Constrained Dix inversion

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. R113-R130 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
Velocity Field ◽  
Velocity Model ◽  
Instantaneous Velocity ◽  
Surface Velocity ◽  
Inversion Method ◽  
Fine Grid ◽  
Lateral Node ◽  
Velocity Models ◽  
Time Migration ◽  
Noisy Input

We propose a stable inversion method to create geologically constrained instantaneous velocities from a set of sparse, irregularly picked stacking- or rms-velocity functions in vertical time. The method is primarily designed for building initial velocity models for curved-ray time migration and initial macromodels for depth migration and tomography. It is mainly applicable in regions containing compacted sediments, in which the velocity gradually increases with depth and can be laterally varying. Inversion is done in four stages: establishing a global initial background-velocity trend, applying an explicit unconstrained inversion, performing a constrained least-squares inversion, and finally, fine gridding. The method can be applied to create a new velocity field (create mode) or to update an existing one (update mode). In the create mode, initially, the velocity trend is assumed an exponential, asymptotically bounded function, defined locally by three parameters at each lateral node and calculated from a reference datum surface. Velocity picks related to nonsediment rocks, such as salt flanks or basalt boundaries, require different trend functions and therefore are treated differently. In the update mode, the velocity trend is a background-velocity field, normally used for time or depth imaging. The unconstrained inversion results in a piecewise-constant, residual instantaneous velocity with respect to the velocity trend and is mainly used for regularizing the input data. The constrained inversion is performed individually for each rms-velocity function in vertical time, and the lateral and vertical continuities are controlled by the global velocity-trend function. A special damping technique suppresses vertical oscillations of the results. Finally, smoothing and gridding (interpolation) are done for the resulting instantaneous velocity to generate a regular, fine grid in space and time. This method leads to a stable and geologically plausible velocity model, even in cases of noisy input rms-velocity or residual rms-velocity data.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

2021 ◽  
Vol 225 (2) ◽  
pp. 1020-1031
Author(s):  
Huachen Yang ◽  
Jianzhong Zhang ◽  
Kai Ren ◽  
Changbo Wang
Keyword(s):  
Turning Points ◽  
Analytical Formula ◽  
Velocity Model ◽  
Western China ◽  
Inversion Method ◽  
Mountain Area ◽  
Traveltime Inversion ◽  
Static Correction ◽  
Velocity Models ◽  
First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

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.

Nonlinear velocity inversion by a two‐step Monte Carlo method.

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Side Jin ◽  
Raul Madariaga
Keyword(s):  
Monte Carlo ◽  
Velocity Model ◽  
Small Scale ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Ray Theory ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Reference Velocity

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.

Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

Azimuthally dependent anisotropic velocity model update

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. C27-C53 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
High Resolution ◽  
Velocity Field ◽  
Phase Angle ◽  
Velocity Model ◽  
Background Model ◽  
Physical Parameters ◽  
Model Parameters ◽  
Effective Parameters ◽  
Velocity Models

We consider a case where a 3D depth migration has been performed in the local angle domain (LAD) using rich-azimuth seismic data (e.g., conventional land surveys). The subsurface geologic model is characterized by considerable azimuthally anisotropic velocity variations. The background velocity field used for the migration can consist of azimuthally independent, e.g., vertical transverse isotropy, and/or azimuthally dependent (e.g., orthorhombic), velocity layers. The resulting 3D full-azimuth reflection angle gathers generated by the LAD migration represent in situ high-resolution amplitude preserved reflectivities associated with opening angles between incident and reflected slowness vectors in the specular directions. Residual moveouts (RMOs) automatically picked on these 3D image gathers along major horizons can indicate considerable residual periodic azimuthal variations. This situation is typical in depth imaging applied to unconventional shale plays, where the background velocity model doesn’t yet account for the aligned stress/fracture systems that exist in some of the target layers. We use the azimuthally dependent, phase-angle RMOs to update the interval parameters of the background model, accounting for the azimuthal anisotropy effect. Until now, this problem was mainly treated in the unmigrated time-offset domain, which is limited in describing the actual in situ changes of the velocity field with azimuths. The subsurface full-azimuth phase-angle domain RMOs provide better physical parameters to analyze the in situ azimuthal variations of the anisotropic media. Our method is grounded in a newly derived generalized Dix-based theory, where locally the background and updated models are assumed to be 1D anisotropic velocity models. At each lateral location, the orthorhombic axis [Formula: see text] points in the vertical direction across all layers, but the azimuthal orientations of the orthorhombic layers change from layer to layer. An effective model for such a layered structure (background or updated) is represented by a single layer with a vertical time identical to that of the whole package, effective fast and slow normal moveout (NMO) velocities, and an effective azimuthal orientation of the slow NMO velocity. Our approach begins with computation of these effective parameters for the background model and conversion of the high-resolution RMOs into a dense set of updated, effective, azimuthally dependent NMO velocities, which are then converted into three effective parameters of the updated model. Next, we apply a generalized Dix-based inversion approach to estimate the local NMO parameters for each updated layer. Finally, we convert the local parameters into interval azimuthally varying anisotropic model parameters (e.g., TTI, orthorhombic, or tilted orthorhombic) within each layer. The 1D Dix-based approach presented in this work should not be considered an alternative to more accurate 3D global inversion approaches, such as global anisotropic tomography. However, the proposed method can be effectively used for moderately laterally varying models, and some of the principal physical rules derived for the 1D model can be further used to improve the formulation and geophysical constraints applied to 3D global inversion methods.

scholarly journals Optimal coding of blended seismic sources for 2D full waveform inversion in time

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Katherine Flórez ◽  
Sergio Alberto Abreo Carrillo ◽  
Ana Beatriz Ramírez Silva
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Computational Time ◽  
Inversion Method ◽  
Single Shot ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Seismic Image ◽  
Blended Data

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired. Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration. In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

Velocity model estimation with data‐derived wavefront attributes

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 265-274 ◽  
Author(s):  
Eric Duveneck
Keyword(s):  
Velocity Model ◽  
Inversion Method ◽  
Data Set ◽  
Velocity Models ◽  
Common Reflection Surface ◽  
Data Points ◽  
Inversion Procedure ◽  
Optimum Model ◽  
Zero Offset ◽  
Kinematic Information

Kinematic information for constructing velocity models can be extracted in a robust way from seismic prestack data with the common‐reflection‐surface (CRS) stack. This data‐driven process results, in addition to a simulated zero‐offset section, in a number of wavefront attributes—wavefront curvatures and normal ray emergence angles—associated with each simulated zero‐offset sample. A tomographic inversion method is presented that uses this kinematic information to determine smooth, laterally heterogeneous, isotropic subsurface velocity models for depth imaging. The input for the inversion consists of wavefront attributes picked at a number of locations in the simulated zero‐offset section. The smooth velocity model is described by B‐splines. An optimum model is found iteratively by minimizing the misfit between the picked data and the corresponding modeled values. The required forward‐modeled quantities are obtained during each iteration by dynamic ray tracing along normal rays pertaining to the input data points. Fréchet derivatives for the tomographic matrix are calculated by ray perturbation theory. The inversion procedure is demonstrated on a 2D synthetic prestack data set.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

Seismic modeling and expression of common fold-thrust structures

2020 ◽  
Vol 8 (1) ◽  
pp. T55-T65
Author(s):  
Jianjun Li ◽  
Shankar Mitra
Keyword(s):  
Velocity Model ◽  
Fault Geometry ◽  
Seismic Modeling ◽  
Fault Propagation ◽  
Lateral Velocity ◽  
Slip Ratio ◽  
Velocity Models ◽  
Time Migration ◽  
The Common

We have conducted seismic modeling of common fold-thrust structures to understand the common geologic parameters influencing seismic data and to understand the common pitfalls associated with interpreting prestack time migration (PSTM) and prestack depth migration (PSDM) data. Mode 1 fault-bend folds are generally well-imaged in PSTM data, provided the correct migration velocities are used for the dipping back and front limbs. Seismic pull-ups of the footwall related to lateral velocity variations can result in problems in interpreting the fault geometry and the subthrust area underlying the crest. Fault-tip fault-propagation folds also show significant footwall pull-ups and show poor to no imaging of the steep front limbs. The geometry of trishear fault-propagation folds is dependent on the maximum slip on the fault (S) and the fault propagation to slip ratio (P/S ratio). We found that the slip has a strong influence on the dip of the front limb and therefore the quality of imaging whereas the P/S ratio, which controls the degree of folding versus thrust faulting, has only a secondary effect. For the front limb, only the area near the synclinal axial plan is well-imaged, so that the fault geometry and extent of propagation are typically difficult to interpret. The front limb dips are also sensitive to the accuracy of the rms velocity model used for migration. Lower velocities result in steeper dipping reflectors, whereas higher velocities result in shallower dips. In general, PSDM provides better imaging of the structures; however, the accuracy and quality of the image are dependent on the velocity models and interpretation derived from the PSTM data.

Integrating high‐resolution refraction data into near‐surface seismic reflection data processing and interpretation

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1339-1347 ◽  
Author(s):  
Kate C. Miller ◽  
Steven H. Harder ◽  
Donald C. Adams ◽  
Terry O’Donnell
Keyword(s):  
Seismic Reflection ◽  
Velocity Model ◽  
Surface Velocity ◽  
Seismic Profiles ◽  
Seismic Reflection Data ◽  
Near Surface ◽  
Interval Velocity ◽  
Velocity Models ◽  
Reflection Data ◽  
Seismic Reflection Profiles

Shallow seismic reflection surveys commonly suffer from poor data quality in the upper 100 to 150 ms of the stacked seismic record because of shot‐associated noise, surface waves, and direct arrivals that obscure the reflected energy. Nevertheless, insight into lateral changes in shallow structure and stratigraphy can still be obtained from these data by using first‐arrival picks in a refraction analysis to derive a near‐surface velocity model. We have used turning‐ray tomography to model near‐surface velocities from seismic reflection profiles recorded in the Hueco Bolson of West Texas and southern New Mexico. The results of this analysis are interval‐velocity models for the upper 150 to 300 m of the seismic profiles which delineate geologic features that were not interpretable from the stacked records alone. In addition, the interval‐velocity models lead to improved time‐to‐depth conversion; when converted to stacking velocities, they may provide a better estimate of stacking velocities at early traveltimes than other methods.

Sign in / Sign up

Export Citation Format

Share Document