Schlumberger

"Data and Model Compression Approaches for improving the efficiency of Seismic Full-Waveform Inversion"

Seismic full-waveform inversion (FWI) method is expected to be the ultimate geophysical seismic processing tool. However, the underlying problem is an ill-posed one. Furthermore, it is also a large-scale computational problem because we have to deal with a large number of data points as well as a large number of unknown model parameters. We attempt to cope with the ill-posedness by using automatic regularization approaches and constraints to narrow down the physical solution. In this talk we focus on the use of compression approaches for reducing the computational time and memory requirement of seismic FWI algorithms:

(1) To deal with a large number of sources and receivers, we employ the so-called source-receiver compression scheme. By detecting and quantifying the extent of redundancy in the data, we assemble a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey. Because the number of these simultaneous sources and receivers can be significantly less than those of the physical sources and receivers, the computational time and memory usage of any gradient-type inversion method such as Gauss-Newton, nonlinear conjugate gradient, or contrast source inversion methods can be tremendously reduced. The scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data compression is done through the elimination of the small eigenvalues.

(2) As for the large-number of unknown model parameters (such as P-wave velocity, S-wave velocity, and mass-density), we employ the so-called model compression scheme. In this scheme the unknown model parameters are represented in terms of a basis such as Fourier, cosine, or wavelet. By applying a proper truncation criterion, the model may then be approximated by a reduced number of basis functions, which is usually much less than the number of the model parameters. This model compression scheme significantly accelerates the computational time as well as reduces the memory usage of both Gauss-Newton and nonlinear conjugate gradient method.

(3) An additional bottleneck of the Gauss-Newton method is the Jacobian matrix storage and the computational cost of calculating the Gauss-Newton step (the inner-loop calculation). We reduce the memory usage by calculating the Jacobian matrix on the fly in each inner-loop iteration. By doing so the computational cost of calculating the Gauss-Newton step increases; however, this overhead is mitigated by compressing the field matrices (which contain redundancy) using the Adaptive Cross Approximation scheme. For some cases, this compressed implicit Jacobian scheme may even speed-up the Gauss-Newton step calculation and further regularizes the Gauss-Newton method.

As demonstrations of these approaches, we show various inversion results of well-known benchmark models such as Marmousi, BP/EAGE Salt, and 3D SEG/EAGE Salt models. When time permits, we also show a field data case study.