A matching pursuit approach to the geophysical inverse problem of seismic travel time tomography under the ray theory approximation

Seismic travel time tomography is a geophysical imaging method to infer the 3-D interior structure of the solid Earth. Most commonly formulated as a linear(ized) inverse problem, it maps differences between observed and expected wave travel times to interior regions where waves propagate faster or slower than the expected average. The Earth's interior is typically parametrized by a single kind of localized basis function. Here we present an alternative approach that uses matching pursuits on large dictionaries of basis functions. Within the past decade the (Learning) Inverse Problem Matching Pursuits ((L)IPMPs) have been developed. They combine global and local trial functions. An approximation is built in a so-called best basis, chosen iteratively from an intentionally overcomplete set or dictionary. In each iteration, the choice for the next best basis element reduces the Tikhonov-Phillips functional. This is in contrast to classical methods that use either global or local basis functions. The LIPMPs have proven its applicability in inverse problems like the downward continuation of the gravitational potential as well as the MEG-/EEG-problem from medical imaging. Here, we remodel the Learning Regularized Functional Matching Pursuit (LRFMP), which is one of the LIPMPs, for travel time tomography in a ray theoretical setting. In particular, we introduce the operator, some possible trial functions and the regularization. We show a numerical proof of concept for artificial travel time delays obtained from a contrived model for velocity differences. The corresponding code is available at https://doi.org/10.5281/zenodo.8227888 under the licence CC-BY-NC-SA 3.0 DE

How and when plume zonation appeared during the 132 Myr evolution of the Tristan Hotspot

Increasingly, spatial geochemical zonation, present as geographically distinct, subparallel trends, is observed along hotspot tracks, such as Hawaii and the Galapagos. The origin of this zonation is currently unclear. Recently zonation was found along the last B70 Myr of the Tristan-Gough hotspot track. Here we present new Sr–Nd–Pb–Hf isotope data from the older parts of this hotspot track (Walvis Ridge and Rio Grande Rise) and re-evaluate published data from the Etendeka and Parana flood basalts erupted at the initiation of the hotspot track. We show that only the enriched Gough, but not the less-enriched Tristan, component is present in the earlier (70–132 Ma) history of the hotspot. Here we present a model that can explain the temporal evolution and origin of plume zonation for both the Tristan-Gough and Hawaiian hotspots, two end member types of zoned plumes, through processes taking place in the plume sources at the base of the lower mantle

Community-Driven Data Analysis Training for Biology

The primary problem with the explosion of biomedical datasets is not the data, not computational resources, and not the required storage space, but the general lack of trained and skilled researchers to manipulate and analyze these data. Eliminating this problem requires development of comprehensive educational resources. Here we present a community-driven framework that enables modern, interactive teaching of data analytics in life sciences and facilitates the development of training materials. The key feature of our system is that it is not a static but a continuously improved collection of tutorials. By coupling tutorials with a web-based analysis framework, biomedical researchers can learn by performing computation themselves through a web browser without the need to install software or search for example datasets. Our ultimate goal is to expand the breadth of training materials to include fundamental statistical and data science topics and to precipitate a complete re-engineering of undergraduate and graduate curricula in life sciences. This project is accessible at https://training.galaxyproject.org. We developed an infrastructure that facilitates data analysis training in life sciences. It is an interactive learning platform tuned for current types of data and research problems. Importantly, it provides a means for community-wide content creation and maintenance and, finally, enables trainers and trainees to use the tutorials in a variety of situations, such as those where reliable Internet access is unavailable

Communicating over single-or multiple-antenna channels having both temporal and spectral fluctuations: United States Patent 8625691 (B2)

This inventions provides techniques for estimating both temporal and spectral channel fluctuations with the duration of a data symbol. Certain pulse shaping functions are Discrete Prolate Spheroidal Sequences (DPSSs) and are used primarily because of their relatively limited Inter-Symbol Interference (ISI) properties. During reception, these properties allow one or more parameters of a joint time-frequency channel model to be more easily determined. Once the one or more parameters are determined, they can be applied to received symbols to correct the temporal fluctuations, spectral fluctuations, or both of the channel over which a communication took place. The techniques may be adapted for the Multiple-In, Multiple-Out communication situation

Communicating over nonstationary nonflat wireless channels

We develop the concept of joint time-frequency estimation of wireless channels. The motivation is to optimize channel usage by increasing the signal-to-noise ratio (SNR) after demodulation while keeping training overhead at a moderate level. This issue is important for single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems but particularly so for the latter. Linear operators offer a general mathematical framework for symbol modulation in channels that vary both temporally and spectrally within the duration and bandwidth of one symbol. In particular, we present a channel model that assumes first-order temporal and spectral fluctuations within one symbol or symbol block. Discrete prolate spheroidal sequences (Slepian sequences) are used as pulse-shaping functions. The channel operator in the Slepian basis is almost tridiagonal, and the simple intersymbol interference pattern can be exploited for efficient and fast decoding using Viterbi's algorithm. To prove the concept, we use the acoustic channel as a meaningful physical analogy to the radio channel. In acoustic 2 × 2 MIMO experiments, our method produced estimation results that are superior to first-order time-only, frequency-only, and zeroth-order models by 7.0, 9.4, and 11.6 db. In computer simulations of cellular wireless channels with realistic temporal and spectral fluctuations, time-frequency estimation gains us 12 to 18 db over constant-only estimation in terms of received SNR when signal-to-receiver-noise is 10 to 20 db. The bit error rate (BER) decreases by a factor of two for a binary constellation. © 2005 IEEE