Multicomponent Kirchhoff migration

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 861-873 ◽  
Author(s):  
Ketil Hokstad

This paper presents a method for elastic and viscoelastic imaging of multicomponent seismic data. The method is based on Claerbout’s survey‐sinking concept and the (visco)elastic Kirchhoff integral for the displacement field. Assuming a multishot and multireceiver experiment, the migration process is formulated as a wavefield reconstruction problem, using the (visco)elastic Kirchhoff integral twice. First, the receiver coordinates are downward continued. Second, the source coordinates are downward continued. The multicomponent seismic data are treated as a vector wavefield in which the data measurements may be displacement velocity or traction (pressure). The theoretical formulation is based on the viscoelastic Hooke’s law and Newton’s equation of motion as the physical model for seismic wave propagation. It is valid for linear viscoelastic media with any anisotropic symmetry. When the lowest‐order ray approximation is introduced, the migration equation takes a form similar to conventional Kirchhoff migration. To obtain the imaging equations, the downward‐continued wavefield is related to the ray‐Born approximation. Numerical results are shown from elastic imaging of synthetic and real marine walkaway vertical seismic profiling (VSP) data.

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N29-N40
Author(s):  
Modeste Irakarama ◽  
Paul Cupillard ◽  
Guillaume Caumon ◽  
Paul Sava ◽  
Jonathan Edwards

Structural interpretation of seismic images can be highly subjective, especially in complex geologic settings. A single seismic image will often support multiple geologically valid interpretations. However, it is usually difficult to determine which of those interpretations are more likely than others. We have referred to this problem as structural model appraisal. We have developed the use of misfit functions to rank and appraise multiple interpretations of a given seismic image. Given a set of possible interpretations, we compute synthetic data for each structural interpretation, and then we compare these synthetic data against observed seismic data; this allows us to assign a data-misfit value to each structural interpretation. Our aim is to find data-misfit functions that enable a ranking of interpretations. To do so, we formalize the problem of appraising structural interpretations using seismic data and we derive a set of conditions to be satisfied by the data-misfit function for a successful appraisal. We investigate vertical seismic profiling (VSP) and surface seismic configurations. An application of the proposed method to a realistic synthetic model shows promising results for appraising structural interpretations using VSP data, provided that the target region is well-illuminated. However, we find appraising structural interpretations using surface seismic data to be more challenging, mainly due to the difficulty of computing phase-shift data misfits.


1986 ◽  
Vol 26 (1) ◽  
pp. 226
Author(s):  
R.L. Ireson

Vertical Seismic Profiling (VSP) techniques have been developed which have found application in the development and production of hydrocarbons as well as in exploration.A VSP is initiated by outlining the objectives of the survey and, using a model of the geology in the vicinity of the borehole, applying inversion techniques to determine the VSP method best suited to provide the required data. Reflection coverage, critical refractions, and mode conversion data (using 3-component geophones) can be used to obtain a structural, lithologic, and petrophysical interpretation.Structural interpretations using recently developed migration techniques based on the scalar wave equation can now provide images of the sub-surface which are superior to those obtained using previous ray-trace schemes.Acoustic impedance estimates from VSP surveys processed with deterministic deconvolution techniques and optimal amplitude recovery to obtain maximum temporal resolution can be more accurate than those obtained from surface seismic data. Offset VSP data can also give an estimate of reservoir porosity variations away from the borehole.


Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1631-1640 ◽  
Author(s):  
Genmeng Chen ◽  
Janusz Peron ◽  
Luis Canales

Vertical seismic profiling‐common depth point (VSPCDP) mapping with rapid ray tracing in a horizontally layered velocity model is used to create 3-D image volumes using Blackfoot and Oseberg 3-D vertical seismic profiling (VSP) data. The ray‐tracing algorithm uses Fermat’s principle and is specially programmed for the layered model. The algorithm is about ten times faster than either a 3-D VSP-CDP mapping program with an eikonal traveltime computation method or a 3-D VSP Kirchhoff migration program. The mapping method automatically separates the image zone from the nonimage zone within the 3-D image volume. The Oseberg data example shows that the lateral extent of the image zone created by the 3D VSP-CDP mapping is larger than that created by 3-D VSP Kirchhoff migration. The same sample result also provides high‐frequency events at target zones. We include an analysis of the imaging error induced from using a horizontally layered model for the Oseberg data, indicating that the method is reliable in the presence of gently dipping structure.


2007 ◽  
Author(s):  
Zhongping Qian ◽  
Xiang‐Yang Li ◽  
Mark Chapman ◽  
Yonggang Zhang ◽  
Yanguang Wang

2021 ◽  
Vol 14 (13) ◽  
Author(s):  
Jianguang Han ◽  
Zhiwei Liu ◽  
Yun Wang ◽  
Jiayong Yan ◽  
Bingluo Gu

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1793-1805 ◽  
Author(s):  
Herman H. Jaramillo ◽  
Norman Bleistein

The Kirchhoff approximation provides a representation of seismic data as a summation of imaged data along isochron surfaces (demigration). The asymptotic inversion of this representation provides a migration as a summation of seismic data along diffraction surfaces. We replace Born inversion techniques with Kirchhoff inversion techniques and further show the link between the Kirchhoff and Born representations after the Born linearized reflection coefficient is replaced by the Kirchhoff reflection coefficient.


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