Solution of an acoustic transmission inverse problem by extended inversion

Study of a simple single-trace transmission example shows how an extended source formulation full-waveform inversion can produce optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via Newton-like methods. The data consist single trace extracted from causal pressure field, propagating in homogeneous fluid according to linear acoustics, and recorded at given distance transient point energy source. intensity ("wavelet") is presumed quasi-impulsive, with zero for time lags greater than specified maximum lag. inverse is: the trace, recover both sound velocity or slowness wavelet support, so that fit prescribed RMS relative error. least-squares objective function has multiple large residual minimizers. permits spread time, replaces lag constraint by weighted quadratic penalty. A companion paper proper choice weight operator, any stationary produces good approximation global minimizer least squares objective, error bounded assumed noise level. This summarizes theory developed presents numerical experiments demonstrating accuracy predictions concrete instances. We also show dynamically adjust penalty scale during iterative improve estimate.