多重尺度震波走時層析成像
Date Issued
2001
Date
2001
Author(s)
DOI
892611M002043
Abstract
Seismic travel time tomography is commonly
discretized by a truncated expansion of the pursued
model in terms of chosen basis functions. The
robustness of the resulting Earth model as well as
whether parameterization affects the actual resolving
power of a given data set have long been seriously
debated. From the perspective of the model
resolution, however, there is one important aspect of
the parameterization issue of seismic tomography that
has yet to be systematically explored, that is, the
space-frequency localization of a chosen
parameterization. In fact, the two most common
parameterizations tend to enforce resolution in each of
their own particular domains. Namely, the
parameterization in terms of spherical harmonics with
global support tends to emphasize spectral resolution
while sacrificing the spatial resolution, whereas the
compactly supported pixels tend to behave conversely.
Some of the significant discrepancies among
tomographic models are very likely to be
manifestations of this effect, when dealing with data
set with non-uniform sampling. With an example of
the tomographic inversion for the lateral shear wave
heterogeneity of the D” layer using S-SKS travel times,
we demonstrate an alternative parameterization in
terms of the multi-resolution representation of the
pursued model function. Unlike previous attempts of
multi-scale inversion that invoke pixels with variable
sizes, or overlay several layers of tessellation with
different grid intervals, our formulation invokes the
biorthogonal generalized Harr wavelets on the sphere.
We show that the multi-resolution representation can
be very easily constructed from an existing
blocks-based discretization. A natural scale
hierarchy of the pursued model structure constrained
by the resolving power of the given sampling is
embedded within the obtained solution. It provides a
natural regularization scheme based on the actual
ray-paths sampling and is thus free from a priori
prejudices intrinsic to most regularization schemes.
Unlike solutions obtained through spherical harmonics
or spherical blocks, that tend to collapse structures
onto ray-paths, our parameterization imposes
regionally varying Nyquist limits, that is, the robustly
resolvable local wavelength bands within the obtained
solution
Subjects
continuous inverse problem
seismic tomography
multiresolution analysis
space-scale localization
spherical wavelets
Publisher
臺北市：國立臺灣大學海洋研究所
Type
report
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