2. 5D Kirchhoff Inversion Theory applied to VSP data

Technical Report · Wed Jan 01 04:00:00 EST 1992

OSTI ID:7235840

Bleistein, N ^[1]

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1. Colorado School of Mines, Golden, CO (United States). Center for Wave Phenomena

Offset VSP (or Walk-away VSP) and Crosshole Tomography are special commonshot experiments. In the former, the receiver array is in a borehole with the source at the surface. In the latter, both receiver array and source array are in boreholes. For these two recording configurations, a two-and-one-half dimensional (2.5D) inversion is the method of choice if amplitude information of the data is used to extract medium parameters. By 2.5D, we mean 3D wave propagation within a 2D medium. Similar to the 2.5D inversion formulation of surface line seismic data, we formulate an inversion algorithm in the paper for VSP geometry. The resulting formula is equally applicable to Crosshole experiments. Our basic assumption is that wave propagation is governed by the acoustic wave equation. We also assume VSP data are high frequency so that the asymptotic evaluation of integrals is justified. This inversion algorithm consists of two transform kernels, which, when applied to VSP or Crosshole data, produce the subsurface reflector map. For one kernel, the reflector map is delineated by the singular functions of interface with peak amplitude being the angularly dependent geometrical optics reflection coefficient. For the other, we obtain the same reflector map, but the amplitude of the singular function is the product of the cosine of the incident angle with the reflection coefficient. From these two outputs, lower medium propagation speed can be estimated if densities are known. To estimate both the speed and density of the lower medium, two independent inversions, illuminating points on the reflector from distinct incidence angles, are needed. In practice, many experiments are used to limit the effect of noise. The inversion operator is tested on synthetic data for both kinematic (imaging) and dynamic (amplitude details) performance, and on field VSP data for imaging only. The results highlight the advantages and limitations of the method.

• Research Organization: Massachusetts Inst. of Tech., Cambridge, MA (United States). Dept. of Earth, Atmospheric and Planetary Sciences; Colorado School of Mines, Golden, CO (United States). Center for Wave Phenomena
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: FG02-89ER14079; FG02-89ER14084
• OSTI ID: 7235840
• Report Number(s): DOE/ER/14079-18; CWP--101P; ON: DE92018642
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
422000 -- Engineering-- Mining & Underground Engineering-- (1980-)
58 GEOSCIENCES
580000* -- Geosciences
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
BOREHOLES
CAVITIES
DIAGNOSTIC TECHNIQUES
DIFFERENTIAL EQUATIONS
EQUATIONS
GEOPHYSICAL SURVEYS
KERNELS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
SEISMIC SURVEYS
SEISMIC WAVES
SURVEYS
TOMOGRAPHY
WAVE EQUATIONS
WAVE PROPAGATION