Multiresolution spherical wavelet analysis in global seismic
tomography
Creators: name: Carannante, Simona <1976>
Publisher: name: Alma Mater Studiorum - Università di Bologna
Year: 2008
Subjects: GEO/10 Geofisica della terra solida

description: Every seismic event produces seismic waves which travel throughout the Earth.
Seismology is the science of interpreting measurements to derive information about the structure of the
Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's
interiors. Tomographic models obtained at the global and regional scales are an underlying tool for
determination of geodynamical state of the Earth, showing evident correlation with other geophysical and
geological characteristics. The global tomographic images of the Earth can be written as a linear
combinations of basis functions from a specifically chosen set, defining the model parameterization. A
number of different parameterizations are commonly seen in literature: seismic velocities in the Earth
have been expressed, for example, as combinations of spherical harmonics or by means of the simpler
characteristic functions of discrete cells.
With this work we are interested to focus our attention on this aspect, evaluating a new type of
parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory
that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is
often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only
frequency resolution and no time resolution.
The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the
shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal
according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency
components, and then study each component with resolution matched to its scale, so they are especially
useful in the analysis of non stationary process that contains multi-scale features, discontinuities and
sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or
signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel
for analysis to extract information about the process.
These two types of applications of wavelets in geophysical field, are object of study of this work.
At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse
Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet
analysis in the representation of two different type of synthetic models; then we apply it to real data,
obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an
other type of parametrization (i.e., block parametrization).
For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform
in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability
and then apply the same analysis to real data to obtain Local Correlation Maps between different model
at same depth or between different profiles of the same model.