Depth migration before stack

Geophysics ◽  
1980 ◽  
Vol 45 (3) ◽  
pp. 376-393 ◽  
Author(s):  
Philip S. Schultz ◽  
John W. C. Sherwood
Keyword(s):  
Seismic Data ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Signal Amplitude ◽  
Scalar Wave ◽  
Lateral Velocity ◽  
Seismic Section ◽  
Depth Migration ◽  
Velocity Gradients ◽  
Zero Offset

When seismic data are migrated using operators derived from the scalar wave equation, an assumption is normally made that the seismic velocity in the propagating medium is locally laterally invariant. This simplifying assumption causes reflectors to be imaged incorrectly when lateral velocity gradients exist, irrespective of the degree of accuracy to which the subsurface velocity structure is known. A finite‐difference method has been implemented for migration of unstacked data in the presence of lateral velocity gradients, where the operation of wave field extrapolation is done in increments of depth rather than time. Performing this depth migration on unstacked data results in the imaging of reflectors on the zero‐offset trace, whereupon a zero‐offset section becomes a fully imaged‐in‐depth seismic section. Such a section, in addition to being a correctly migrated depth section, shows the same order of signal amplitude enhancement as in a normal stacking process.

Slowness‐weighted diffraction stack for migrating wide‐angle seismic data in laterally varying media

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1046-1052 ◽  
Author(s):  
Harm J. A. Van Avendonk
Keyword(s):  
Seismic Data ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Image Space ◽  
Wide Angle ◽  
Data Set ◽  
Seismic Velocity Structure ◽  
Depth Migration ◽  
Angle Data ◽  
Reflecting Boundaries

Wide‐angle prestack depth migration is an important tool for studying the nature of reflecting boundaries in the earth's crust. The slowness‐weighted diffraction stack (SWDS) method has been used to incorporate both two‐way traveltime constraints and slowness information in the migration. For this purpose, traveltimes and apparent slownesses of reflected arrivals must be calculated in the image space. Earlier applications of SWDS required a 1D or gently varying seismic velocity structure to obtain these quantities by ray tracing in the image space. I show that the apparent slownesses can also be derived directly from one‐way traveltime maps using Fermat's principle. The SDWS is applied to an existing onshore–offshore wide‐angle data set, and the example shows that the method can be used to image detailed reflectivity structure at great depths.

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.

Iterative P-wave velocity inversion using Markov chain Monte Carlo method

2020 ◽  
Author(s):  
Hyunggu Jun ◽  
Hyeong-Tae Jou ◽  
Han-Joon Kim ◽  
Sang Hoon Lee
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
Velocity Structure ◽  
Low Frequency ◽  
P Wave ◽  
Velocity Analysis ◽  
Seismic Section ◽  
Traveltime Tomography ◽  
P Wave Velocity ◽  
Frequency Components

<p>Imaging the subsurface structure through seismic data needs various information and one of the most important information is the subsurface P-wave velocity. The P-wave velocity structure mainly influences on the location of the reflectors during the subsurface imaging, thus many algorithms has been developed to invert the accurate P-wave velocity such as conventional velocity analysis, traveltime tomography, migration velocity analysis (MVA) and full waveform inversion (FWI). Among those methods, conventional velocity analysis and MVA can be widely applied to the seismic data but generate the velocity with low resolution. On the other hands, the traveltime tomography and FWI can invert relatively accurate velocity structure, but they essentially need long offset seismic data containing sufficiently low frequency components. Recently, the stochastic method such as Markov chain Monte Carlo (McMC) inversion was applied to invert the accurate P-wave velocity with the seismic data without long offset or low frequency components. This method uses global optimization instead of local optimization and poststack seismic data instead of prestack seismic data. Therefore, it can avoid the problem of the local minima and limitation of the offset. However, the accuracy of the poststack seismic section directly affects the McMC inversion result. In this study, we tried to overcome the dependency of the McMC inversion on the poststack seismic section and iterative workflow was applied to the McMC inversion to invert the accurate P-wave velocity from the simple background velocity and inaccurate poststack seismic section. The numerical test showed that the suggested method could successfully invert the subsurface P-wave velocity.</p>

SEISMIC VELOCITIES IN THE SOUTHEASTERN SAN JOAQUIN VALLEY OF CALIFORNIA

Geophysics ◽  
1941 ◽  
Vol 6 (4) ◽  
pp. 327-355
Author(s):  
E. J. Stulken
Keyword(s):  
Seismic Data ◽  
Seismic Velocity ◽  
San Joaquin Valley ◽  
Seismic Velocities ◽  
Velocity Measurements ◽  
Constant Depth ◽  
Entire Area ◽  
Velocity Gradients ◽  
Velocity Changes ◽  
First Time

For the first time, seismic velocity measurements from well surveys have been made intensively enough to justify an analysis of the velocity field in an entire area instead of just along lines between wells. Maps are drawn showing velocity changes in the southeastern San Joaquin Valley of California. A portion of the valley floor in the neighborhood of Bakersfield, about twenty‐five miles wide and thirty‐five miles long, was chosen for study because of the number of wells in the area whose velocities were known. Differences in average velocity of 1700 feet per second for a constant depth are observed, and horizontal velocity gradients averaging over 100 feet per second per mile are computed. Correction schemes for the adjustment of seismic data are suggested, and correction maps shown. An attempt is made to establish a connection between stratigraphy and seismic velocity. Comparative study of the logs of wells and the velocities observed in them yields certain qualitative conclusions, but attempts to express the relation in a quantitative way fail.

Accurate depth migration by a generalized phase‐shift method

Geophysics ◽  
1987 ◽  
Vol 52 (8) ◽  
pp. 1074-1084 ◽  
Author(s):  
Dan Kosloff ◽  
David Kessler
Keyword(s):  
Phase Shift ◽  
Velocity Structure ◽  
Shift Method ◽  
Depth Migration ◽  
Integration Techniques ◽  
Matrix Diagonalization ◽  
Offset Time ◽  
Zero Offset ◽  
Spatially Variant ◽  
Phase Shift Method

A new depth migration method derived in the space‐frequency domain is based on a generalized phase‐shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase‐shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase‐shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero‐offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high‐cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge‐Kutta method or the Taylor method.

Seismic structure of basalt flows from surface seismic data, borehole measurements, and synthetic seismogram modeling

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1925-1936 ◽  
Author(s):  
Moritz M. Fliedner ◽  
Robert S. White
Keyword(s):  
Velocity Structure ◽  
Seismic Velocity ◽  
Synthetic Seismogram ◽  
P Wave ◽  
Wide Angle ◽  
Seismic Velocities ◽  
Seismic Structure ◽  
Low Velocity ◽  
Amplitude Variation With Offset ◽  
Velocity Gradients

We use the wide‐angle wavefield to constrain estimates of the seismic velocity and thickness of basalt flows overlying sediments. Wide angle means the seismic wavefield recorded at offsets beyond the emergence of the direct wave. This wide‐angle wavefield contains arrivals that are returned from within and below the basalt flows, including the diving wave through the basalts as the first arrival and P‐wave reflections from the base of the basalts and from subbasalt structures. The velocity structure of basalt flows can be determined to first order from traveltime information by ray tracing the basalt turning rays and the wide‐angle base‐basalt reflection. This can be refined by using the amplitude variation with offset (AVO) of the basalt diving wave. Synthetic seismogram models with varying flow thicknesses and velocity gradients demonstrate the sensitivity to the velocity structure of the basalt diving wave and of reflections from the base of the basalt layer and below. The diving‐wave amplitudes of the models containing velocity gradients show a local amplitude minimum followed by a maximum at a greater range if the basalt thickness exceeds one wavelength and beyond that an exponential amplitude decay. The offset at which the maximum occurs can be used to determine the basalt thickness. The velocity gradient within the basalt can be determined from the slope of the exponential amplitude decay. The amplitudes of subbasalt reflections can be used to determine seismic velocities of the overburden and the impedance contrast at the reflector. Combining wide‐angle traveltimes and amplitudes of the basalt diving wave and subbasalt reflections enables us to obtain a more detailed velocity profile than is possible with the NMO velocities of small‐offset reflections. This paper concentrates on the subbasalt problem, but the results are more generally applicable to situations where high‐velocity bodies overlie a low‐velocity target, such as subsalt structures.

Image mispositioning due to dipping TI media: A physical seismic modeling study

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1230-1238 ◽  
Author(s):  
J. Helen Isaac ◽  
Don C. Lawton
Keyword(s):  
Seismic Velocity ◽  
Transversely Isotropic ◽  
Step Function ◽  
Depth Migration ◽  
Velocity Anisotropy ◽  
Depth Images ◽  
Thrust Belts ◽  
Migration Velocity Analysis ◽  
Seismic Velocity Anisotropy ◽  
Zero Offset

A scaled physical model was constructed to investigate the magnitudes of imaging errors incurred by the use of isotropic processing code when there is seismic velocity anisotropy present in the dipping overburden. The model consists of a block of transversely isotropic (TI) phenolic material with the TI axis of symmetry dipping at an angle of 45°. Its scaled thickness is 1500 m, and it is intended to simulate the dipping clastic sequences found in many fold‐thrust belts. A piece of isotropic Plexiglas, affixed to the underside of the anisotropic block, has a step function in it to simulate a target reef edge or fault. The anisotropy parameters of the material are δ = 0.1 and ε = 0.24. On zero‐offset data the imaged position of the target is shifted laterally 320 m in the updip direction of the beds, whereas on time‐ and depth‐migrated multichannel sections the shift is 300 m. The lateral shift is offset dependent, with the amount of shift in any common‐midpoint gather decreasing from 320 m on the near offsets to 280 m on the far offsets. Prestack depth‐migration velocity analysis based upon obtaining consistent depth images in the common‐offset domain results in the base of the anisotropic section being imaged 50 m (about 3%) too deep.

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.

Integrated seismic and electromagnetic model building applied to improve subbasalt depth imaging in the Faroe-Shetland Basin

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. E57-E68 ◽  
Author(s):  
Martin Panzner ◽  
Jan Petter Morten ◽  
Wiktor Waldemar Weibull ◽  
Børge Arntsen
Keyword(s):  
Seismic Data ◽  
Model Building ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Real Data ◽  
Magnetotelluric Data ◽  
Electromagnetic Data ◽  
Data Inversion ◽  
Seismic Image ◽  
Imaging Results

Subbasalt imaging has gained significant interest in the last two decades, driven by the urge to better understand the geologic structures beneath volcanic layers, which can be up to several kilometers thick. This understanding is crucial for the development and risking of hydrocarbon play models in these areas. However, imaging based on the reflection seismic data alone suffers from severe amplitude transmission losses and interbed multiples in the volcanic sequence, as well as from poor definition of the subbasalt velocity structure. We have considered a sequential imaging workflow, in which the resistivity model from joint controlled-source electromagnetic and magnetotelluric data inversion was used to update the velocity model and to improve the structural definition in the migrated seismic image. The quantitative link between resistivity and velocity was derived from well data. The workflow used standard procedures for seismic velocity analysis, electromagnetic data inversion, and well analysis, and thereby allowed detail control and input based on additional geophysical knowledge and experience in each domain. Using real data sets from the Faroe-Shetland Basin, we can demonstrate that the integration of seismic and electromagnetic data significantly improved the imaging of geologic structures covered by up to several-kilometer-thick extended volcanic sequences. The improved results might alter the interpretation compared with the imaging results from seismic data alone.

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