Seismic mapping of subsurface cavities Page: 4 of 12
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In the present case it is assumed that the cavity is located in the subsurface at a
depth within reach of a borehole. The geometry for the synthetic experiment is taken
from a combination of a reverse VSP and single well survey with sources located in a
borehole and receivers located in the borehole and at the surface. Thus backscattered
energy is recorded in the borehole while side scattered energy is recorded at the
surface. However, sources and receivers are freely exchangeable.
The "field" data is generated using an analytical solution for the scattering of
elastic waves by a cavity (Korneev and Johnson, 1996), and using a fixed location
and volume of the cavity. The analytic solution contains near and far field terms and
is valid for all frequencies. Thus it models the data acquired in the field during a VSP
survey. The method used to invert the data is based on the Mie approximation for the
scattering of elastic waves by a sphere (Korneev and Johnson, 1993) which is an
approximation to the exact solution in the low to intermediate frequency range. It
offers the advantage of fast computational speed.
The geometry of the numerical experiment consists of a 20m deep borehole
containing 21 equally spaced sources and 11 receivers, while 5 additional receivers
are located at the surface extending away from the borehole (Figure 1b). To generate
the initial data, a cavity with a chosen radius is fixed in space and the scattered
wavefield is computed based on the analytic solution. To estimate the location of the
cavity, the search area is subdivided into 200 grid points (10x20) and the scattered
wavefield based on the Mie approximation is subsequently computed for a cavity of
fixed radius at each point. The scattered wavefield is computed for a total of 22
frequencies ranging from 100-1000Hz. After the generation of the wavefields for all
200 possible cavity locations, a correlation coefficient is computed between the
wavefields based on the exact and the approximate solution for each grid point. The
correlation coefficient is defined as,
where Ue and Ua are the wavefields computed using the exact solution and the Mie
approximation, respectively, while * denotes the complex conjugate. At each grid
point this coefficient is computed for all source receiver combinations and stacked
over all frequencies. A map of the correlation coefficients shows the most likely
location of the cavity (see Figure lb). In a second step, the location of the cavity is
fixed at the point of highest correlation, and its radius is varied between R=0.1-5.0m.
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Gritto, R. & Majer, E.L. Seismic mapping of subsurface cavities, article, November 1, 1999; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc702876/m1/4/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.