The Collaborative Seismic Earth Model: Generation 1.

We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first-generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors today's computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first-generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal- to continental-scale models. A global full-waveform inversion ensures that regional refinements translate into whole-Earth structure.

Toward Speed-of-Sound Anisotropy Quantification in Muscle With Pulse-Echo Ultrasound.

The velocity of ultrasound longitudinal waves (speed of sound) is emerging as a valuable biomarker for a wide range of diseases, including musculoskeletal disorders. Muscles are fiber-rich tissues that exhibit anisotropic behavior, meaning that velocities vary with the wave-propagation direction. Therefore, quantifying anisotropy is essential to improve velocity estimates while providing a new metric related to muscle composition and architecture. For the first time, this work presents a method to estimate speed-of-sound anisotropy in transversely isotropic tissues using pulse-echo ultrasound. We assume elliptical anisotropy and consider an experimental setup with a flat reflector parallel to the linear probe, with the muscle in between. This setup allows us to measure first-arrival reflection traveltimes using multistatic operation. Unknown muscle parameters are the orientation angle of the anisotropy symmetry axis and the velocities along and across this axis. We derive analytical expressions for the nonlinear relationship between traveltimes and anisotropy parameters, including reflector inclinations. These equations are exact for homogeneous media and are useful to estimate the effective average anisotropy in muscles. To analyze the structure of this forward problem, we formulate the inversion statistically using the Bayesian framework. We demonstrate that anisotropy parameters can be uniquely constrained by combining traveltimes from different reflector inclinations. Numerical results from wide-ranging acquisition and anisotropy properties show that uncertainties in velocity estimates are substantially lower than expected velocity differences in the muscle. Thus, our approach could provide meaningful muscle anisotropy estimates in future clinical applications.

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media.

We present a probabilistic seismic point source inversion, taking into account 3-D heterogeneous Earth structure. Our method rests on (1) reciprocity and numerical wavefield simulations in complex media and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models to provide reliable uncertainty information on the timing, location, and mechanism of the source. Using spectral element simulations of 3-D, viscoelastic, anisotropic wave propagation, we precompute receiver side strain tensors in time and space. This enables the fast computation of synthetic seismograms for any hypothetical source within the volume of interest, and thus a Bayesian solution of the inverse problem. To improve efficiency, we developed a variant of Hamiltonian Monte Carlo sampling. Taking advantage of easily computable derivatives, numerical examples indicate that Hamiltonian Monte Carlo can converge to the posterior probability density with orders of magnitude less samples than the derivative-free Metropolis-Hastings algorithm, which we use for benchmarking. Exact numbers depend on observational errors and the quality of the prior. We apply our method to the Japanese Islands region where we previously constrained 3-D structure of the crust and upper mantle using full-waveform inversion with a minimum period of 15 s.