Article,
2D inversion of refraction traveltime curves using homogeneous functions
Geophysical Prospecting, 49 (4): 461--482 (July 2001)
DOI: 10.1046/j.1365-2478.2001.00270.x
Abstract
A method using simple inversion of refraction traveltimes for the
determination of 2D velocity and interface structure is presented.
The method is applicable to data obtained from engineering seismics
and from deep seismic investigations. The advantage of simple inversion,
as opposed to ray-tracing methods, is that it enables direct calculation
of a 2D velocity distribution, including information about interfaces,
thus eliminating the calculation of seismic rays at every step of
the iteration process. The inversion method is based on a local approximation
of the real velocity cross-section by homogeneous functions of two
coordinates. Homogeneous functions are very useful for the approximation
of real geological media. Homogeneous velocity functions can include
straight-line seismic boundaries. The contour lines of homogeneous
functions are arbitrary curves that are similar to one another. The
traveltime curves recorded at the surface of media with homogeneous
velocity functions are also similar to one another. This is true
for both refraction and reflection traveltime curves. For two reverse
traveltime curves, non-linear transformations exist which continuously
convert the direct traveltime curve to the reverse one and vice versa.
This fact has enabled us to develop an automatic procedure for the
identification of waves refracted at different seismic boundaries
using reverse traveltime curves. Homogeneous functions of two coordinates
can describe media where the velocity depends significantly on two
coordinates. However, the rays and the traveltime fields corresponding
to these velocity functions can be transformed to those for media
where the velocity depends on one coordinate. The 2D inverse kinematic
problem, i.e. the computation of an approximate homogeneous velocity
function using the data from two reverse traveltime curves of the
refracted first arrival, is thus resolved. Since the solution algorithm
is stable, in the case of complex shooting geometry, the common-velocity
cross-section can be constructed by applying a local approximation.
This method enables the reconstruction of practically any arbitrary
velocity function of two coordinates. The computer program, known
as godograf, which is based on this theory, is a universal program
for the interpretation of any system of refraction traveltime curves
for any refraction method for both shallow and deep seismic studies
of crust and mantle. Examples using synthetic data demonstrate the
accuracy of the algorithm and its sensitivity to realistic noise
levels. Inversions of the refraction traveltimes from the Salair
ore deposit, the Moscow region and the Kamchatka volcano seismic
profiles illustrate the methodology, practical considerations and
capability of seismic imaging with the inversion method.
