A platform for Kirchhoff data mapping in scalar models of data acquisition

Journal Article · Sat Jan 01 04:00:00 EST 2000 · Geophysical Prospecting

DOI:https://doi.org/10.1046/j.1365-2478.2000.00178.x· OSTI ID:20014503

Bleistein, N; Jaramillo, H

Kirchhoff data mapping (KDM) is a procedure for transforming data from a given input source/receiver configuration and background earth model to data corresponding to a different output source/receiver configuration and background model. The generalization of NMO/DMO, datuming and offset continuation are three examples of KDM applications. This paper describes a platform for KDM for scalar wavefields. The word, platform, indicates that no calculations are carried out in this paper that would adapt the derived formula to any one of a list of KDMs that are presented in the text. Platform formulae are presented in 3D and in 2.5D. For the latter, the validity of the platform equation is verified--within the constraints of high-frequency asymptotics--by applying it to a Kirchhoff approximate representation of the upward scattered data from a single reflector and for an arbitrary source/receiver configuration. The KDM formalism is shown to map this Kirchhoff model data in the input source/receiver configuration to Kirchhoff data in the output source/receiver configuration, with one exception. The method does not map the reflection coefficient. Thus, the authors verify that, asymptotically, the ray theoretical geometrical spreading effects due to propagation and reflection (including reflector curvature) are mapped by this formalism, consistent with the input and output modelling parameters, while the input reflection coefficient is preserved. In this sense, this is a true-amplitude formalism. As with earlier Kirchhoff inversion, a slight modification of the kernel of KDM provides alternative integral operators for estimating the specular reflection angle, both in the input configuration and in the output configuration, thereby providing a basis for amplitude-versus-angle analysis of the data.

• Research Organization: Colorado School of Mines, Golden, CO (US)
• Sponsoring Organization: US Department of Energy
• OSTI ID: 20014503
• Journal Information: Geophysical Prospecting, Journal Name: Geophysical Prospecting Journal Issue: 1 Vol. 48; ISSN GPPRAR; ISSN 0016-8025
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
DATA ANALYSIS
GEOLOGIC DEPOSITS
MAPPING
SEISMIC SURVEYS
SEISMIC WAVES
WAVE PROPAGATION