Seismic inversion using fine grain parallel computers
, by Peter Mora

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 theorectical developments and advances in computer technology, this
dream is on the verge of being realized. 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 alogorithm 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 i sparametrized 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. 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". Results suggest that by using such fine grain parallel
computers, realistic sized inverse problems can be solved for the first time!