相关论文: Problems in computational helioseismology

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in…

We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…

In local helioseismology numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the equations of motions include convective modes…

A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…

Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar…

We apply time-distance helioseismology, local correlation tracking and Fourier spatial-temporal filtering methods to realistic supergranule scale simulations of solar convection and compare the results with high-resolution observations from…

Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is…

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…

Helioseismology has been widely acclaimed as having been a great success: it appears to have answered nearly all the questions that we originally asked, some with unexpectedly high precision. We have learned how the sound speed and matter…

A model-independent reconstruction of mechanical profiles (density, pressure) of the solar interior is outlined using the adiabatic sound speed and bouyancy frequency profiles. These can be inferred from helioseismology if both p- and…

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…

This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…

A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field,…

As helioseismology matures and turns into a precision science, modeling finite-frequency, geometric and systematical effects is becoming increasingly important. Here we introduce a general formulation for treating perturbations of arbitrary…

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained…

We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…