Waveform Inversion of Synthetic Ocean Models in the Laplace Domain

Abstract:

In seismic oceanography, the processed images show where small temperature changes (as little as 0.03°C) occur, although they do not give absolute temperatures. To get a 2-D temperature map, the data must be inverted for sound speed, which is then converted to temperature using equations of state.

Full waveform inversion requires a starting model that is iteratively updated until the residuals converge. Global search algorithms such as Genetic Algorithm do not require a starting model close to the true model, but are computationally exhausting. Local search inversion is less expensive, but requires a reasonably accurate starting model. Unfortunately, most marine seismic data has little associated hydrographic data and so it is difficult to create starting models close enough to the true model for convergence throughout the target area. In addition, the band-limited nature of seismic data makes it inherently challenging to extract the long wavelength sound speed trend directly from seismic data. Laplace domain inversion (LDI) developed by Changsoo Shin and colleagues requires only a rudimentary starting model to produce smooth background sound speed models without requiring prior information about the medium. It works by transforming input data to the Laplace domain, and then examining the zero frequency component of the damped wavefield to extract a smooth sound speed model – basically, removing higher frequency fluctuations to expose background trends. This ability to use frequencies below those effectively propagated by the seismic source is what enables LDI to produce the smooth background trend from the data.

We applied LDI to five synthetic data sets based on simplified models of oceanographic features. Using LDI, we were able to recover smoothed versions of our synthetic models, showing the viability of the method for creating sound speed profiles suitable for use as starting models for other methods of inversion that output more detailed models.