scholarly journals Time-to-depth conversion and seismic velocity estimation using time-migration velocity

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE205-VE210 ◽  
Author(s):  
Maria Cameron ◽  
Sergey Fomel ◽  
James Sethian
Keyword(s):  
Time Domain ◽  
Seismic Velocity ◽  
Migration Velocity ◽  
Two Dimensions ◽  
Velocity Estimation ◽  
Three Dimensions ◽  
Velocity Models ◽  
Time Migration ◽  
Geometric Spreading ◽  
Paraxial Ray

The objective was to build an efficient algorithm (1) to estimate seismic velocity from time-migration velocity, and (2) to convert time-migrated images to depth. We established theoretical relations between the time-migration velocity and seismic velocity in two and three dimensions using paraxial ray-tracing theory. The relation in two dimensions implies that the conventional Dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays. We formulated an inverse problem of finding seismic velocity from the Dix velocity and developed a numerical procedure for solving it. The procedure consists of two steps: (1) computation of the geometric spreading of image rays and the true seismic velocity in time-domain coordinates from the Dix velocity; (2) conversion of the true seismic velocity from the time domain to the depth domain and computation of the transition matrices from time-domain coordinates todepth. For step 1, we derived a partial differential equation (PDE) in two and three dimensions relating the Dix velocity and the geometric spreading of image rays to be found. This is a nonlinear elliptic PDE. The physical setting allows us to pose a Cauchy problem for it. This problem is ill posed, but we can solve it numerically in two ways on the required interval of time, if it is sufficiently short. One way is a finite-difference scheme inspired by the Lax-Friedrichs method. The second way is a spectral Chebyshev method. For step 2, we developed an efficient Dijkstra-like solver motivated by Sethian’s fast marching method. We tested numerical procedures on a synthetic data example and applied them to a field data example. We demonstrated that the algorithms produce a significantly more accurate estimate of seismic velocity than the conventional Dix inversion. This velocity estimate can be used as a reasonable first guess in building velocity models for depth imaging.

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.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

Image-ray tracing for joint 3D seismic velocity estimation and time-to-depth conversion

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S99-S114 ◽  
Author(s):  
Einar Iversen ◽  
Martin Tygel
Keyword(s):  
Velocity Field ◽  
Seismic Velocity ◽  
A Priori ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
P Waves ◽  
Data Set ◽  
Time Migration ◽  
Elementary Waves

Seismic time migration is known for its ability to generate well-focused and interpretable images, based on a velocity field specified in the time domain. A fundamental requirement of this time-migration velocity field is that lateral variations are small. In the case of 3D time migration for symmetric elementary waves (e.g., primary PP reflections/diffractions, for which the incident and departing elementary waves at the reflection/diffraction point are pressure [P] waves), the time-migration velocity is a function depending on four variables: three coordinates specifying a trace point location in the time-migration domain and one angle, the so-called migration azimuth. Based on a time-migration velocity field available for a single azimuth, we have developed a method providing an image-ray transformation between the time-migration domain and the depth domain. The transformation is obtained by a process in which image rays and isotropic depth-domain velocity parameters for their propagation are esti-mated simultaneously. The depth-domain velocity field and image-ray transformation generated by the process have useful applications. The estimated velocity field can be used, for example, as an initial macrovelocity model for depth migration and tomographic inversion. The image-ray transformation provides a basis for time-to-depth conversion of a complete time-migrated seismic data set or horizons interpreted in the time-migration domain. This time-to-depth conversion can be performed without the need of an a priori known velocity model in the depth domain. Our approach has similarities as well as differences compared with a recently published method based on knowledge of time-migration velocity fields for at least three migration azimuths. We show that it is sufficient, as a minimum, to give as input a time-migration velocity field for one azimuth only. A practical consequence of this simplified input is that the image-ray transformation and its corresponding depth-domain velocity field can be generated more easily.

Nonlinear 3-D traveltime inversion of crosshole data with an application in the area of the Middle Ural Mountains

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 627-636 ◽  
Author(s):  
Pantelis M. Soupios ◽  
Constantinos B. Papazachos ◽  
Christopher Juhlin ◽  
Gregory N. Tsokas
Keyword(s):  
Seismic Velocity ◽  
Null Space ◽  
Fresnel Zone ◽  
A Priori ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Estimation ◽  
Three Dimensions ◽  
Ural Mountains ◽  
Velocity Models

This paper deals with the problem of nonlinear seismic velocity estimation from first‐arrival traveltimes obtained from crosshole and downhole experiments in three dimensions. A standard tomographic procedure is applied, based on the representation of the crosshole area into a number of cells which have an initial slowness assigned. For the forward modeling, the raypath matrix is computed using the revisited ray bending method, supplemented by an approximate computation of the first Fresnel zone at each point of the ray, hence using physical and not only mathematical rays. Since 3-D ray tracing is incorporated, the inversion technique is nonlinear. Velocity images are obtained by a constrained least‐squares inversion scheme using both “damping” and “smoothing” factors. The appropriate choice of these factors is defined by the use of appropriate criteria such as the L-curve. The tomographic approach is improved by incorporating a priori information about the media to be imaged into our inversion scheme. This improvement in imaging is achieved by projecting a desirable solution onto the null space of the inversion, and including this null‐space contribution with the standard non‐null‐space inversion solution. The efficiency of the inversion scheme is tested through a series of tests with synthetic data. Moreover, application in the area of the Ural Mountains using real data demonstrates that the proposed technique produces more realistic velocity models than those obtained by other standard approaches.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part II: Applications on synthetic and real data

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1213-1224 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Heterogeneous Media ◽  
Real Data ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Efficient Computation ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray

We demonstrate a method for estimating 2‐D velocity models from synthetic and real seismic reflection data in the framework of migration velocity analysis (MVA). No assumption is required on the reflector geometry or on the unknown background velocity field, provided that the data only contain primary reflections/diffractions. In the prestack depth‐migrated volume, locations where the reflectivity exhibits local coherency are automatically picked without interpretation in two panels: common image gathers (CIGs) and common offset gathers (COGs). They are characterized by both their positions and two slopes. The velocity is estimated by minimizing all slopes picked in the CIGs. We test the applicability of the method on a real data set, showing the possibility of an efficient inversion using (1) the migration of selected CIGs and COGs, (2) automatic picking on prior uncorrelated locally coherent events, (3) efficient computation of the gradient of the cost function via paraxial ray tracing from the picked events to the surface, and (4) a gradient‐type optimization algorithm for convergence.

scholarly journals Simultaneous time imaging, velocity estimation, and multiple suppression using local event slopes

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA65-WCA73 ◽  
Author(s):  
Dennis Cooke ◽  
Andrej Bóna ◽  
Benn Hansen
Keyword(s):  
Temporal Frequency ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Data Set ◽  
Image Domain ◽  
Kirchhoff Migration ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Input Formula

Starting with the double-square-root equation we derive expressions for a velocity-independent prestack time migration and for the associated migration velocity. We then use that velocity to identify multiples and suppress them as part of the imaging step. To describe our algorithm, workflow, and products, we use the terms velocity-independent and oriented. While velocity-independent imaging does not require an input migration velocity, it does require input [Formula: see text]-values (also called local event slopes) measured in both the shot and receiver domains. There are many possible methods of calculating these required input [Formula: see text]-values, perhaps the simplest is to compute the ratio of instantaneous spatial frequency to instantaneous temporal frequency. Using a synthetic data set rich in multiples, we test the oriented algorithm and generate migrated prestack gathers, the oriented migration velocity field, and stacked migrations. We use oriented migration velocities for prestack multiple suppression. Without this multiple suppression step, the velocity-independent migration is inferior to a conventional Kirchhoff migration because the oriented migration will flatten primaries and multiples alike in the common image domain. With this multiple suppression step, the velocity-independent are very similar to a Kirchhoff migration generated using the known migration velocity of this test data set.

MULTIDOMAIN PSEUDOSPECTRAL TIME-DOMAIN (PSTD) METHOD FOR ACOUSTIC WAVES IN LOSSY MEDIA

2004 ◽  
Vol 12 (03) ◽  
pp. 277-299 ◽  
Author(s):  
YAN QING ZENG ◽  
QING HUO LIU ◽  
GANG ZHAO
Keyword(s):  
Acoustic Wave ◽  
Time Domain ◽  
Acoustic Waves ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Computational Domain ◽  
Complex Objects ◽  
Lossy Media

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics.

3D diffraction imaging with Kirchhoff time migration using vertical traveltime difference gathers

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S555-S566 ◽  
Author(s):  
Zhengwei Li ◽  
Jianfeng Zhang
Keyword(s):  
Fresnel Zone ◽  
Lateral Position ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Small Scale ◽  
Imaging Method ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Dip Angle ◽  
Angle Gather

We have built a vertical traveltime difference (VTD) gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The VTD gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip angles, which is closely related to the 2D dip-angle gather. In VTD gathers, diffraction events exhibit flattening, whereas reflection events have convex upward-sloping shapes. Different from the 2D dip-angle gather, Fresnel zone-related specular reflections are precisely focused on the given regions over all offsets and azimuths, thus leaving more diffraction energy after muting. To image linear diffractors, such as faults in three dimensions, the VTD gather can be extended into two dimensions by adding a dip-azimuth dimension. This makes it possible to correct phases of edge diffractions and detect the orientations of the linear diffractors. The memory requirement of the VTD or VTD plus azimuth gathers is much less than that of the 2D dip-angle gathers. We can store the gathers at each lateral position and then correct the phase and enhance the weak diffractions in 3D cases. Synthetic and field data tests demonstrate the effectiveness of our 3D diffraction imaging method.

Scale‐dependent seismic velocity in heterogeneous media

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1222-1233 ◽  
Author(s):  
Tapan Mukerji ◽  
Gary Mavko ◽  
Daniel Mujica ◽  
Nathalie Lucet
Keyword(s):  
Short Wavelength ◽  
Heterogeneous Media ◽  
Seismic Velocity ◽  
Scale Effects ◽  
Propagation Distance ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Small Scale ◽  
Measured Velocity ◽  
Wavelength Limit

The measurable traveltimes of seismic events propagating in heterogeneous media depend on the geologic scale, the seismic wavelength, and the propagation distance. In general, the velocity inferred from arrival times is slower when the wavelength is longer than the scale of heterogeneity and faster when the wavelength is shorter. For normal incidence propagation in stratified media, this is the difference between averaging seismic slownesses in the short wavelength limit, and averaging elastic compliances in the long wavelength limit. In two and three dimensions there is also the path effect. Shorter wavelengths tend to find faster paths, thus biasing the traveltimes to lower values. In the short wavelength limit, the slowness inferred from the average traveltime is smaller than the mean slowness of the medium. When the propagation distance is much larger than the scale of the heterogeneity, the path effect causes the velocity increase from long to short wavelengths to be much larger in two dimensions than in one dimension, and even larger in three dimensions. The amount of velocity dispersion can be understood theoretically, but there is some discrepancy between theory and experiment as to what ratio of wavelength to heterogeneity scale separates the long and short wavelength limits. The scale‐dependent traveltime implies that a measured velocity depends not just on rock properties, but also on the scale of the measurement relative to the scale of the geology. When comparing measurements made at different scales, for example logs and surface seismic, it is not always correct to simply apply the Backus average; the correct procedure will vary from case to case with the scale of the geology. Scale effects must be included with other viscoelastic mechanisms of dispersion when comparing measurements made at different frequencies. The amount of observed scale‐dependent dispersion also depends on the spatial resolution of the receiver array. For example, the first‐break time of the average trace from a stack, a large group array, or a large laboratory transducer may be earlier than the average of first‐break times measured with individual small‐scale receivers.

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