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An alternative approach to acquire transmission travel time data is proposed, exploiting the geometry of devices commonly used in ultrasound computed tomography for medical imaging or non-destructive testing with ultrasonic waves. The intent is to (i) shorten acquisition time for devices with a large number of emitters, (ii) to eliminate the calibration step, and (iii) to suppress instrument noise. Inspired by seismic ambient field interferometry, the method rests on the active excitation of diffuse ultrasonic wavefields and the extraction of deterministic travel time information by inter-station correlation. To reduce stochastic errors and accelerate convergence, ensemble interferograms are obtained by phase-weighted stacking of observed and computed correlograms, generated with identical realizations of random sources. Mimicking an imaging setup, the accuracy of the travel time measurements as a function of the number of emitters and random realizations can be assessed both analytically and with spectral-element simulations for phantoms mimicking the model parameter distribution. The results warrant tomographic reconstructions with straight- or bent-ray approaches, where the effect of inherent stochastic fluctuations can be made significantly smaller than the effect of subjective choices on regularisation. This work constitutes a first conceptual study and a necessary prelude to future implementations.

SUMMARY Markov chain Monte Carlo (MCMC) sampling of solutions to large-scale inverse problems is, by many, regarded as being unfeasible due to the large number of model parameters. This statement, however, is only true if arbitrary, local proposal distributions are used. If we instead use a global proposal, informed by the physics of the problem, we may dramatically improve the performance of MCMC and even solve highly nonlinear inverse problems with vast model spaces. We illustrate this by a seismic full-waveform inverse problem in the acoustic approximation, involving close to 106 parameters. The improved performance is mainly seen as a dramatic shortening of the burn-in time (the time used to reach at least local equilibrium), but also the algorithm’s ability to explore high-probability regions (through more accepted perturbations) is potentially better. The sampling distribution of the algorithm asymptotically converges to the posterior probability distribution, but as with all other inverse methods used to solve highly nonlinear inverse problems we have no guarantee that we have seen all high-probability solutions in a finite number of iterations. On the other hand, with the proposed method it is possible to sample more high-probability solutions in a shorter time, without sacrificing asymptotic convergence. This may be a practical advantage for problems with many parameters and computer-intensive forward calculations.

We propose a guided dropout regularizer for deep networks based on the evidence of a network prediction defined as the firing of neurons in specific paths. In this work, we utilize the evidence at each neuron to determine the probability of dropout, rather than dropping out neurons uniformly at random as in standard dropout. In essence, we dropout with higher probability those neurons which contribute more to decision making at training time. This approach penalizes high saliency neurons that are most relevant for model prediction, i.e. those having stronger evidence. By dropping such high-saliency neurons, the network is forced to learn alternative paths in order to maintain loss minimization, resulting in a plasticity-like behavior, a characteristic of human brains too. We demonstrate better generalization ability, an increased utilization of network neurons, and a higher resilience to network compression using several metrics over four image/video recognition benchmarks.

In state-of-the-art deep single-label classification models, the top- $k$ k $(k=2,3,4, \dots)$ ( k = 2 , 3 , 4 , ⋯ ) accuracy is usually significantly higher than the top-1 accuracy. This is more evident in fine-grained datasets, where differences between classes are quite subtle. Exploiting the information provided in the top $k$ k predicted classes boosts the final prediction of a model. We propose Guided Zoom, a novel way in which explainability could be used to improve model performance. We do so by making sure the model has “the right reasons” for a prediction. The reason/evidence upon which a deep neural network makes a prediction is defined to be the grounding, in the pixel space, for a specific class conditional probability in the model output. Guided Zoom examines how reasonable the evidence used to make each of the top- $k$ k predictions is. Test time evidence is deemed reasonable if it is coherent with evidence used to make similar correct decisions at training time. This leads to better informed predictions. We explore a variety of grounding techniques and study their complementarity for computing evidence. We show that Guided Zoom results in an improvement of a model's classification accuracy and achieves state-of-the-art classification performance on four fine-grained classification datasets. Our code is available at https://github.com/andreazuna89/Guided-Zoom .

We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high‐dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low‐dimensional toy example and with high‐dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively., Geophysical Research Letters, 46 (2), ISSN:0094-8276, ISSN:1944-8007

Inverse problems where relationships are linear arise in many fields of science and engineering and, consequently, algorithms for solving them are widespread. However, when the size of the problem increases, the computational challenge becomes huge, hence, unless some simplifying assumptions are yielded, it becomes impossible to solve the problem. Our study addresses these issues for large linear(izable) inverse problems when the uncertainties can be modeled as Gaussian and the forward relationship and covariance matrices can be expressed in terms of Kronecker products. Under these conditions, we illustrate an algorithm capable of addressing very large problems with very limited storage requirements and much faster than the traditional approach. The result is a complete characterization of the posterior distribution in a probabilistic sense in terms of mean and covariance. We extend this method also to nonlinear problems where a Gauss-Newton algorithm is employed. Applications to reflection seismology, magnetic anomaly inversion and image restoration are presented.

[1] Here we discuss the nature of velocity heterogeneities seen in seismic tomography images of Earth's mantle whose origins and relation to thermochemical variations are yet to be understood. We illustrate this by inverting fundamental-mode and higher-order surface-wave phase velocities for radial models of the thermochemical and anisotropic structure of the mantle to 450 km depth. Dispersion data are linked to thermochemical parameters through a thermodynamic formalism for computing mantle mineral phase equilibria and physical properties. The inverse problem is solved using a probabilistic inference approach whereby robust uncertainty estimates are obtained. We find that both compositional and thermal anomalies are required if observations are to be satisfied. Mantle thermochemical variations extend to 250 km depth beneath western and central Australia and are characterized by increased Mg/Fe and Mg/Si values relative to surrounding mantle. Correlated herewith are thermal variations that closely follow surface tectonics. We also observe a strong contribution to lateral variations in structure and topography across the “410 km” seismic discontinuity from thermochemically induced phase transformations that appear much stronger than lateral variations immediately above and below. Inside the transition zone, a general decoupling of structure relative to that of the upper mantle occurs driven by a reversal in Mg/Si, while thermal anomalies are smoothed out. Comparison of presently derived shear-wave tomography models with other regional models is encouraging. Radial anisotropy is strongest at 150/200 km depth beneath oceanic/continental areas, respectively, and appears weak and homogeneous below. Finally, geoid anomalies are computed for a subset of sampled model and compared to observations.

In archaeological magnetic prospecting, most targets can be modeled by a single layer of constant burial depth and thickness. With this assumption, recovery of the magnetization distribution of the buried layer from magnetic surface measurements is a 2D deconvolution problem. Because this problem is ill posed, it requires regularization techniques to be solved. In analogy with image reconstruction, the solution showing the resolved subsoil features can be considered a focused version of the blurred and noisy magnetic image. Exploiting image deconvolution tools, two iterative reconstruction methods are applied to minimize the least-squares functional: the standard projected Landweber method and a proposed modification of the iterative space reconstruction algorithm. Different regularization functionals inject a priori information in the optimization problem, and the split-gradient method modifies the algorithms. Numerical simulations in the case of perfect knowledge of the impulse response functions demonstrate that the edge-preserving, total-variation functionals give the best results. An iterative semiblind deconvolution method to estimate the burial depth of the source layer was used with a real data set to test the effectiveness of the method.