Elastic modeling and wave equation finite difference prestack depth migration in a complex offshore California geologic setting

2001 ◽  
Author(s):  
John Weigant ◽  
Gary Hoover ◽  
Jaime A. Stein ◽  
Bradley J. Clark
2021 ◽  
Author(s):  
Olaf Hellwig ◽  
Stefan Buske

<p>The polymetallic, hydrothermal deposit of the Freiberg mining district in the southeastern part of Germany is characterised by ore veins that are framed by Proterozoic orthogneiss. The ore veins consist mainly of quarz, sulfides, carbonates, barite and flourite, which are associated with silver, lead and tin. Today the Freiberg University of Mining and Technology is operating the shafts Reiche Zeche and Alte Elisabeth for research and teaching purposes with altogether 14 km of accessible underground galleries. The mine together with the most prominent geological structures of the central mining district are included in a 3D digital model, which is used in this study to study seismic acquisition geometries that can help to image the shallow as well as the deeper parts of the ore-bearing veins. These veins with dip angles between 40° and 85° are represented by triangulated surfaces in the digital geological model. In order to import these surfaces into our seismic finite-difference simulation code, they have to be converted into bodies with a certain thickness and specific elastic properties in a first step. In a second step, these bodies with their properties have to be discretized on a hexahedral finite-difference grid with dimensions of 1000 m by 1000 m in the horizontal direction and 500 m in the vertical direction. Sources and receiver lines are placed on the surface along roads near the mine. A Ricker wavelet with a central frequency of 50 Hz is used as the source signature at all excitation points. Beside the surface receivers, additional receivers are situated in accessible galleries of the mine at three different depth levels of 100 m, 150 m and 220 m below the surface. Since previous mining activities followed primarily the ore veins, there are only few pilot-headings that cut through longer gneiss sections. Only these positions surrounded by gneiss are suitable for imaging the ore veins. Based on this geometry, a synthetic seismic data set is generated with our explicit finite-difference time-stepping scheme, which solves the acoustic wave equation with second order accurate finite-difference operators in space and time. The scheme is parallelised using a decomposition of the spatial finite-difference grid into subdomains and Message Passing Interface for the exchange of the wavefields between neighbouring subdomains. The resulting synthetic seismic shot gathers are used as input for Kirchhoff prestack depth migration as well as Fresnel volume migration in order to image the ore veins. Only a top mute to remove the direct waves and a time-dependent gain to correct the amplitude decay due to the geometrical spreading are applied to the data before the migration. The combination of surface and in-mine acquisition helps to improve the image of the deeper parts of the dipping ore veins. Considering the limitations for placing receivers in the mine, Fresnel volume migration as a focusing version of Kirchhoff prestack depth migration helps to avoid migration artefacts caused by this sparse and limited acquisition geometry.</p>


Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. S67-S74 ◽  
Author(s):  
Jun Cao ◽  
Ru-Shan Wu

Wave-equation-based acquisition aperture correction in the local angle domain can improve image amplitude significantly in prestack depth migration. However, its original implementation is inefficient because the wavefield decomposition uses the local slant stack (LSS), which is demanding computationally. We propose a faster method to obtain the image and amplitude correction factor in the local angle domain using beamlet decomposition in the local wavenumber domain. For a given frequency, the image matrix in the local wavenumber domain for all shots can be calculated efficiently. We then transform the shot-summed image matrix from the local wavenumber domain to the local angle domain (LAD). The LAD amplitude correction factor can be obtained with a similar strategy. Having a calculated image and correction factor, one can apply similar acquisition aperture corrections to the original LSS-based method. For the new implementation, we compare the accuracy and efficiency of two beamlet decompositions: Gabor-Daubechies frame (GDF) and local exponential frame (LEF). With both decompositions, our method produces results similar to the original LSS-based method. However, our method can be more than twice as fast as LSS and cost only twice the computation time of traditional one-way wave-equation-based migrations. The results from GDF decomposition are superior to those from LEF decomposition in terms of artifacts, although GDF requires a little more computing time.


2003 ◽  
Vol 46 (5) ◽  
pp. 966-977 ◽  
Author(s):  
Jiubing CHENG ◽  
Huazhong WANG ◽  
Zaitian MA

2001 ◽  
Author(s):  
Phil Kitchenside ◽  
Uwe Albertin ◽  
Wenfong Chang ◽  
Clement Kostov ◽  
Alexandre Kleitz ◽  
...  

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 246-255 ◽  
Author(s):  
Oong K. Youn ◽  
Hua‐wei Zhou

Depth imaging with multiples is a prestack depth migration method that uses multiples as the signal for more accurate boundary mapping and amplitude recovery. The idea is partially related to model‐based multiple‐suppression techniques and reverse‐time depth migration. Conventional reverse‐time migration uses the two‐way wave equation for the backward wave propagation of recorded seismic traces and ray tracing or the eikonal equation for the forward traveltime computation (the excitation‐time imaging principle). Consequently, reverse‐time migration differs little from most other one‐way wave equation or ray‐tracing migration methods which expect only primary reflection events. Because it is almost impossible to attenuate multiples without degrading primaries, there has been a compelling need to devise a tool to use multiples constructively in data processing rather than attempting to destroy them. Furthermore, multiples and other nonreflecting wave types can enhance boundary imaging and amplitude recovery if a full two‐way wave equation is used for migration. The new approach solves the two‐way wave equation for both forward and backward directions of wave propagation using a finite‐difference technique. Thus, it handles all types of acoustic waves such as reflection (primary and multiples), refraction, diffraction, transmission, and any combination of these waves. During the imaging process, all these different types of wavefields collapse at the boundaries where they are generated or altered. The process goes through four main steps. First, a source function (wavelet) marches forward using the full two‐way scalar wave equation from a source location toward all directions. Second, the recorded traces in a shot gather march backward using the full two‐way scalar wave equation from all receiver points in the gather toward all directions. Third, the two forward‐ and backward‐propagated wavefields are correlated and summed for all time indices. And fourth, a Laplacian image reconstruction operator is applied to the correlated image frame. This technique can be applied to all types of seismic data: surface seismic, vertical seismic profile (VSP), crosswell seismic, vertical cable seismic, ocean‐bottom cable (OBC) seismic, etc. Because it migrates all wave types, the input data require no or minimal preprocessing (demultiple should not be done, but near‐surface or acquisition‐related problems might need to be corrected). Hence, it is only a one‐step process from the raw field gathers to a final depth image. External noise in the raw data will not correlate with the forward wavefield except for some coincidental matching; therefore, it is usually unnecessary to do signal enhancement processing before the depth imaging with multiples. The input velocity model could be acquired from various methods such as iterative focusing analysis or tomography, as in other prestack depth migration methods. The new method has been applied to data sets from a simple multiple‐generating model, the Marmousi model, and a real offset VSP. The results show accurate imaging of primaries and multiples with overall significant improvements over conventionally imaged sections.


2005 ◽  
Author(s):  
Jiaxiang Ren ◽  
Clive Gerrard ◽  
James McClean ◽  
Mikhail Orlovich

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1412-1422
Author(s):  
Alvin K. Benson

An explicit, unconditionally stable, finite‐difference depth migration and modeling algorithm is formulated and implemented for the fifteen‐degree wave equation in poststack, directional (rotational), and prestack modes for inhomogeneous media. It is about two times faster than implicit schemes. The simplicity, unconditional stability, and speed of the algorithm are appealing for numerous applications, especially prestack and three‐dimensional data sets.


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