Full Waveform Inversion (FWI) is a depth imaging technique that takes advantage of the
full information contained in recorded seismic data. FWI provide high resolution images
of subsurface properties, usually seismic velocities or related parameters, although in theory
it could image any property used to formulate the wave equation. The computational
cost of the methodology has historically limited its application to 3D acoustic approximations
but recent developments in hardware capabilities have increased computer power
to the point that more realistic approximations are viable. In this work the traditional
acoustic approximation is extended to include elastic effects by introducing the elastic
wave equation as the governing law that describes wave propagation.
I have developed a software based on finite-differences to solve the elastic wave equation
in 3D, which I applied in the development of a full-waveform inversion algorithm. The
software is fully parallelised for both distributed and shared-memory systems. The first
level of parallelisation distributes seismic sources across cluster nodes. Each node solves
the 3D elastic wave equation in the whole computational domain. The second level of
parallelisation takes advantage of present multi-core computer processor units (CPU) to
decompose the computational domain into different volumes that are solved independently
by each core. Such parallel design allows the algorithm to handle models of realistic sizes,
increasing the computational times only a factor of two compared to those of 3D acoustic
full-waveform inversion on the same mesh. I have also implemented a perfectly matched
layer absorbing boundary condition to reproduce a semi-infinite model geometry and
prevent spurious reflections from the model boundaries from contaminating the modelled
wavefields.
The inversion algorithm is based upon the adjoint-state method, which I reformulated
for the wave equation that I implemented, which was based on particle-velocities and
stresses, providing a comparison and demonstration of equivalence with previous developments.
To examine the performance of the code, I have inverted several synthetic problems
of increasing realism. I have principally used only pressure sources and receivers to assess
the potential of the method's application to the most common industry surveys: streamer
data for offshore and vertical geophones (only one component) for onshore exploration
surveys. The results show that the imaged properties increase with the heterogeneity of
the models, due to the increase in P-S-P conversions which provides the main source of
information to invert shear-wave velocity models from pressure sources and receivers.
It remains to demonstrate the inversion of field datasets and my future research project
will focused on achieving this goal.