation with depth‐focusing analysis

Geophysics ◽  
1992 ◽  
Vol 57 (12) ◽  
pp. 1608-1622 ◽  
Author(s):  
Scott MacKay ◽  
Ray Abma
Keyword(s):  
Velocity Estimation ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Focal Surface ◽  
Seismic Image ◽  
Surface Image ◽  
Zero Offset ◽  
Imaging Conditions ◽  
Zero Time ◽  
Migration Velocities

Prestack depth migration uses two imaging conditions, zero time and zero offset, during downward continuation to form a migrated depth section. When the migration velocities are exact, the two imaging conditions act in a complementary fashion to yield a focused image. When the migration velocities are in error, reflected energy collapses to zero offset at depths that are inconsistent with the zero‐time imaging condition. The result is a deteriorated seismic image. However, by interpreting the nonzero times at which focusing actually occurs, the migration velocities can be updated iteratively in a process called depth‐focusing analysis. To produce a well‐focused seismic image, the goal of depth‐focusing analysis must be the elimination of focusing errors; however, practical considerations can prevent this goal from being achieved. Therefore, to relax the sensitivity of the migrated image to focusing errors, we introduce a nonzero‐time imaging condition by extracting the data along the interpreted surface of focusing from the depth‐focusing analysis volume. This method, called focal‐surface imaging, estimates the results of prestack depth migration using the updated velocities. Depth‐focusing analysis is shown to be a robust approach to velocity estimation and imaging. Limitations arising from constant‐velocity and low‐dip approximations are reduced in the presence of increasing velocities with depth. Lateral velocity errors, sources of exaggerated focusing errors and diverging velocity solutions, can also be addressed by applying a damping factor to the interpreted depth errors. Velocity estimation and focal‐surface imgaging, using iterative prestack depth migration, were applied to a southern North Sea data set. Starting with a regional velocity function, the first iteration provided an updated velocity field that more accurately conformed to the known lithologies. The focal‐surface image, formed from the same iteration, contained significantly more focused energy than the conventional section formed by prestack depth migration. However, structural differences between the two sections indicated the need for another iteration of migration using the updated velocities. The second iteration indicated smaller velocity errors and enough similarity between the migrated section and the new focal‐surface image to indicate that further iterations were unnecessary.

Velocity estimation in laterally varying media

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 884-897 ◽  
Author(s):  
Walter S. Lynn ◽  
Jon F. Claerbout
Keyword(s):  
Taylor Series Expansion ◽  
Velocity Estimation ◽  
Lateral Resolution ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Derivative Term ◽  
Fourth Derivative ◽  
Zero Offset ◽  
Lateral Variations

In areas of large lateral variations in velocity, stacking velocities computed on the basis of hyperbolic moveout can differ substantially from the actual root mean square (rms) velocities. This paper addresses the problem of obtaining rms or migration velocities from stacking velocities in such areas. The first‐order difference between the stacking and the vertical rms velocities due to lateral variations in velocity are shown to be related to the second lateral derivative of the rms slowness [Formula: see text]. Approximations leading to this relation are straight raypaths and that the vertical rms slowness to a given interface can be expressed as a second‐order Taylor series expansion in the midpoint direction. Under these approximations, the effect of the first lateral derivative of the slowness on the traveltime is negligible. The linearization of the equation relating the stacking and true velocities results in a set of equations whose inversion is unstable. Stability is achieved, however, by adding a nonphysical fourth derivative term which affects only the higher spatial wavenumbers, those beyond the lateral resolution of the lateral derivative method (LDM). Thus, given the stacking velocities and the zero‐offset traveltime to a given event as a function of midpoint, the LDM provides an estimate of the true vertical rms velocity to that event with a lateral resolution of about two mute zones or cable lengths. The LDM is applicable when lateral variations of velocity greater than 2 percent occur over the mute zone. At variations of 30 percent or greater, the internal assumptions of the LDM begin to break down. Synthetic models designed to test the LDM when the different assumptions are violated show that, in all cases, the results are not seriously affected. A test of the LDM on field data having a lateral velocity variation caused by sea floor topography gives a result which is supported by depth migration.

Wave-equation migration velocity analysis by focusing diffractions and reflections

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U19-U27 ◽  
Author(s):  
Paul C. Sava ◽  
Biondo Biondi ◽  
John Etgen
Keyword(s):  
Wave Equation ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis ◽  
Inversion Procedure ◽  
Velocity Information ◽  
Zero Offset

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top interface by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estimation improves the continuity of reflectors while focusing the diffracted energy.

Response by Arthur E. Barnes to the reply by the authors

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1947-1947 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Pulse Distortion ◽  
Velocity Variations ◽  
Zero Offset ◽  
Complex Geology

I appreciate the thoughtful and thorough response given by Tygel et al. They point out that even for a single dipping reflector imaged by a single non‐zero offset raypath, pulse distortion caused by “standard processing” (NM0 correction‐CMP sort‐stack‐time migration) and pulse distortion caused by prestack depth migration are not really the same, because the reflecting point is mispositioned in standard processing. Within a CMP gather, this mispositioning increases with offset, giving rise to “CMP smear.” CMP smear degrades the stack, introducing additional pulse distortion. Where i‐t is significant, and where lateral velocity variations or reflection curvature are large, such as for complex geology, the pulse distortion of standard processing can differ greatly from that of prestack depth migration.

Unified imaging of multichannel seismic data: Combining traveltime inversion and prestack depth migration

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE269-VE280 ◽  
Author(s):  
Priyank Jaiswal ◽  
Colin A. Zelt
Keyword(s):  
Seismic Data ◽  
Joint Inversion ◽  
Velocity Model ◽  
Depth Image ◽  
Prestack Depth Migration ◽  
Traveltime Inversion ◽  
Depth Migration ◽  
Interval Velocity ◽  
Wide Aperture ◽  
Zero Offset

Imaging 2D multichannel land seismic data can be accomplished effectively by a combination of traveltime inversion and prestack depth migration (PSDM), referred to as unified imaging. Unified imaging begins by inverting the direct-arrival times to estimate a velocity model that is used in static corrections and stacking velocity analysis. The interval velocity model (from stacking velocities) is used for PSDM. The stacked data and the PSDM image are interpreted for common horizons, and the corresponding wide-aperture reflections are identified in the shot gathers. Using the interval velocity model, the stack interpretations are inverted as zero-offset reflections to constrain the corresponding interfaces in depth; the interval velocity model remains stationary. We define a coefficient of congruence [Formula: see text] that measures the discrepancy between horizons from the PSDM image andtheir counterparts from the zero-offset inversion. A value of unity for [Formula: see text] implies that the interpreted and inverted horizons are consistent to within the interpretational uncertainties, and the unified imaging is said to have converged. For [Formula: see text] greater than unity, the interval velocity model and the horizon depths are updated by jointly inverting the direct arrivals with the zero-offset and wide-aperture reflections. The updated interval velocity model is used again for both PSDM and a zero-offset inversion. Interpretations of the new PSDM image are the updated horizon depths. The unified imaging is applied to seismic data from the Naga Thrust and Fold Belt in India. Wide-aperture and zero-offset data from three geologically significant horizons are used. Three runs of joint inversion and PSDM are required in a cyclic manner for [Formula: see text] to converge to unity. A joint interpretation of the final velocity model and depth image reveals the presence of a triangle zone that could be promising for exploration.

Prestack depth migration by symmetric nonstationary phase shift

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 594-603 ◽  
Author(s):  
Robert J. Ferguson ◽  
Gary F. Margrave
Keyword(s):  
Phase Shift ◽  
Symmetric Operator ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Velocity Model ◽  
Computational Effort ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Zero Offset

A new depth migration method suitable for heterogeneous media is presented. The well‐known phase shift plus interpolation (PSPI) method and the recently introduced nonstationary phase‐shift (NSPS) method are combined into a single symmetric operator with improved accuracy and stability and with similar computational effort. For prestack depth migration, the symmetric operator is used in a recursive wavefield extrapolation to compute incident and reflected wavefields at any desired depth, and the ratio of the incident and reflected wavefields at a particular depth is used to estimate seismic reflectivity. When the velocity model is made piecewise constant laterally, the symmetric extrapolation operator can be computed efficiently using ordinary phase‐shift extrapolation for a series of reference velocities and appropriate spatial windowing. Migration of the Marmousi synthetic data set by symmetric nonstationary phase shift (SNPS) provides an image that compares favorably with an image of the zero‐offset reflectivity derived from the Marmousi velocity model.

A unified 3‐D seismic workflow

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1699-1713 ◽  
Author(s):  
Öz Yilmaz ◽  
Irfan Tanir ◽  
Cyril Gregory
Keyword(s):  
Seismic Data ◽  
Velocity Estimation ◽  
Earth Model ◽  
Initial Model ◽  
Prestack Depth Migration ◽  
Final Model ◽  
Depth Migration ◽  
Inversion Methods ◽  
Image Volume ◽  
First Time

A geophysicist who practices seismic data analysis for earth modeling and imaging in depth is overwhelmed by the prolific number of inversion methods to estimate layer velocities and delineate reflector geometries—the two constituents of a seismically defined earth model in depth. Given a specific type of structural play, the key to estimating an accurate earth model in depth, however, is a workflow that is based on a judicious combination of inversion methods appropriately selected for their robustness. We present a Unified workflow for processing, inversion, and interpretation of 3‐D seismic data that is applicable to low‐relief structures and complex structures associated with extensional and compressional tectonics. With some modifications, the workflow also is applicable to complex overburden structures associated with salt and overthrust tectonics. Although doing it right the first time is most desirable, there is never a situation where this is possible when estimating an earth model in depth, A fundamental problem with inversion for earth modeling is velocity‐depth ambiguity. This means that an error in layer velocity can be indistinguishable from an error in reflector geometry, The velocity‐depth ambiguity that is inherent to seismic inversion makes it very difficult to obtain the right answer (an adequate representation of the true geological model), let alone do it the first time. Limitations in the resolving power of the methods to estimate layer velocities that arise from the band‐limited nature of the recorded data and finite cable length used in recording further compound the problem. Additionally, traveltime picking that is needed for most velocity estimation techniques and time‐to‐depth conversion as well as picking depth horizons from depth‐migrated data to delineate reflector geometries are all adversely affected by noise present in the data. AII things Considered, we can only expect to do our best in estimating what may be called an initial model, and update this model to get an acceptable final model. The objective behind the design of the seismic workflow described in this paper is to attain the best estimate of a structurally consistent initial model based on rms velocities associated with migrated data, so as to minimize the work required to update the model. The unified workflow involves analysis of seismic data both in time and depth, and follows a pathway that starts with the application of 3‐D dip‐moveout correction and 3‐D prestack time migration to derive an rms velocity field. This is followed by estimation of an accurate, structurally consistent initial model by Dix conversion of rms velocities and interpretation of a set of depth horizons from 3‐D poststack depth migration. To update the initial model, the image gathers derived from 3‐D prestack depth migration are analyzed for residual moveout. The resulting final model is then used to perform 3‐D prestack depth migration to obtain an image volume in depth. The final phase of the workflow includes structural and stratigraphic interpretation of the image volume with the ultimate objective of obtaining a seismically derived reservoir model.

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.

Simulation of a seismic survey with combined surface and in-mine data acquisition for imaging steeply dipping ore veins

2021 ◽  
Author(s):  
Olaf Hellwig ◽  
Stefan Buske
Keyword(s):  
Finite Difference ◽  
Message Passing Interface ◽  
Seismic Survey ◽  
Difference Operators ◽  
Mining District ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Difference Grid ◽  
Triangulated Surfaces

<p>The polymetallic, hydrothermal deposit of the Freiberg mining district in the southeastern part of Germany is characterised by ore veins that are framed by Proterozoic orthogneiss. The ore veins consist mainly of quarz, sulfides, carbonates, barite and flourite, which are associated with silver, lead and tin. Today the Freiberg University of Mining and Technology is operating the shafts Reiche Zeche and Alte Elisabeth for research and teaching purposes with altogether 14 km of accessible underground galleries. The mine together with the most prominent geological structures of the central mining district are included in a 3D digital model, which is used in this study to study seismic acquisition geometries that can help to image the shallow as well as the deeper parts of the ore-bearing veins. These veins with dip angles between 40° and 85° are represented by triangulated surfaces in the digital geological model. In order to import these surfaces into our seismic finite-difference simulation code, they have to be converted into bodies with a certain thickness and specific elastic properties in a first step. In a second step, these bodies with their properties have to be discretized on a hexahedral finite-difference grid with dimensions of 1000 m by 1000 m in the horizontal direction and 500 m in the vertical direction. Sources and receiver lines are placed on the surface along roads near the mine. A Ricker wavelet with a central frequency of 50 Hz is used as the source signature at all excitation points. Beside the surface receivers, additional receivers are situated in accessible galleries of the mine at three different depth levels of 100 m, 150 m and 220 m below the surface. Since previous mining activities followed primarily the ore veins, there are only few pilot-headings that cut through longer gneiss sections. Only these positions surrounded by gneiss are suitable for imaging the ore veins. Based on this geometry, a synthetic seismic data set is generated with our explicit finite-difference time-stepping scheme, which solves the acoustic wave equation with second order accurate finite-difference operators in space and time. The scheme is parallelised using a decomposition of the spatial finite-difference grid into subdomains and Message Passing Interface for the exchange of the wavefields between neighbouring subdomains. The resulting synthetic seismic shot gathers are used as input for Kirchhoff prestack depth migration as well as Fresnel volume migration in order to image the ore veins. Only a top mute to remove the direct waves and a time-dependent gain to correct the amplitude decay due to the geometrical spreading are applied to the data before the migration. The combination of surface and in-mine acquisition helps to improve the image of the deeper parts of the dipping ore veins. Considering the limitations for placing receivers in the mine, Fresnel volume migration as a focusing version of Kirchhoff prestack depth migration helps to avoid migration artefacts caused by this sparse and limited acquisition geometry.</p>

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