Prestack migration velocity estimation using nonlinear methods

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 138-150 ◽  
Author(s):  
Michael Jervis ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Optimization Methods ◽  
Velocity Estimation ◽  
Model Parameters ◽  
Waveform Data ◽  
Nonlinear Methods ◽  
Depth Migration ◽  
Computationally Intensive

We describe here methods of estimating interval velocities based on two nonlinear optimization methods; very fast simulated annealing (VFSA) and a genetic algorithm (GA). The objective function is defined using prestack seismic data after depth migration. This inverse problem involves optimizing the lateral consistency of reflectors between adjacent migrated shot records. In effect, the normal moveout correction in velocity analysis is replaced by prestack depth migration. When the least‐squared difference between each pair of migrated shots is at a minimum, the true velocity model has been found. Our model is parameterized using cubic‐B splines distributed on a rectangular grid. The main advantages of using migrated data are that they do not require traveltime picking, knowledge of the source wavelet, and expensive computation of synthetic waveform data to assess the degree of data‐model fit. Nonlinear methods allow automated determination of the global minimum without relying on estimates of the gradient of the objective function, the starting model, or making assumptions about the nature of the objective function itself. For the velocity estimation problem, the VFSA converges 4 to 5 times faster than the GA for both a 2-D synthetic example and a structurally complex real data example from the Gulf of Mexico. Though computationally intensive, this problem requires few model parameters, and use of a fast traveltime code for Kirchhoff migration makes the algorithm tractable for real earth problems.

Velocity inversion by global optimization using finite-offset common-reflection-surface stacking applied to synthetic and Tacutu Basin seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R165-R174 ◽  
Author(s):  
Marcelo Jorge Luz Mesquita ◽  
João Carlos Ribeiro Cruz ◽  
German Garabito Callapino
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Data Sets ◽  
Layer By Layer ◽  
Velocity Inversion ◽  
Very Fast Simulated Annealing ◽  
Target Layer ◽  
Common Reflection Surface ◽  
The Mean

Estimation of an accurate velocity macromodel is an important step in seismic imaging. We have developed an approach based on coherence measurements and finite-offset (FO) beam stacking. The algorithm is an FO common-reflection-surface tomography, which aims to determine the best layered depth-velocity model by finding the model that maximizes a semblance objective function calculated from the amplitudes in common-midpoint (CMP) gathers stacked over a predetermined aperture. We develop the subsurface velocity model with a stack of layers separated by smooth interfaces. The algorithm is applied layer by layer from the top downward in four steps per layer. First, by automatic or manual picking, we estimate the reflection times of events that describe the interfaces in a time-migrated section. Second, we convert these times to depth using the velocity model via application of Dix’s formula and the image rays to the events. Third, by using ray tracing, we calculate kinematic parameters along the central ray and build a paraxial FO traveltime approximation for the FO common-reflection-surface method. Finally, starting from CMP gathers, we calculate the semblance of the selected events using this paraxial traveltime approximation. After repeating this algorithm for all selected CMP gathers, we use the mean semblance values as an objective function for the target layer. When this coherence measure is maximized, the model is accepted and the process is completed. Otherwise, the process restarts from step two with the updated velocity model. Because the inverse problem we are solving is nonlinear, we use very fast simulated annealing to search the velocity parameters in the target layers. We test the method on synthetic and real data sets to study its use and advantages.

Redatuming through a salt canopy and target-oriented salt-flank imaging

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S63-S71 ◽  
Author(s):  
Rongrong Lu ◽  
Mark Willis ◽  
Xander Campman ◽  
Jonathan Ajo-Franklin ◽  
M. Nafi Toksöz
Keyword(s):  
Velocity Gradient ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Estimation Model ◽  
Depth Migration ◽  
Prestack Migration

We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank through an overburden salt canopy. We tested its performance and capabilities on 2D synthetic acoustic seismic data from a Gulf of Mexico style model. We first redatumed surface shots, using seismic interferometry, from a walkaway vertical seismic profile survey as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving surface shots through the salt canopy, without any knowledge of overburden velocity structure. After redatuming, we can apply multiple passes of prestack migration from the reference datum of the bore-hole. In our example, first-pass migration, using only a simple vertical velocity gradient model, reveals the outline of the salt edge. A second pass of reverse-time, prestack depth migration using full two-way wave equation was performed with an updated velocity model that consisted of the velocity gradient and salt dome. The second-pass migration brings out dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank, forming prismatic reflections. In this target-oriented strategy, the computationally fast redatuming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove effects of the salt canopy and surrounding overburden. This might allow this strategy to be used in the field in near real time.

The three‐parameter equation: An efficient tool to enhance the stack

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Pierre D. Thore ◽  
Eric de Bazelaire ◽  
Marisha P. Rays
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Least Square Method ◽  
Maximum Energy ◽  
Computational Effort ◽  
Velocity Estimation ◽  
Least Square ◽  
Waveform Data ◽  
Interval Velocity ◽  
Parameter Equation

We compare the three‐term equation to the normal moveout (NMO) equation for several synthetic data sets to analyze whether or not it is worth making the additional computational effort in the stacking process within various exploration contexts. In our evaluation we have selected two criteria: 1)The quality of the stacked image. 2) The reliability of the stacking parameters and their usefulness for further computation such as interval velocity estimation. We have simulated the stacking process very precisely, despite using only the traveltimes and not the full waveform data. The procedure searches for maximum coherency along the traveltime curve rather than a least‐square regression to it. This technique, which we call the Gaussian‐weighted least square, avoids most of the shortcomings of the least‐square method. The following are our conclusions: 1) The three term equation gives a better stack than the regular NMO. The increase in stacking energy can be more than 30 percent. 2)The calculation of interval velocities using a DIX formula rewritten for the three‐parameter equation is much more stable and accurate than the standard DIX formula. 3) The search for the three parameters is feasible in an efficient way since the shifted hyperbola requires only static corrections rather than dy namic ones. 4) Noise alters the parameters of the maximum energy stack in a way that depends on the noise type. The estimates obtained remain accurate enough for interval velocity estimation (where only two parameters are needed), but the use of the three parameters in direct inversion may be hazardous because of noise corruption. These conclusions should, however, be verified on real data examples.

Noise removal by migration of time-shift images

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S105-S111 ◽  
Author(s):  
Sheng Xu ◽  
Feng Chen ◽  
Bing Tang ◽  
Gilles Lambare
Keyword(s):  
Time Lag ◽  
Real Data ◽  
Velocity Model ◽  
Noise Removal ◽  
Time Shift ◽  
Reverse Time ◽  
Coherent Noise ◽  
Data Set ◽  
Depth Migration ◽  
Time Migration

When using seismic data to image complex structures, the reverse time migration (RTM) algorithm generally provides the best results when the velocity model is accurate. With an inexact model, moveouts appear in common image gathers (CIGs), which are either in the surface offset domain or in subsurface angle domain; thus, the stacked image is not well focused. In extended image gathers, the strongest energy of a seismic event may occur at non-zero-lag in time-shift or offset-shift gathers. Based on the operation of RTM images produced by the time-shift imaging condition, the non-zero-lag time-shift images exhibit a spatial shift; we propose an approach to correct them by a second pass of migration similar to zero-offset depth migration; the proposed approach is based on the local poststack depth migration assumption. After the proposed second-pass migration, the time-shift CIGs appear to be flat and can be stacked. The stack enhances the energy of seismic events that are defocused at zero time lag due to the inaccuracy of the model, even though the new focused events stay at the previous positions, which might deviate from the true positions of seismic reflection. With the stack, our proposed approach is also able to attenuate the long-wavelength RTM artifacts. In the case of tilted transverse isotropic migration, we propose a scheme to defocus the coherent noise, such as migration artifacts from residual multiples, by applying the original migration velocity model along the symmetry axis but with different anisotropic parameters in the second pass of migration. We demonstrate that our approach is effective to attenuate the coherent noise at subsalt area with two synthetic data sets and one real data set from the Gulf of Mexico.

Optimization and sensitivity analysis of seismic depth migrations from Hibernia Field

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2054-2062 ◽  
Author(s):  
Irene Kelly ◽  
Larry R. Lines
Keyword(s):  
Sensitivity Analysis ◽  
Least Squares ◽  
Real Data ◽  
Optimization Method ◽  
Velocity Estimation ◽  
Inversion Method ◽  
Depth Migration ◽  
Velocity Models ◽  
Sensitivity Analysis Method ◽  
Seismic Reflectors

Accurate imaging of seismic reflectors with depth migration requires accurate velocity models. In frontier areas with few well constraints, velocity estimation generally involves the use of methods such as normal moveout analysis, seismic traveltime tomography, or iterative prestack depth migration. These techniques can be effective, but may also be expensive or time‐consuming. In situations where we have information on formation tops from a series of wells which intersect seismic reflectors, we use a least‐squares optimization method to estimate velocity models. This method produces velocity models that optimize depth migrations in terms of well constraints by using least‐squares inversion to match the depth migration images to formation tops. The well log information is used to optimize poststack migration, thereby eliminating some of the time and expense of velocity analysis. In addition to applying an inversion method which optimizes depth migration in terms of formation tops, we can use a sensitivity analysis method of “most‐squares inversion” to explore a range of velocity models which provide mathematically acceptable solutions. This sensitivity analysis quantifies the expected result that our velocity estimates are generally less reliable for thin beds than for thick beds. The proposed optimization method is shown to be successful on synthetic and real data cases from the Hibernia Field of offshore Newfoundland.

Novel strategies for complex foothills seismic imaging — Part 1: Mega-near-surface velocity estimation

2020 ◽  
Vol 8 (3) ◽  
pp. T651-T665
Author(s):  
Yalin Li ◽  
Xianhuai Zhu ◽  
Gengxin Peng ◽  
Liansheng Liu ◽  
Wensheng Duan
Keyword(s):  
Seismic Imaging ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Innovative Approach ◽  
Surface Velocity ◽  
Near Surface ◽  
Depth Migration ◽  
Static Corrections ◽  
Over Time

Seismic imaging in foothills areas is challenging because of the complexity of the near-surface and subsurface structures. Single seismic surveys often are not adequate in a foothill-exploration area, and multiple phases with different acquisition designs within the same block are required over time to get desired sampling in space and azimuths for optimizing noise attenuation, velocity estimation, and migration. This is partly because of economic concerns, and it is partly because technology is progressing over time, creating the need for unified criteria in processing workflows and parameters at different blocks in a study area. Each block is defined as a function of not only location but also the acquisition and processing phase. An innovative idea for complex foothills seismic imaging is presented to solve a matrix of blocks and tasks. For each task, such as near-surface velocity estimation and static corrections, signal processing, prestack time migration, velocity-model building, and prestack depth migration, one or two best service companies are selected to work on all blocks. We have implemented streamlined processing efficiently so that Task-1 to Task-n progressed with good coordination. Application of this innovative approach to a mega-project containing 16 3D surveys covering more than [Formula: see text] in the Kelasu foothills, northwestern China, has demonstrated that this innovative approach is a current best practice in complex foothills imaging. To date, this is the largest foothills imaging project in the world. The case study in Kelasu successfully has delivered near-surface velocity models using first arrivals picked up to 3500 m offset for static corrections and 9000 m offset for prestack depth migration from topography. Most importantly, the present megaproject is a merge of several 3D surveys, with the merge performed in a coordinated, systematic fashion in contrast to most land megaprojects. The benefits of this approach and the strategies used in processing data from the various subsurveys are significant. The main achievement from the case study is that the depth images, after the application of the near-surface velocity model estimated from the megasurveys, are more continuous and geologically plausible, leading to more accurate seismic interpretation.

Practical aspects and applications of 2D stereotomography

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1008-1021 ◽  
Author(s):  
Frederic Billette ◽  
Soazig Le Bégat ◽  
Pascal Podvin ◽  
Gilles Lambaré
Keyword(s):  
Estimation Method ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Common Source ◽  
Depth Migration ◽  
Reflection Seismic ◽  
Velocity Models ◽  
Automatic Picking ◽  
Iterative Inversion

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on synthetic data and on a 2D line extracted from a 3D towed streamer survey shot in West Africa for TotalFinaElf. The examples demonstrate that the method requires only minor human intervention and rapidly converges to a geologically plausible velocity model in these two very different and complex velocity regimes. The quality of the velocity models is verified by prestack depth migration results.

Side Impact Crash Modelling: Development of a Numerical Identification Tool Using Optimization Methods

1999 ◽  
Author(s):  
Jean-Yves Jaskulski ◽  
Mounib Mekhilef
Keyword(s):  
Objective Function ◽  
Automotive Industry ◽  
Evaluation Criteria ◽  
Optimization Methods ◽  
Side Impact ◽  
Model Parameters ◽  
Side Impacts ◽  
Crash Model ◽  
Crash Modelling ◽  
Identification Tool

Abstract Currently, in automotive industry, identification of vehicle crash model parameters on test measurements is a key point. This paper outlines an approach based on optimization methods for this problem in the context of side impacts. It presents the problematic of crash model parameter identification. The engineer’s evaluation criteria of correlation are translated into an optimization objective function. Several optimization strategies are applied to identification of side impact crash model parameters. The comportment on our problem of these strategies are characterized, and numerical results show that the method of tabou search provides a good solution.

From migration to inversion velocity analysis

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S207-S223 ◽  
Author(s):  
Hervé Chauris ◽  
Emmanuel Cocher
Keyword(s):  
Objective Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
Specific Power ◽  
Model Parameters ◽  
Data Sets ◽  
Velocity Analysis ◽  
Low Velocity ◽  
Image Domain ◽  
New Approach

Migration velocity analysis (MVA) is a technique defined in the image domain to determine the background velocity model controlling the kinematics of wave propagation. In the presence of discontinuous interfaces, the velocity gradient used to iteratively update the velocity model exhibits spurious oscillations. For more stable results, we replace the migration part by an inversion scheme. By definition, migration is the adjoint of the Born modeling operator, whereas inversion is its asymptotic inverse. We have developed new expressions in 1D and 2D cases based on two-way wave-equation operators. The objective function measures the quality of the images obtained by inversion in the extended domain depending on the subsurface offset. In terms of implementation, the new approach is very similar to classic MVA. A 1D analysis found that oscillatory terms around the interface positions can be removed by multiplying the inversion result with the velocity at a specific power before evaluating the objective function. Several 2D synthetic data sets are discussed through the computation of the gradient needed to update the model parameters. Even for discontinuous reflectivity models, the new approach provides results without artificial oscillations. The model update corresponds to a gradient of an existing objective function, which was not the case for the horizontal contraction approach proposed as an alternative to deal with gradient artifacts. It also correctly handles low-velocity anomalies, contrary to the horizontal contraction approach. Inversion velocity analysis offers new perspectives for the applicability of image-domain velocity analysis.

MAZ depth-velocity modelling and imaging with azimuthal anisotropy

2010 ◽  
Vol 50 (2) ◽  
pp. 723
Author(s):  
Sergey Birdus ◽  
Erika Angerer ◽  
Iftikhar Abassi
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Azimuthal Velocity ◽  
Velocity Model ◽  
Azimuthal Anisotropy ◽  
Lessons Learned ◽  
Seismic Survey ◽  
Depth Migration ◽  
Velocity Anisotropy ◽  
Interval Velocity

Processing of multi and wide-azimuth seismic data faces some new challenges, and one of them is depth-velocity modelling and imaging with azimuthal velocity anisotropy. Analysis of multi-azimuth data very often reveals noticeable fluctuations in moveout between different acquisition directions. They can be caused by several factors: real azimuthal interval velocity anisotropy associated with quasi-vertical fractures or present day stress field within the sediments; short-wavelength velocity heterogeneities in the overburden; TTI (or VTI) anisotropy in the overburden; or, random distortions due to noise, multiples, irregularities in the acquisition geometry, etcetera. In order to build a velocity model for multi-azimuth pre-stack depth migration (MAZ PSDM) taking into account observed azimuthal anisotropy, we need to recognise, separate and estimate all the effects listed above during iterative depth-velocity modelling. Analysis of seismic data from a full azimuth 3D seismic land survey revealed the presence of strong spatially variable azimuthal velocity anisotropy that had to be taken into consideration. Using real data examples we discuss major steps in depth processing workflow that took such anisotropy into account: residual moveout estimation in azimuth sectors; separation of different effects causing apparent azimuthal anisotropy (see A–D above); iterative depth-velocity modelling with azimuthal anisotropy; and, subsequent MAZ anisotropic PSDM. The presented workflow solved problems with azimuthal anisotropy in our multi-azimuth dataset. Some of the lessons learned during this MAZ project are relevant to every standard narrow azimuth seismic survey recorded in complex geological settings.

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