Two-dimensional anisotropic magnetotelluric inversion using a limited-memory quasi-Newton method

We have developed a two-dimensional (2D) anisotropic magnetotelluric (MT) inversion algorithm that uses a limited-memory quasi-Newton (QN) method for bounds-constrained optimization. This algorithm solves the inverse problem, which is non-linear, by iterative minimization of linearized approximations of the classical Tikhonov regularized objective function. The QN approximation for the Hessian matrix is only implemented for the data-misfit term of the objective function; the part of the Hessian matrix for the regularization is explicitly computed. This adjustment results in a better approximation for the data-misfit term in particular. The inversion algorithm considers arbitrary anisotropy, and is extended for special cases including azimuthal and vertical anisotropy. The algorithm is shown to be stable and converges rapidly for several simple anisotropic models. These synthetic tests also confirm that the anisotropic inversion produces a correct anomaly with different but equivalent anisotropic parameters. We also consider a complex 2D anisotropic model; the successful results for this model further confirm that the inversion algorithm presented here, which uses the novel modified limited-memory QN approach, is capable of solving the 2D anisotropic magnetotelluric inverse problem. Finally, we present a practical application on MT data collected in northern Tibet to demonstrate the effectiveness and stability of our algorithm.

Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

Compressed sensing (CS) has been proposed to improve the efficiency of signal processing by simultaneously sampling and compressing the signal of interest under the assumption that the signal is sparse in a certain domain. This paper aims to improve the CS system performance by constructing a novel sparsifying dictionary and optimizing the measurement matrix. Owing to the adaptability and robustness of the Takenaka–Malmquist (TM) functions in system identification, the use of it as the basis function of a sparsifying dictionary makes the represented signal exhibit a sparser structure than the existing sparsifying dictionaries. To reduce the mutual coherence between the dictionary and the measurement matrix, an equiangular tight frame (ETF) based iterative minimization algorithm is proposed. In our approach, we modify the singular values without changing the properties of the corresponding Gram matrix of the sensing matrix to enhance the independence between the column vectors of the Gram matrix. Simulation results demonstrate the promising performance of the proposed algorithm as well as the superiority of the CS system, designed with the constructed sparsifying dictionary and the optimized measurement matrix, over existing ones in terms of signal recovery accuracy.

Irreversibility and alternate minimization in phase field fracture: a viscosity approach

This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an $$L^{2}$$ L 2 -penalization in the phase field variable, driven by a viscous parameter $$\delta >0$$ δ > 0 , and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t. time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for $$\delta >0$$ δ > 0 and then consider the vanishing viscosity limit $$\delta \rightarrow 0$$ δ → 0 .

Eigenvector Model Descriptors for the Seismic Inverse Problem

<p>We consider the quantitative inverse problem for the recovery of subsurface Earth's properties, which relies on an iterative minimization algorithm. Due to the scale of the domains and lack of apriori information, the problem is severely ill-posed. In this work, we reduce the ill-posedness by using the ``regularization by discretization'' approach: the wave speed is described by specific bases, which limits the number of coefficients in the representation. Those bases are associated with the eigenvectors of a diffusion equation, and we investigate several choices for the PDE, that are extracted from the field of image processing. We first compare the efficiency of these model descriptors to accurately capture the variation with a minimal number of coefficients. In the context of sub-surface reconstruction, we demonstrate that the method can be employed to overcome the lack of low-frequency contents in the data. We illustrate with two and three-dimensional acoustic experiments.</p>

Densities, infrared band strengths, and optical constants of solid methanol

Contact. The increasing capabilities of space missions like the James Webb Space Telescope or ground-based observatories like the European Extremely Large Telescope demand high quality laboratory data of species in astrophysical conditions for the interpretation of their findings. Aims. We provide new physical and spectroscopic data of solid methanol that will help to identify this species in astronomical environments. Methods. Ices were grown by vapour deposition in high vacuum chambers. Densities were measured via a cryogenic quartz crystal microbalance and laser interferometry. Absorbance infrared spectra of methanol ices of different thickness were recorded to obtain optical constants using an iterative minimization procedure. Infrared band strengths were determined from infrared spectra and ice densities. Results. Solid methanol densities measured at eight temperatures vary between 0.64 g cm−3 at 20 K and 0.84 g cm−3 at 130 K. The visible refractive index at 633 nm grows from 1.26 to 1.35 in that temperature range. New infrared optical constants and band strengths are given from 650 to 5000 cm−1 (15.4–2.0 μm) at the same eight temperatures. The study was made on ices directly grown at the indicated temperatures, and amorphous and crystalline phases have been recognized. Our optical constants differ from those previously reported in the literature for an ice grown at 10 K and subsequently warmed. The disagreement is due to different ice morphologies. The new infrared band strengths agree with previous literature data when the correct densities are considered.