Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 954-969 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Grid Point ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Migration Process ◽  
Inversion Process ◽  
Prestack Migration ◽  
Grid Points ◽  
Updating Procedure ◽  
Amplitude Versus ◽  
Focus Point

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migration process of synthesis, updating, and stacking is repeated for all subsurface grid points of interest, leading to the prestack migration result in one‐way image time together with a distribution of updated focusing operators. In a postprocessing step, all operator traveltime information can be used to derive a velocity model for the time‐to‐depth conversion process. Hence, in the presented “CFP technology” the author proposes to estimate the velocity model from the correct focusing operators by a global inversion process after the migration process has been carried out (“beyond depth migration”). For each subsurface grid point, the amplitudes along the pairs of updated traveltime curves provide amplitude‐versus‐offset (AVO) information. In addition, by introducing the grid‐point gather with the aid of an extension of the second focusing process, the author shows that this gather leads to the extraction of pre‐ and postcritical amplitude‐versus‐ray parameter (AVP) information at each grid point. Finally, just as a velocity model can be estimated from all grid‐point‐oriented traveltime information, a lithology model can be estimated from all grid‐point—oriented amplitude information by a postimaging global inversion process.

Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 937-953 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Error Analysis ◽  
Evaluation Method ◽  
Structural Information ◽  
Grid Point ◽  
Velocity Model ◽  
Migration Process ◽  
Prestack Migration ◽  
Post Evaluation ◽  
Focused Beams ◽  
Focus Point

In this paper, the author proposes to extend the synthesis of areal sources (controlled emission) to the synthesis of areal detectors (controlled detection) such that the concept of numerical focusing can be formulated as a special version of target‐oriented synthesis. As a consequence, the insight in the complex prestack migration process can be improved significantly by making use of the concepts “focusing in emission” and “focusing in detection.” Focusing in emission transforms shot records into so‐called common focus‐point (CFP) gathers. Focusing in detection transforms CFP gathers into the prestack migration result. If structural information is sought, the focus point in emission is chosen equal to the focus point in detection: confocal version of CFP migration. If rock and pore information is required as well, the focus point in emission is chosen different from the focus point in detection: bifocal version of CFP migration. Errors in the underlying macro velocity model can be better analysed than before by using CFP gathers as an intermediate migration output. The error analysis involves a comparison between each CFP gather and its related focusing operator. The quality (amplitude accuracy, noise content, resolution) of prestack migration results can be evaluated effectively at each subsurface grid point by analysing the two focused beams involved (pre‐evaluation) and by analyzing the so‐called grid‐point gather (post‐evaluation). The proposed pre‐evaluation method may lead to an improved way of coping with “acquisition footprints” of relatively sparse source and receiver coverage.

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.

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.

Combining full wavefield migration and full waveform inversion, a glance into the future of seismic imaging

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. S43-S50 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Multiple Scattering ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Full Waveform Inversion ◽  
Inversion Process ◽  
Depth Level ◽  
Seismic Migration ◽  
Full Waveform ◽  
Angle Dependent Reflectivity

The next generation seismic migration and inversion technology considers multiple scattering as vital information, allowing the industry to derive significantly better reservoir models — with more detail and less uncertainty—while requiring a minimum of user intervention. Three new insights have been uncovered with respect to this fundamental transition. Unblended or blended multiple scattering can be included in the seismic migration process, and it has been proposed to formulate the imaging principle as a minimization problem. The resulting process yields angle-dependent reflectivity and is referred to as recursive full wavefield migration (WFM). The full waveform inversion process for velocity estimation can be extended to a recursive, optionally blended, anisotropic multiple-scattering algorithm. The resulting process yields angle-dependent velocity and is referred to as recursive full waveform inversion (WFI). The mathematical equations of WFM and WFI have an identical structure, but the physical meaning behind the expressions is fundamentally different. In WFM the reflection process is central, and the aim is to estimate reflection operators of the subsurface, using the up- and downgoing incident wavefields (including the codas) in each gridpoint. In WFI, however, the propagation process is central and the aim is to estimate velocity operators of the subsurface, using the total incident wavefield (sum of up- and downgoing) in each gridpoint. Angle-dependent reflectivity in WFM corresponds with angle-dependent velocity (anisotropy) in WFI. The algorithms of WFM and WFI could be joined into one automated joint migration-inversion process. In the resulting hybrid algorithm, being referred to as recursive joint migration inversion (JMI), the elaborate volume integral solution was replaced by an efficient alternative: WFM and WFI are alternately applied at each depth level, where WFM extrapolates the incident wavefields and WFI updates the velocities without any user interaction. The output of the JMI process offers an integrated picture of the subsurface in terms of angle-dependent reflectivity as well as anisotropic velocity. This two-fold output, reflectivity image and velocity model, offers new opportunities to extract accurate rock and pore properties at a fine reservoir scale.

Traveltime computation in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 272-281 ◽  
Author(s):  
Eduardo L. Faria ◽  
Paul L. Stoffa
Keyword(s):  
Heterogeneous Media ◽  
Grid Point ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Prestack Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
First Arrival ◽  
Grid Points ◽  
Arbitrary Velocity

An approach for calculating first‐arrival traveltimes in a transversely isotropic medium is developed and has the advantage of avoiding shadow zones while still being computationally fast. Also, it works with an arbitrary velocity grid that may have discontinuities. The method is based on Fermat’s principle. The traveltime for each point in the grid is calculated several times using previously calculated traveltimes at surrounding grid points until the minimum time is found. Different ranges of propagation angle are covered in each traveltime calculation such that at the end of the process all propagation angles are covered. This guarantees that the first‐arrival traveltime for a specific grid point is correctly calculated. The resulting algorithm is fully vectorizable. The method is robust and can accurately determine first‐arrival traveltimes in heterogeneous media. Traveltimes are compared to finite‐difference modeling of transversely isotropic media and are found to be in excellent agreement. An application to prestack migration is used to illustrate the usefulness of the method.

Tomographic velocity estimation with plane‐wave synthesis

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1825-1838 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Plane Wave ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Process Measures ◽  
Prestack Migration ◽  
Velocity Models ◽  
Wave Synthesis ◽  
Oriented Plane

In areas with structurally complex geology, tomographic velocity analysis is often required to estimate velocities. In this paper I describe an algorithm for tomographic velocity estimation that uses plane‐wave synthesis imaging as a prestack migration. The classical iterative two‐step process (measures the traveltime errors with the current velocity model and then update the velocity model) is performed as follows. The events are picked in the image space after prestack migration with surface‐oriented plane‐wave synthesis imaging. the traveltime deviations are measured through residual‐moveout (RMO) velocity analysis in common‐surface‐location (CSL) gathers obtained by reflector‐oriented plane‐wave synthesis imaging, and the velocity update is calculated by inverting the traveltime deviations through a conjugate gradient. The results from synthetic data indicate that the tomographic method successfully estimates interval‐velocity models that lead to depth‐migrated images with no residual moveout.

scholarly journals Velocity Analysis Using Separated Diffractions for Lunar Penetrating Radar Obtained by Yutu-2 Rover

2021 ◽  
Vol 13 (7) ◽  
pp. 1387
Author(s):  
Chao Li ◽  
Jinhai Zhang
Keyword(s):  
Dielectric Permittivity ◽  
Lunar Regolith ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Quality Data ◽  
High Quality Data ◽  
Shallow Subsurface ◽  
Subsurface Structures ◽  
Ground Penetrating ◽  
Permittivity Model

The high-frequency channel of lunar penetrating radar (LPR) onboard Yutu-2 rover successfully collected high quality data on the far side of the Moon, which provide a chance for us to detect the shallow subsurface structures and thickness of lunar regolith. However, traditional methods cannot obtain reliable dielectric permittivity model, especially in the presence of high mix between diffractions and reflections, which is essential for understanding and interpreting the composition of lunar subsurface materials. In this paper, we introduce an effective method to construct a reliable velocity model by separating diffractions from reflections and perform focusing analysis using separated diffractions. We first used the plane-wave destruction method to extract weak-energy diffractions interfered by strong reflections, and the LPR data are separated into two parts: diffractions and reflections. Then, we construct a macro-velocity model of lunar subsurface by focusing analysis on separated diffractions. Both the synthetic ground penetrating radar (GPR) and LPR data shows that the migration results of separated reflections have much clearer subsurface structures, compared with the migration results of un-separated data. Our results produce accurate velocity estimation, which is vital for high-precision migration; additionally, the accurate velocity estimation directly provides solid constraints on the dielectric permittivity at different depth.

scholarly journals Image-based textile decoding

2020 ◽  
pp. 1-14
Author(s):  
Siqiang Chen ◽  
Masahiro Toyoura ◽  
Takamasa Terada ◽  
Xiaoyang Mao ◽  
Gang Xu
Keyword(s):  
Deep Learning ◽  
Grid Point ◽  
Intermediate Representation ◽  
Training Set ◽  
Binary Matrix ◽  
The Matrix ◽  
Correct Pattern ◽  
Grid Points ◽  
Textile Fabric ◽  
Direct Correspondence

A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which the warps and wefts cross on a grid is defined in a binary matrix. The binary matrix can define which warp and weft is on top at each grid point of the Jacquard fabric. The process can be regarded as encoding from pattern to textile. In this work, we propose a decoding method that generates a binary pattern from a textile fabric that has been already woven. We could not use a deep neural network to learn the process based solely on the training set of patterns and observed fabric images. The crossing points in the observed image were not completely located on the grid points, so it was difficult to take a direct correspondence between the fabric images and the pattern represented by the matrix in the framework of deep learning. Therefore, we propose a method that can apply the framework of deep learning viau the intermediate representation of patterns and images. We show how to convert a pattern into an intermediate representation and how to reconvert the output into a pattern and confirm its effectiveness. In this experiment, we confirmed that 93% of correct pattern was obtained by decoding the pattern from the actual fabric images and weaving them again.

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.

scholarly journals Data-driven wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA107-WA115 ◽  
Author(s):  
Filippo Broggini ◽  
Roel Snieder ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Single Scattering ◽  
Data Driven ◽  
Multiple Reflections ◽  
Prestack Migration ◽  
Reflection Data ◽  
Internal Multiples

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e., waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image them as ghost reflectors. These artifacts can mislead interpreters in locating potential hydrocarbon reservoirs. Recently, we introduced a new approach for retrieving the Green’s function recorded at the acquisition surface due to a virtual source located at depth. We refer to this approach as data-driven wavefield focusing. Additionally, after applying source-receiver reciprocity, this approach allowed us to decompose the Green’s function at a virtual receiver at depth in its downgoing and upgoing components. These wavefields were then used to create a ghost-free image of the medium with either crosscorrelation or multidimensional deconvolution, presenting an advantage over standard prestack migration. We tested the robustness of our approach when an erroneous background velocity model is used to estimate the first-arriving waves, which are a required input for the data-driven wavefield focusing process. We tested the new method with a numerical example based on a modification of the Amoco model.

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