scholarly journals Fast time-to-depth conversion and interval velocity estimation in the case of weak lateral variations

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S227-S235 ◽  
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel
Keyword(s):  
Velocity Model ◽  
Velocity Estimation ◽  
Fast Time ◽  
Lateral Velocity ◽  
First Order ◽  
Interval Velocity ◽  
Order Of Magnitude ◽  
Efficient Alternative ◽  
Homogeneous Media ◽  
Lateral Variations

Time-domain processing has a long history in seismic imaging and has always been a powerful workhorse that is routinely used. It generally leads to an expeditious construction of the subsurface velocity model in time, which can later be expressed in the Cartesian depth coordinates via a subsequent time-to-depth conversion. The conventional practice of such a conversion is done using Dix inversion, which is exact in the case of laterally homogeneous media. For other media with lateral heterogeneity, the time-to-depth conversion involves solving a more complex system of partial differential equations (PDEs). We have developed an efficient alternative for time-to-depth conversion and interval velocity estimation based on the assumption of weak lateral velocity variations. By considering only first-order perturbative effects from lateral variations, the exact system of PDEs required to accomplish the exact conversion reduces to a simpler system that can be solved efficiently in a layer-stripping (downward-stepping) fashion. Numerical synthetic and field data examples show that our method can achieve reasonable accuracy and is significantly more efficient than previously proposed methods with a speedup by an order of magnitude.

Velocity estimation by beam stack

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 1034-1047 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Estimation Method ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Gradient Algorithm ◽  
Stratified Medium ◽  
Detailed Knowledge ◽  
Low Velocity ◽  
Velocity Anomaly ◽  
Interval Velocity ◽  
Lateral Variations

Imaging seismic data requires detailed knowledge of the propagation velocity of compressional waves in the subsurface. In conventional seismic processing, the interval velocity model is usually derived from stacking velocities. Stacking velocities are determined by measuring the coherency of the reflections along hyperbolic moveout trajectories in offset. This conventional method becomes inaccurate in geologically complex areas because the conversion of stacking velocities to interval velocities assumes a horizontally stratified medium and mild lateral variations in velocity. The tomographic velocity estimation proposed in this paper can be applied when there are dipping reflectors and strong lateral variations. The method is based on the measurements of moveouts by beam stacks. A beam stack measures local coherency of reflections along hyperbolic trajectories. Because it is a local operator, the beam stack can provide information on nonhyperbolic moveouts in the data. This information is more reliable than traveltimes of reflections picked directly from the data because many seismic traces are used for computing beam stacks. To estimate interval velocity, I iteratively search for the velocity model that best predicts the events in beam‐stacked data. My estimation method does not require a preliminary picking of the data because it directly maximizes the beam‐stack’s energy at the traveltimes and surface locations predicted by ray tracing. The advantage of this formulation is that detection of the events in the beam‐stacked data can be guided by the imposition of smoothness constraints on the velocity model. The optimization problem of maximizing beam‐stack energy is solved by a gradient algorithm. To compute the derivatives of the objective function with respect to the velocity model, I derive a linear operator that relates perturbations in velocity to the observed changes in the beam‐stack kinematics. The method has been successfully applied to a marine survey for estimating a low‐velocity anomaly. The estimated velocity function correctly predicts the nonhyperbolic moveouts in the data caused by the velocity anomaly.

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.

scholarly journals Seismic velocity estimation: A deep recurrent neural-network approach

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. U21-U29
Author(s):  
Gabriel Fabien-Ouellet ◽  
Rahul Sarkar
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Model Building ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Interval Velocity ◽  
Velocity Model Building ◽  
3D Velocity Model

Applying deep learning to 3D velocity model building remains a challenge due to the sheer volume of data required to train large-scale artificial neural networks. Moreover, little is known about what types of network architectures are appropriate for such a complex task. To ease the development of a deep-learning approach for seismic velocity estimation, we have evaluated a simplified surrogate problem — the estimation of the root-mean-square (rms) and interval velocity in time from common-midpoint gathers — for 1D layered velocity models. We have developed a deep neural network, whose design was inspired by the information flow found in semblance analysis. The network replaces semblance estimation by a representation built with a deep convolutional neural network, and then it performs velocity estimation automatically with recurrent neural networks. The network is trained with synthetic data to identify primary reflection events, rms velocity, and interval velocity. For a synthetic test set containing 1D layered models, we find that rms and interval velocity are accurately estimated, with an error of less than [Formula: see text] for the rms velocity. We apply the neural network to a real 2D marine survey and obtain accurate rms velocity predictions leading to a coherent stacked section, in addition to an estimation of the interval velocity that reproduces the main structures in the stacked section. Our results provide strong evidence that neural networks can estimate velocity from seismic data and that good performance can be achieved on real data even if the training is based on synthetics. The findings for the 1D problem suggest that deep convolutional encoders and recurrent neural networks are promising components of more complex networks that can perform 2D and 3D velocity model building.

Interval velocity estimation via NMO-based differential semblance

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. U75-U88 ◽  
Author(s):  
Jintan Li ◽  
William W. Symes
Keyword(s):  
Velocity Model ◽  
Velocity Estimation ◽  
Imaging Method ◽  
Velocity Analysis ◽  
Multiple Reflections ◽  
Coherent Noise ◽  
Interval Velocity ◽  
Velocity Models ◽  
Mean Square Difference ◽  
Rich Data

The differential semblance method of velocity analysis flattens image gathers automatically by updating interval velocity to minimize the mean square difference of neighboring traces. We detail an implementation using hyperbolic normal moveout correction as the imaging method. The algorithm is fully automatic, accommodates arbitrary acquisition geometry, and outputs 1D, 2D, or 3D interval velocity models. This variant of differential semblance velocity analysis is effective within the limits of its imaging methodology: mild lateral heterogeneity and data dominated by primary events. Coherent noise events such as multiple reflections tend to degrade the quality of the velocity model estimated by differential semblance. We show how to combine differential semblance velocity analysis with dip filtering to suppress multiple reflections and thus improve considerably the accuracy of the velocity estimate. We illustrate this possibility using multiple-rich data from a 2D marine survey.

scholarly journals QUALITY IMPROVEMENT OF SEISMIC IMAGE FROM 2D PSDM (PRE STACK DEPTH MIGRATION) USING TOMOGRAPHY FOR INTERVAL VELOCITY MODEL REFINEMENT

2016 ◽  
Vol 28 (2) ◽  
pp. 43
Author(s):  
Hagayudha Timotius ◽  
Yulinar Firdaus
Keyword(s):  
Velocity Model ◽  
Seismic Exploration ◽  
Lateral Velocity ◽  
Model Refinement ◽  
Initial Interval ◽  
Depth Migration ◽  
Interval Velocity ◽  
Imaging Tool ◽  
Main Challenge ◽  
Seismic Image

The main goal of seismic exploration is to get an accurate image of subsurface section so it can be easily interpreted. Pre Stack Depth Migration (PSDM) is such a powerful imaging tool especially for complex area such an area where strong lateral velocity variations exist. The main challenge of PSDM is the need of accurate interval velocity model.In this research, Dix Transformation, coherency inversion, and tomography are used for initial interval velocity model, and then tomography is used for interval velocity model refinement. We compare also between seismic image resulted from PSDM and PSTM to determine the best method. The seismic data that processed in this paper is derived from north western part of Australian Waters. Kata kunci: Pre Stack Depth Migration, Dix Transformation, coherency inversion, tomography. Tujuan utama dari eksplorasi seismik adalah menghasilkan citra yang akurat dari penampang bawah permukaan sehingga diinterpretasi lebih mudah. Pre Stack Depth Migration (PSDM) merupakan suatu metode yang memberikan hasil peningkatan kualitas citra seismik pada daerah kompleks dimana terjadi variasi kecepatan lateral yang signifikan. Salah satu syarat penting yang harus dipenuhi agar hasil PSDM lebih optimal adalah model kecepatan interval yang akurat. Dalam penelitian ini Transformasi Dix, inversi koheren, dan tomografi digunakan untuk memenuhi syarat tersebut. Perbandingan hasil penampang seimik PSDM dan PSTM dilakukan untuk menentukan metode terbaik. Data seismik yang diolah dalam tulisan ini berasal dari wilayah Perairan Baratlaut Australia. Kata kunci: Pre Stack Depth Migration, Transformasi Dix, inversi koheren, tomografi

Vertical seismic profiling depth migration of a salt dome flank

Geophysics ◽  
1986 ◽  
Vol 51 (5) ◽  
pp. 1087-1109 ◽  
Author(s):  
N. D. Whitmore ◽  
Larry R. Lines
Keyword(s):  
Data Processing ◽  
Survey Design ◽  
Velocity Model ◽  
Salt Dome ◽  
Velocity Estimation ◽  
Seismic Profiles ◽  
Depth Migration ◽  
Vertical Seismic Profiles ◽  
Interval Velocity ◽  
Vsp Data

Vertical seismic profiles (VSPs) can supply information about both velocity and subsurface interface locations. Properly designed VSPs can be used to map steeply dipping interfaces such as salt dome flanks. Mapping subsurface interfaces with VSP data requires careful survey design, appropriate data processing, interval velocity estimation, and reflector mapping. The first of these four ingredients is satisfied, in most cases, by preacquisition modeling. The second is accomplished by careful data processing. Initial velocity estimates are provided by seismic tomography. Velocity‐model refinement is accomplished by a combination of iterative modeling and iterative least‐squares inversion. Finally, the resultant interval velocities are used in depth migration of the processed VSP. These four ingredients have been combined to map a salt dome flank.

scholarly journals Using constraints to address the instabilities of automated prestack velocity analysis

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 404-419 ◽  
Author(s):  
Christof Stork ◽  
Robert W. Clayton
Keyword(s):  
Initial Velocity ◽  
Variable Interval ◽  
Velocity Model ◽  
Velocity Fields ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Interval Velocity ◽  
Additional Information ◽  
Analysis Methods ◽  
Automated Methods

Generalized prestack velocity analysis methods that use an automated approach to resolve laterally variable interval velocity fields are beset by a series of problems. The problem of resolving lateral velocity variations has inherent complications that prevent automated methods from being robust enough to be applied routinely to data from a variety of geologic provinces. The use of automated prestack velocity analysis methods will not eliminate the step of carefully producing an initial velocity model derived from regional geologic information and an interpretation of a conventionally processed section. For the methods to regularly produce useful additional information, the unique characteristics of each application must be input into the prestack velocity analysis with the use of inversion constraints. These constraints serve either to adapt the generalized prestack velocity analysis to a focused objective in a particular area or to provide iterative, interpretational tools that help the user produce a velocity model.

CRP-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. U21-U28 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Velocity Model ◽  
Migration Velocity ◽  
Data Sets ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Interval Velocity ◽  
Model Parameterization ◽  
Migration Velocity Analysis ◽  
Local Interval

A new migration velocity analysis is developed by combining the speed of parsimonious prestack depth migration with velocity adjustments estimated within and across common-reflection-point (CRP) gathers. The proposed approach is much more efficient than conventional tomographic velocity analysis because only the traces that contribute to a series of CRP gathers are depth migrated at each iteration. The local interval-velocity adjustments for each CRP are obtained by maximizing the stack amplitude over the predicted (nonhyperbolic) moveout in each CRP gather; this does not involve retracing rays. At every iteration, the velocity in each pixel is updated by averaging over all the predicted velocity updates. Finally, CRP positions and orientations are updated by parsimonious migration, and rays are retraced to define new CRP gathers for the next iteration; this ensures internal consistency between the updated velocity model and the CRP gather. Because the algorithm has a gridded-model parameterization, no explicit representation or fitting of reflectors is involved. Strong lateral-velocity variations, such as those found at salt flanks, can be handled. Application to synthetic and field data sets show that the proposed algorithm works effectively and efficiently.

Time-to-depth conversion and velocity estimation by image-wavefront propagation

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. U75-U85 ◽  
Author(s):  
Leandro da S. Sadala Valente ◽  
Henrique B. Santos ◽  
Jessé C. Costa ◽  
Jörg Schleicher
Keyword(s):  
Ray Tracing ◽  
Model Building ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Time Step ◽  
Velocity Anomaly ◽  
Interval Velocity ◽  
Velocity Models ◽  
Wavefront Propagation ◽  
Velocity Model Building

A new strategy for time-to-depth conversion and interval-velocity estimation is based entirely on image-wavefront propagation without the need to follow individual image rays. The procedure has three main features: (1) It computes the velocity field and the traveltime directly, allowing us to dispense with dynamic ray tracing; (2) it requires only the knowledge of the image wavefront at the previous time step; and (3) it inherently smooths the image wavefront, inhibiting the formation of caustics. As a consequence, the method tends to be faster than the usual techniques and does not carry the constraints and limitations inherent to common ray-tracing strategies. Synthetic tests using a Gaussian velocity anomaly as well as the Marmousi velocity model, and two smoothed versions of it show the feasibility of the method. A field-data example demonstrates the use of different numerical procedures. Our results indicate that the present strategy can be used to construct reasonable depth-velocity models that can be used as reliable starting models for velocity-model building in depth migration or for tomographic methods.

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