Postmap migration of crosswell reflection seismic data

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 135-146 ◽  
Author(s):  
Joongmoo Byun ◽  
James W. Rector III ◽  
Tamas Nemeth
Keyword(s):  
Constant Velocity ◽  
Guided Waves ◽  
Synthetic Data ◽  
Velocity Model ◽  
Lateral Resolution ◽  
Velocity Variation ◽  
Coherent Noise ◽  
Image Domain ◽  
Seismic Reflection Data ◽  
Specific Implementation

Vertical seismic profiling/common depth point (VSP‐CDP) mapping is often preferred to crosswell migration when imaging crosswell seismic reflection data. The principal advantage of VSP‐CDP mapping is that it can be configured as a one‐to‐one operation between data in the acquisition domain and data in the image domain and therefore does not smear coherent noise such as tube waves, guided waves, and converted waves as crosswell migration could. However, unlike crosswell migration, VSP‐CDP mapping cannot collapse diffractions; therefore, the lateral resolution of reflection events suffers. We present a migration algorithm that is applied to the crosswell data after they have been mapped. By performing crosswell migration in two distinct steps—mapping followed by diffraction stacking—noise events can be identified and filtered in the mapped domain without smearing effects commonly associated with conventional crosswell migration operators. Tests on noise‐free synthetic crosswell data indicate that the two‐step migration yields results nearly identical with conventional crosswell migration. Our specific implementation of the two‐step migration algorithm maps the data using an estimate of the interwell velocity field and then performs diffraction stacking using a constant‐velocity assumption. The migrated results are confined to the mapped region to reduce edge effects commonly associated with conventional crosswell migration. Results from synthetic data indicate that the constant‐velocity assumption used for diffraction stacking is remarkably robust, even for models with large vertical velocity variation. It is, however, important that the data are mapped with the correct interwell velocity model. After applying postmap migration to two field data sets mapped by VSP‐CDP mapping, better fault resolution was achieved and the lateral resolution was improved significantly.

Fast acoustic velocity tomography of focusing operators

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R121-R131 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan
Keyword(s):  
Constant Velocity ◽  
Null Space ◽  
Focal Point ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
The Stability ◽  
Starting Model ◽  
Velocity Tomography ◽  
Focus Point

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

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.

Exponential asymptotically bounded velocity model: Part II — Ray tracing

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. T67-T85 ◽  
Author(s):  
Igor Ravve ◽  
Zvi Koren
Keyword(s):  
Ray Tracing ◽  
Constant Velocity ◽  
Critical Angle ◽  
Velocity Model ◽  
Velocity Variation ◽  
Infinite Depth ◽  
Source Point ◽  
Shallow Zone ◽  
Takeoff Angle ◽  
2D And 3D

A ray-tracing procedure is derived for the new exponential asymptotically bounded (EAB) velocity model introduced in Part I of this paper. The model inherits the properties of a medium with linear-velocity variation in depth in the shallow zone and of a medium with constant velocity in the deep zone. Two types of rays departing from the source point on the earth’s surface exist in this model, depending on the takeoff angles. The rays of the first kind are symmetric arcs that return up to the earth’s surface and have a limited maximum depth of propagation. The rays of the second kind propagate down to infinite depth. In the shallow region, they are curved lines, but at large depth they become asymptotically straight. The form of the ray is governed by the takeoff angle at the source point, where a critical angle splits the two kinds of rays. This critical angle depends only on the ratio between the velocity at the source point and the asymptotic velocity of the EAB model. We derive the formulae required to calculate the two kinds of rays and solve the inverse problem of two-point ray tracing. Finally, we construct the 2D- and 3D-isochron surfaces for a finite offset.

Velocity model building for a single-offset 3C VSP data via deformable-layer tomography: a Texas salt dome example

Geophysics ◽  
2021 ◽  
pp. 1-44
Author(s):  
Yukai Wo ◽  
Jingjing Zong ◽  
Hao Hu ◽  
Hua-Wei Zhou ◽  
Robert R. Stewart
Keyword(s):  
Velocity Model ◽  
Salt Dome ◽  
P Wave ◽  
Velocity Variation ◽  
Shear Mode ◽  
P Waves ◽  
Data Set ◽  
Image Domain ◽  
Vsp Data ◽  
Geometric Variation

We have applied multiscale deformable-layer tomography (DLT) to build a laterally varying velocity model, using a single-offset vertical seismic profile (VSP) data set acquired for a salt proximity survey in southern Texas. The purpose of the VSP survey is to delineate the 2D salt flank using the P-wave reflections. Previous study has identified an anhydrate layer as the cap rock of the salt dome. The large impedance contrasts of this anhydrite layer generate strong downgoing P (sediment)-S (anhydrite)-P (salt) waves recorded by downhole geophones. Incidentally, the P-S-P-waves have similar traveltimes as those of the P-wave salt flank reflections, thus contaminating the imaging of the salt flank. Identifying shear-mode contamination requires an accurate velocity model of anhydrite. However, the extremely poor coverage of the single-offset VSP greatly challenges tomographic techniques to determine the lateral velocity variation. We tackle this problem using multiscale DLT, which characterizes the velocity field by a set of deformable layers. We constrain the layer velocities using the check-shot data and invert for the geometric variation. The inverted model indicates that the anhydrite layer has a “thick-thin-thick” lateral variation with offset, and the S-wave in the anhydrite layer helps in imaging the P-S-P-waves along the well track. The estimated anhydrite layer geometry is validated by the kinematic accuracies of P-waves in the data domain and P-S-P-waves in the image domain. Some in-salt dipping structures are determined by multiscale DLT as well. This field data example indicates that multiscale DLT is feasible for estimating velocities using VSP data of the single-offset situation. An accurate velocity model is the key for modeling and adaptive subtraction of the shear-mode contamination related to the salt geometry.

Coupling direct inversion to common-shot image-domain velocity analysis

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R497-R514 ◽  
Author(s):  
Yubing Li ◽  
Hervé Chauris
Keyword(s):  
Objective Function ◽  
Velocity Gradient ◽  
Large Scale ◽  
Synthetic Data ◽  
Essential Element ◽  
Velocity Model ◽  
Data Sets ◽  
Velocity Analysis ◽  
Image Domain ◽  
Direct Inversion

Migration velocity analysis is a technique used to estimate the large-scale structure of the subsurface velocity model controlling the kinematics of wave propagation. For more stable results, recent studies have proposed to replace migration, adjoint of Born modeling, by the direct inverse of the modeling operator in the context of extended subsurface-offset domain. Following the same strategy, we have developed a two-way-wave-equation-based inversion velocity analysis (IVA) approach for the original surface-oriented shot gathers. We use the differential semblance optimization (DSO) objective function to evaluate the quality of inverted images depending on shot positions and to derive the associated gradient, an essential element to update the macromodel. We evaluate the advantages and limitations through applications of 2D synthetic data sets, first on simple models with a single-reflector embedded in various background velocities and then on the Marmousi model. The direct inverse attenuates migration smiles by compensating for geometric spreading and uneven illuminations. We slightly modified the original DSO objective function to remove spurious oscillations around interface positions in the velocity gradient. These oscillations are related to the fact that the locations of events in the image domain depend on the macromodel. We pay attention to the presence of triplicated wavefields. It appears that IVA is robust even if artifacts are observed in the seismic migrated section. The velocity gradient leads to a stable update, especially after a Gaussian smoothing over a wavelength distance. Coupling common-shot direct inversion to velocity analysis offers new possibilities for the extension to 3D in the future.

scholarly journals Identification of image artifacts from internal multiples

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S123-S132 ◽  
Author(s):  
Alison E. Malcolm ◽  
Maarten V. de Hoop ◽  
Henri Calandra
Keyword(s):  
Synthetic Data ◽  
Velocity Model ◽  
Single Scattering ◽  
Image Artifacts ◽  
Coherent Noise ◽  
First Order ◽  
Inverse Scattering Series ◽  
The Common ◽  
Internal Multiples ◽  
Seismic Images

First-order internal multiples are a source of coherent noise in seismic images because they do not satisfy the single-scattering assumption fundamental to most seismic processing. There are a number of techniques to estimate internal multiples in data; in many cases, these algorithms leave some residual multiple energy in the data. This energy produces artifacts in the image, and the location of these artifacts is unknown because the multiples were estimated in the data before the image was formed. To avoid this problem, we propose a method by which the artifacts caused by internal multiples are estimated directly in the image. We use ideas from the generalized Bremmer series and the Lippmann-Schwinger scattering series to create a forward-scattering series to model multiples and an inverse-scattering series to describethe impact these multiples have on the common-image gather and the image. We present an algorithm that implements the third term of this series, responsible for the formation of first-order in-ternal multiples. The algorithm works as part of a wave-equation migration; the multiple estimation is made at each depth using a technique related to one used to estimate surface-related multi-ples. This method requires knowledge of the velocity model to the depth of the shallowest reflector involved in the generation of the multiple of interest. This information allows us to estimate internal multiples without assumptions inherent to other methods. In particular, we account for the formation of caustics. Results of the techniques on synthetic data illustrate the kinematic accuracy of predicted multiples, and results on field data illustrate the potential of estimating artifacts caused by internal multiples in the image rather than in the data.

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.

Marchenko multiple elimination and full wavefield migration in a resonant pinch-out model

Geophysics ◽  
2021 ◽  
pp. 1-59
Author(s):  
Evert Slob ◽  
Lele Zhang ◽  
Eric Verschuur
Keyword(s):  
Constant Velocity ◽  
Local Minimum ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Data Sampling ◽  
Multiple Reflections ◽  
Linear Inversion ◽  
Acoustic Reflection ◽  
Reflection Data ◽  
Multiple Elimination

Marchenko multiple elimination schemes are able to attenuate all internal multiple reflections in acoustic reflection data. These can be implemented with and without compensation for two-way transmission effects in the resulting primary reflection dataset. The methods are fully automated and run without human intervention, but require the data to be properly sampled and pre-processed. Even when several primary reflections are invisible in the data because they are masked by overlapping primaries, such as in the resonant wedge model, all missing primary reflections are restored and recovered with the proper amplitudes. Investigating the amplitudes in the primary reflections after multiple elimination with and without compensation for transmission effects shows that transmission effects are properly accounted for in a constant velocity model. When the layer thickness is one quarter of the wavelength at the dominant frequency of the source wavelet, the methods cease to work properly. Full wavefield migration relies on a velocity model and runs a non-linear inversion to obtain a reflectivity model which results in the migration image. The primary reflections that are masked by interference with multiples in the resonant wedge model, are not recovered. In this case, minimizing the data misfit function leads to the incorrect reflector model even though the data fit is optimal. This method has much lower demands on data sampling than the multiple elimination schemes, but is prone to get stuck in a local minimum even when the correct velocity model is available. A hybrid method that exploits the strengths of each of these methods could be worth investigating.

scholarly journals Rapid estimation of earthquake locations using waveform traveltimes

2019 ◽  
Vol 217 (3) ◽  
pp. 1727-1741 ◽  
Author(s):  
D W Vasco ◽  
Seiji Nakagawa ◽  
Petr Petrov ◽  
Greg Newman
Keyword(s):  
Standard Error ◽  
Random Noise ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
Source Location ◽  
Model Errors ◽  
Average Deviation ◽  
Origin Time ◽  
Data Set

SUMMARY We introduce a new approach for locating earthquakes using arrival times derived from waveforms. The most costly computational step of the algorithm scales as the number of stations in the active seismographic network. In this approach, a variation on existing grid search methods, a series of full waveform simulations are conducted for all receiver locations, with sources positioned successively at each station. The traveltime field over the region of interest is calculated by applying a phase picking algorithm to the numerical wavefields produced from each simulation. An event is located by subtracting the stored traveltime field from the arrival time at each station. This provides a shifted and time-reversed traveltime field for each station. The shifted and time-reversed fields all approach the origin time of the event at the source location. The mean or median value at the source location thus approximates the event origin time. Measures of dispersion about this mean or median time at each grid point, such as the sample standard error and the average deviation, are minimized at the correct source position. Uncertainty in the event position is provided by the contours of standard error defined over the grid. An application of this technique to a synthetic data set indicates that the approach provides stable locations even when the traveltimes are contaminated by additive random noise containing a significant number of outliers and velocity model errors. It is found that the waveform-based method out-performs one based upon the eikonal equation for a velocity model with rapid spatial variations in properties due to layering. A comparison with conventional location algorithms in both a laboratory and field setting demonstrates that the technique performs at least as well as existing techniques.

scholarly journals Study on the limitations of travel-time inversion applied to sub-basalt imaging

Solid Earth ◽  
2013 ◽  
Vol 4 (2) ◽  
pp. 543-554 ◽  
Author(s):  
I. Flecha ◽  
R. Carbonell ◽  
R. W. Hobbs
Keyword(s):  
Oil Industry ◽  
Velocity Model ◽  
Time Inversion ◽  
Wide Angle ◽  
Seismic Reflection Data ◽  
Additional Information ◽  
Velocity Models ◽  
Reflection Data ◽  
Travel Time Inversion ◽  
Tomographic Inversions

Abstract. The difficulties of seismic imaging beneath high velocity structures are widely recognised. In this setting, theoretical analysis of synthetic wide-angle seismic reflection data indicates that velocity models are not well constrained. A two-dimensional velocity model was built to simulate a simplified structural geometry given by a basaltic wedge placed within a sedimentary sequence. This model reproduces the geological setting in areas of special interest for the oil industry as the Faroe-Shetland Basin. A wide-angle synthetic dataset was calculated on this model using an elastic finite difference scheme. This dataset provided travel times for tomographic inversions. Results show that the original model can not be completely resolved without considering additional information. The resolution of nonlinear inversions lacks a functional mathematical relationship, therefore, statistical approaches are required. Stochastic tests based on Metropolis techniques support the need of additional information to properly resolve sub-basalt structures.

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