ISSN:
1365-2478
Quelle:
Blackwell Publishing Journal Backfiles 1879-2005
Thema:
Geologie und Paläontologie
,
Physik
Notizen:
We present a method for calculating the anisotropy parameter of a buried layer by inverting the total traveltimes of direct arrivals travelling from a surface source to a well-bore receiver in a vertical seismic profiling (VSP) geometry. The method assumes two-dimensional media. The medium above the layer of interest (and separated from it by a horizontal interface) can exhibit both anisotropy and inhomogeneity. Both the depth of the interface as well as the velocity field of the overburden are assumed to be known. We assume the layer of interest to be homogeneous and elliptically anisotropic, with the anisotropy described by a single parameter χ. We solve the function describing the traveltime between source and receiver explicitly for χ. The solution is expressed in terms of known quantities, such as the source and receiver locations, and in terms of quantities expressed as functions of the single argument xr, which is the horizontal coordinate of the refraction point on the interface. In view of Fermat's principle, the measured traveltime T possesses a stationary value or, considering direct arrivals, a minimum value, 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR0361:GPR_0361_m101" location="equation/GPR_0361_m101.gif"/〉. This gives rise to a key result -- the condition that the actual anisotropy parameter 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR0361:GPR_0361_m102" location="equation/GPR_0361_m102.gif"/〉. Owing to the explicit expression 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR0361:GPR_0361_m103" location="equation/GPR_0361_m103.gif"/〉, this result allows a direct calculation of 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR0361:GPR_0361_m104" location="equation/GPR_0361_m104.gif"/〉 in the layer of interest. We perform an error analysis and show this inverse method to be stable. In particular, for horizontally layered media, a traveltime error of one millisecond results in a typical error of about 20% in the anisotropy parameter. This is almost one order of magnitude less than the error inherent in the slowness method, which uses a similar set of experimental data. We conclude by detailing possible extensions to non-elliptical anisotropy and a non-planar interface.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1046/j.1365-2478.2003.00361.x
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