SUMMARY The sensitivity of Rayleigh wave amplitude to Earth structure has applications to seismic tomography, both in cases where amplitude information is used to supplement phase velocity data to improve images of elastic parameters, and to correct amplitudes for local Earth structure in attenuation tomography. We review the theoretical basis of the ray theoretical approximation, in which the wave amplitudes are controlled by a combination of geometrical spreading and local changes in energy density due to Earth structure. We focus mainly on the latter effect, which we term the constant energy flux approximation. We investigate the ray theoretical basis for this approximation, test it against a full waveform simulation that verifies its accuracy and show how it can be used to compute the sensitivity of amplitude to elastic moduli and density. We investigate how perturbing these parameters in a set of simple Earth models affects Rayleigh wave amplitudes, and demonstrate that a slow velocity heterogeneity can cause either increased or reduced amplitudes, depending upon the depth of the heterogeneity and the observation frequency. Consequently, amplitude sensitivity can be either positive or negative, and its magnitude can vary significantly with frequency. Although an added complication, the very different behaviour of phase velocity and amplitudes to changes in Earth structure implies that the two types of data are complementary and suggest the effectiveness of using both in Rayleigh wave tomography.
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Ionospheric Radio Beacon Signal Analysis and Parameter Estimation Using Automatic Differentiation
Abstract Continuous wave signals from a network of high frequency (HF) beacons in Peru and other instruments are used to reconstruct the regional ionospheric electron number density in the volume surrounding the network. The continuous wave (CW) HF signals employ binary phase codes with pseudorandom noise (PRN) encoding, and the observables include propagation time or pseudorange, Doppler shift or beat carrier phase, and amplitude. A forward model based on geometric optics in an inhomogeneous, anisotropic, lossy plasma is used to relate plasma number density to the observables. Plasma number density is parametrized in terms of a modified Chapman profile in the vertical and biquintic B‐splines in the horizontal. Sensitivity analysis is required both to model the ray amplitudes and to solve the two‐point boundary problem for each ray. Sensitivity analysis is performed here using reverse‐mode automatic differentiation. In particular, we use an LLVM compiler (Clang), the corresponding OpenMP library, and the Enzyme Automatic Differentiation Framework plugin to compute the sensitivity (gradients) of ray endpoints with respect to their initial bearings. The resulting algorithm exhibits no performance penalty compared to variational sensitivity analysis and is far simpler to implement.
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- Award ID(s):
- 2213849
- PAR ID:
- 10588967
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Machine Learning and Computation
- Volume:
- 1
- Issue:
- 4
- ISSN:
- 2993-5210
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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