Large Scale Elastic Wavefield Inversion

Seismic recordings depend on the seismic source, the properties of the Earth, the location of the seismic receiver stations, and the physics of seismic wave propagation. It has always been a dream in seismology to predict the Earth properties directly from the seismograms using our knowledge of how seismic waves are affected by the rocks. Thanks to theoretical developments and advances in computer technology, this dream is on the verge of being achievable. The Earth properties can be estimated using a least squares conjugate gradient algorithm to solve for the Earth model which predicts seismograms that best match the observed data. A new theory puts the gradient direction required by this algorithm in terms of wave simulations. In the past, wave simulations in realistic Earth models were too CPU intensive for this formulation to be practical but this no longer appears to be the case. A well understood method to do wave simulations in media of arbitrary complexity is by directly solving the discretized wave equation using the method of finite differences. The Earth is parametrized as a grid with each node of the grid associated with the elastic properties governing seismic wave propagation. Finite differences are used at each node to propagate the seismic waves from one instant of time to the next. At any instant of time, the calculations at a given node are independent from the calculations at other nodes (though data stored at a few nearby nodes must be accessed). Therefore, the calculations at an instant of time can be done at all nodes simultaneously. Hence, the method is ideally suited to fine grain parallel computer architectures such as that of the Connection Machine¯¹ which is capable of rapid parallel communications between a large number of nodes. Results suggest that by using such fine grain parallel computers, realistic sized inverse problems can be solved for the first time!