## Imaging and Computing Seminar

### Tristan van Leeuwen, Dept of Geotechnology, Delft University

**Title:**

Correlation-based inversion of seismic data

**Abstract:**

The aim of waveform inversion is to infer subsurface medium properties from
seismic (reflection) data. Such an inverse problem may be posed as a
PDE-constrained least-sqaures optimization problem. However, due to the
band-limited nature of the data, the data depends very nonlinearly on the
medium parameters that control the kinematics of the data. If a
kinematically accurate initial guess is not provided, a gradient-based
optimization algorithm will most likely get stuck in a local minimum of the
least-squares objective functional.
This calls for a reformulation of the inverse problem into a traveltime
tomography problem. The basic idea is that the traveltimes of the data
depend more linearly on the velocity than the waveforms themselves. A
standard technique involves a correlation of the modeled and observed
waveforms to extract the traveltime difference. We propose a novel way to
measure the traveltime misfit from the correlation and show that this can be
immediately used to define an alternative objective functional that
mitigates the local minima that plague the least-squares approach. The
proposed method can be adapted for both transmission and reflection
tomography. We illustrate the workings on synthetic and real data examples.