scholarly journals Diffraction of a Plane Elastic Wave by a Gradient Transversely Isotropic Layer

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Anastasiia Anufrieva ◽  
Dmitrii Tumakov
Keyword(s):  
Elastic Wave ◽  
Piecewise Linear ◽  
Grid Method ◽  
Young Modulus ◽  
Transversely Isotropic ◽  
Isotropic Layer ◽  
Transform Method ◽  
Transversely Isotropic Layer ◽  
The Fourier Transform ◽  
Overdetermined Boundary Value Problem

The problem of diffraction of a plane elastic wave by a gradient transversely isotropic layer is considered. Using the method of overdetermined boundary value problem in combination with the Fourier transform method, the system of ordinary differential equations of the second order with boundary conditions of the third type is obtained which is solved by the grid method. Results of calculations obtained using the above-mentioned technique for the case of piecewise linear profiles for the Young modulus of the layer are given.

The effect of transverse isotropy on isotropic traveltime inversion of vertical seismic profile data—A modeling study

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1235-1241 ◽  
Author(s):  
Jan Douma
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Vertical Axis ◽  
Seismic Profile ◽  
Isotropic Layer ◽  
Low Velocity ◽  
Traveltime Inversion ◽  
Axis Of Symmetry ◽  
Transversely Isotropic Layer

Traveltime inversion of multioffset VSP data can be used to determine the depths of the interfaces in layered media. Many inversion schemes, however, assume isotropy and consequently may introduce erroneous structures for anisotropic media. Synthetic traveltime data are computed for layered anisotropic media and inverted assuming isotropic layers. Only the interfaces between these layers are inverted. For a medium consisting of a horizontal isotropic low‐velocity layer on top of a transversely isotropic layer with a horizontal axis of symmetry (e.g., anisotropy due to aligned vertical cracks), 2-D isotropic inversion results in an anticline. For a given axis of symmetry the form of this anticline depends on the azimuth of the source‐borehole direction. The inversion result is a syncline (in 3-D a “bowl” structure), regardless of the azimuth of the source‐borehole direction for a vertical axis of symmetry of the transversely isotropic layer (e.g., anisotropy due to horizontal bedding).

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