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.

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.

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.

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.

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.

Full-waveform inversion for full-wavefield imaging: Decades in the making

2021 ◽  
Vol 40 (5) ◽  
pp. 324-334
Author(s):  
Rongxin Huang ◽  
Zhigang Zhang ◽  
Zedong Wu ◽  
Zhiyuan Wei ◽  
Jiawei Mei ◽  
...  
Keyword(s):  
Model Building ◽  
Seismic Imaging ◽  
Structural Information ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Types ◽  
Velocity Models ◽  
Full Waveform

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

Kinematics of common-image gathers — Part 1: Theory

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S437-S447 ◽  
Author(s):  
Jean-Philippe Montel ◽  
Gilles Lambaré
Keyword(s):  
Velocity Model ◽  
General Assumption ◽  
Azimuth Angle ◽  
Velocity Analysis ◽  
Migration Process ◽  
Kinematic Behavior ◽  
Migration Velocity Analysis ◽  
Model Update ◽  
The Common

Common-image gathers are a useful output of the migration process. Their kinematic behavior (i.e., the way they curve up or down) is an indicator of the quality of the velocity model used for migration. Traditionally, when used for migration velocity analysis, we pick structural dips in the common attribute panels (offset, angle, etc.) and residual moveout (RMO) in the gathers. The measured RMO will then tell us how much we need to update the velocity model to improve the gather’s flatness. Understanding the kinematics of the picked events is the key to an accurate model update. This point has been widely underestimated in many cases. For example, when dealing with angle gathers, there is a general assumption that the associated tomographic rays are fully defined by the picked structural dips and the gather opening and azimuth angle, and that if the velocity model is correctly updated down to a given horizon, it is not necessary to shoot the tomographic rays upward through this horizon. We find through an original theoretical analysis that both of these assumptions have to be modified when the gathers exhibit RMO. Using a kinematic analysis, we determine that knowledge of the RMO slopes is necessary to compute the tomographic rays.

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