Publication Date:
2015-09-13
Description:
Employing dynamic reciprocity can be an effective tool to simplify the calculation of elastic wavefields for borehole problems and to check the results. We analytically obtain the reciprocity relations for the elastodynamic fields generated by multipole sources in a fluid–solid configuration: if the multipole sources are located in the fluid, the particle displacement due to a dipole source is reciprocal to the particle acceleration due to a single force; the fluid pressure due to a dipole source is reciprocal to the particle acceleration due to a monopole source; the particle displacement due to a quadrupole source is reciprocal to the spatial partial derivative of the particle acceleration due to a single force; the fluid pressure due to a quadrupole source is reciprocal to the spatial partial derivative of the particle acceleration due to a monopole source. These relations are tested by numerical experiments for different borehole problems, including acoustic logging, single-well imaging and vertical seismic profiling. A reciprocity test can be used as a quick check of a finite-difference algorithm and the implementation of the sources, although it cannot detect errors due to improper discretization of the interfaces.
Keywords:
Marine Geosciences and Applied Geophysics
Print ISSN:
0956-540X
Electronic ISSN:
1365-246X
Topics:
Geosciences
Published by
Oxford University Press
on behalf of
The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
