Automatic 1-D waveform inversion of marine seismic refraction data

SUMMARY Full waveform synthetic seismograms are now used as standard in the interpretation of marine refraction data, but only with a laborious trial-and-error fitting procedure. We show how the matching of observed waveforms with WKBJ synthetic seismograms can be efficiently and automatically performed for 1-D earth models. Automation of the inversion is difficult because of the multi-modal, irregular form of the misfit of data and synthetics. A sequence of three steps is required for a complete inversion: location of the deepest valley of the misfit function, descent to the global minimum, and description of the neighbourhood of the minimum for error analysis. The first step is accomplished with a Monte Carlo search through a very large model space defined by poor prior knowledge of velocities and gradients of the solution. Weak traveltime constraints are used to eliminate poorly fitting models from waveform calculations. A comparison of the traveltime and waveform misfits of the Monte Carlo models clearly illustrates that waveforms are providing more information than traveltimes alone. Bayesian statistics are used to construct marginal probability distributions and the covariance matrix, which give a rough preliminary error analysis. In the second step, damped least-squares linearized inversion makes small adjustments to the best-fitting Monte Carlo model as it descends to the global minimum. Finally the immediate neighbourhood of the global minimum is explored with constrained least-squares inversion. Realistic error bounds on each parameter are defined from the resulting slices through the misfit function. These bounds are much narrower than traveltime inversion provides. Correlations between parameters are obtained from the covariance matrix constructed from models examined during this error analysis. The inversion methods are illustrated on the FF2 refraction data set of the Scripps Institution of Oceanography. The Monte Carlo search successfully locates the valley of the global minimum as well as a nearby secondary minimum. The error analysis puts realistic error bounds on the detailed inversion of this data set by Spudich & Orcutt.