The Cagniard method in complex time revisited

Technical Report · Fri Mar 01 00:00:00 EST 1991

OSTI ID:5919976

Bleistein, N; Cohen, J K

The Cagniard-de Hoop method is ideally suited to the analysis of wave propagation problems in stratified media. The method applies to the integral transform representation of the solution in the transform variables (s,p) dual of the time and transverse distance. The objective of the method is to make the p-integral take the form of a forward Laplace transform, so that the cascade of the two integrals can be identified as a forward and inverse transform, thereby making the actual integration unnecessary. Typically, the method is applied to an integral that represents one body wave plus other types of waves. In this approach, the saddle point of w(p) that produces the body wave plays a crucial role because it is always a branch point of the integrand in the {tau}-domain integral. Furthermore, the paths of steepest ascent from the saddlepoint are always the tails of the Cagniard path along which w(p) {yields} {infinity}. This motivates the definition of a primary p-domain-the domain between the imaginary axis and the steepest descent paths- and its image in the {tau}-domain-the primary {tau}-domain. In terms of these regions, singularities in the primary p-domain have images in the primary {tau}-domain and the deformation of contour onto the real axis in the {tau}-domain must include contributions from these singularities. In developing the method the authors examine the transformation from a frequency domain representation of the solution (w) to a Laplace representation (s). Many users start from the frequency domain representation of solutions of wave propagation problems. There are issues of movement of singularities under the transformation from w to s to be concerned with here. They discuss this anomaly in the context of the Sommerfield half-plane problem. 15 refs., 10 figs.

• Research Organization: Colorado School of Mines, Golden, CO (USA). Center for Wave Phenomena
• Sponsoring Organization: USDOE; USDOE, Washington, DC (USA)
• DOE Contract Number: FG02-89ER14079
• OSTI ID: 5919976
• Report Number(s): DOE/ER/14079-5; CWP-098; ON: DE91011042
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
SEISMIC SURVEYS
CALCULATION METHODS
DATA ANALYSIS
FREQUENCY ANALYSIS
GEOLOGIC STRATA
LAPLACE TRANSFORMATION
SADDLE-POINT METHOD
SEISMIC WAVES
SOMMERFELD INTEGRALS
WAVE PROPAGATION
GEOLOGIC STRUCTURES
GEOPHYSICAL SURVEYS
INTEGRAL TRANSFORMATIONS
INTEGRALS
SURVEYS
TRANSFORMATIONS
580000* - Geosciences
990200 - Mathematics & Computers