Related papers: Multi-Channel Three-Dimensional SOLA Inversion for…
Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic…
Helioseismic techniques such as ring-diagram analysis have often been used to determine the subsurface structural differences between solar active and quiet regions. Results obtained by inverting the frequency differences between the…
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spaces. In particular, our inverse results are now formulated…
Recent progress in realistic simulations of solar convection have given us an unprecedented opportunity to evaluate the robustness of solar interior structures and dynamics obtained by methods of local helioseismology. We present results of…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
Helioseismic inversions reveal a major discrepancy in sound speed between the Sun and the standard solar model just below the base of solar convection zone. We demonstrate that this discrepancy is caused by the inherent shortcomings of the…
Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath.…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
Extracting subsurface velocity information from seismic data is mainly an undetermined problem that requires injecting a priori information to constrain the inversion process. Machine learning has offered a platform to do so through the…
The solar tachocline at the bottom of the convection zone is an important region for the dynamics of the Sun and the solar dynamo. In this region, the sound speed inferred by global helioseismology exhibits a bump of approximately 0.4%…
Helioseismology studies the structure and dynamics of the Sun's interior by observing oscillations on the surface. These studies provide information about the physical processes that control the evolution and magnetic activity of the Sun.…
This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…
We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse reconstruction problem and, hence, can be solved using compressive sensing (CS) algorithms. This paper proposes solutions for two notorious problems in this field:…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
For numerous earth observation applications, one may benefit from various satellite sensors to address the reconstruction of some process or information of interest. A variety of satellite sensors deliver observation data with different…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
The inverse problem in Seismology is tackled in this paper under three particular circumstances. First, the inverse problem is defined as the determination of the seismic-moment tensor from the far-field seismic waves (P and S waves). We…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…