Implementing efficient global optimization methods in full waveform inversion

Full Waveform Inversion (FWI) is slowly becoming the standard for velocity estimation from seismic data. It uses the full wave equation to estimate high resolution models capable of recovering finer details compared to traditional methods like tomography. FWI is constructed as a least squares optimization problem that iteratively updates an initial model until the misfit between modeled and observed data are within a pre-specified tolerance. The local nature of FWI makes it sensitive to the choice of starting model which has to be in the global minimum trough of the misfit function. If the starting model lies outside the global minimum trough, FWI converges to a local minima giving an incorrect estimation of subsurface properties. In this thesis, I eliminate the sensitivity to the starting model when performing FWI. This is done by recasting FWI into a global optimization problem using a combination of sparse parameterization methods. The starting model is generated by a global optimization method that is not sensitive to the starting model. The result from the global optimization method is then used as a starting model for conventional FWI using a dense set of parameters. In chapter 2, I apply global optimization with a sparse parameterization technique for 2D models using a combination of interfaces and velocities. Chapter 3 extends the sparse parameterization for salt bodies using ellipse sets and level-set methods. Lastly, chapter 4 extends sparse parameterization in three dimensions to perform FWI without a starting guess. I demonstrate that the proposed approaches are not sensitive to the source of starting model and discuss some sources of uncertainty.

Another issue that prevents implementation of FWI on a regular basis is its computational cost. Expensive forward evaluations need to be performed multiple times across several iterations to obtain the final model. It is of particular significance in 3D where in addition to posing a computational cost problem, it also creates a data reversal problem when computing the gradient. I propose two approaches to reduce the computational cost of forward modeling and gradient computation in the time and frequency domains. The frequency domain approach discussed in chapter 5 exploits the contribution of unchanging zones in an inversion workflow to be reused over subsequent iterations of FWI. The final chapter discusses how to run a gradient computation on GPUs using faster interconnect and on-node memory. I provide a template to apply it to a general adjoint problem with specific example on FWI. I obtain a 20-40% and 82-207% improvement in runtimes in the frequency and time domain, respectively, using the proposed methods.