Abstract
The WKBJ or path integral approximation to the solution of the elas- todynamic equations in a slightly heterogeneous Earth allows us to partition the inverse problem for a large set of observed seismograms along different wavepaths. We first find a collection of one-dimensional (1D) Earth models by nonlinear optimization, each of which predicts the observed waveforms along one particular path. Diagonalization of the Hessian matrix involved in the optimization allows us to isolate those features of the 1D models that are uniquely determined. These features — integrals over depth along the wavepath—are then used as constraints in a linear inversion for three dimensional (3D) Earth structure. We illustrate the theory with a synthetic example.
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Nolet, G. (1997). Partitioned Nonlinear Optimization for the Interpretation of Seismograms. In: Chavent, G., Sacks, P., Papanicolaou, G., Symes, W.W. (eds) Inverse Problems in Wave Propagation. The IMA Volumes in Mathematics and its Applications, vol 90. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1878-4_19
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DOI: https://doi.org/10.1007/978-1-4612-1878-4_19
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