Prestack elastic Kirchhoff migration for multicomponent seismic data in variable velocity media

Author(s):  
Aimin Xue ◽  
George A. McMechan
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.


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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