Internal velocity estimation in laterally inhomogeneous areas by deconvolution of stacking velocity profiles.
The problem of inferring the velocity field is central to exploration seismology.
Conventional velocity analysis is based on the hypothesis that reflection traveltime is
a hyperbolic function of the distance between the source and the receiver. This is
basis upon which interval velocities are obtained using Dix's equation for a horizontally
layered model and Shah's equation for a dipping layered structure. However, in
laterally inhomogeneous areas, traveltimes do not follow hyperbolae, hence, hyperbola
based velocity estimation techniques fail in such areas. Although many sophisticated
techniques, such as tomography, migration and model based velocity analysis
can be used to obtain accurate velocity fields from seismic data in such areas, these
methods are very computationally expensive.
In this thesis, a simple, quicker and accurate velocity estimation technique is
proposed. This technique does not abandon conventional velocity analysis, but gives
further processing to stacking velocity data provided by conventional techniques.
The new technique is based on the hypothesis that stacking slowness variations
due to lateral interval slowness anomalies can be represented by the outputs of a
linear impulse response system. The inputs of the system are the interval slowness
anomalies. The system is space invariant for a horizontally layered model, but is
space variant for a dipping layered model. A pre-determined background model is
required to compute the linear system.
Since the linear system is space invariant for a horizontally layered model and
space variant for a dipping layered model, there are two schemes for velocity estimation
for these two cases.
In horizontal geology, the relationship between stacking slowness variations
and interval slowness anomalies can be expressed by a set of linear equations in the
wavenumber domain. The singular value decomposition method is used to solve the
set of linear equations to obtain interval slowness anomalies from stacking slowness variations.
In dipping geology, the relationship between stacking slowness variations and
interval slowness anomalies cannot be written as a set of linear equations in the
wavenumber domain. Interval slownesses must in this case be derived in the least
square sense. Basis functions are introduced to construct interval slowness
Once the interval slowness anomalies have been estimated, interval slownesses
(and hence velocities) are obtained by adding these to the background interval
Finally, the sensitivity of the linear system to data errors and model errors is
investigated through a series of synthetic examples, the applications of these velocity
estimation techniques and suggestions for further studies of the linear system are discussed