A parameterization analysis for acoustic fullwaveform inversion of subwavelength anomalies
Abstract
In the case of multiparameter fullwaveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradientbased minimization is used, different choices of parameterization can be interpreted as different preconditioners that change the condition number of the Hessian. If the nonlinear inverse problem is wellposed, then the inversion should converge to a bandlimited version of the true solution irrespective of the parameterization choice, provided we start sufficiently close to the global minimum. However, the choice of parameterization will affect the rate of convergence to the exact solution and the best choice of parameterization is the one with the fastest rate. In this paper, we search for the best choice for acoustic multiparameter fullwaveform inversion, where 1. anomalies with a size less than a quarter of the dominant wavelength have to be estimated without the risk of converging to a local minimum; 2. the scattered wavefield is recorded at all the scattering angles; 3. a steepestdescent minimization scheme is used. Our examples suggest that the best choice of parameterization depends on the contrast of the subsurface scatterer that the inversion tries to estimate. Based on the results, we observe that there is no best parameterization choice for fullwaveform inversion. We also observe that a parameterization using the acoustic impedance and mass density has the worst convergence rate. Finally, we also show that the parameterization analysis during a hierarchical inversion, where the data have limited scattering angles, only helps to select a subspace for monoparameter inversion. For multiparameter hierarchical inversion, the search for the best parameterization in terms of the convergence speed might be obfuscated by nonuniqueness problems.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.01184
 Bibcode:
 2018arXiv180401184B
 Keywords:

 Physics  Geophysics;
 Physics  Computational Physics