Inverse problems for second-order elliptic equations

Lavrentiev,; Romanov,; Vasiliev,

doi:10.1007/bfb0067433

Cited by 3 publications

(2 citation statements)

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“…As I mentioned before, there are many scientist and researcher have been working on inverse scattering and more specifically on inverse source problems. To expand your knowledge and further mathematical development in this field of research, please see the result authors in [29][30][31][32][33][34][35][36][37][38][39][40][41], which were discussed different aspects of the problems.…”

Section: Discussionmentioning

confidence: 99%

Inverse Scattering Source Problems

Entekhabi¹

2020

Advances in Complex Analysis and Applications

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The purpose of this chapter is to discuss some of the highlights of the mathematical theory of direct and inverse scattering and inverse source scattering problem for acoustic, elastic and electromagnetic waves. We also briefly explain the uniqueness of the external source for acoustic, elastic and electromagnetic waves equation. However, we must first issue a caveat to the reader. We will also present the recent results for inverse source problems. The resents results including a logarithmic estimate consists of two parts: the Lipschitz part data discrepancy and the high frequency tail of the source function. In general, it is known that due to the existence of non-radiation source, there is no uniqueness for the inverse source problems at a fixed frequency.

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Section: Discussionmentioning

confidence: 99%

Inverse Scattering Source Problems

Entekhabi¹

2020

Advances in Complex Analysis and Applications

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“…Roma nov, M.M. Lavrentiev [Lavrentiev, Romanov, 1966], Aki K., Christoffersson A., and Hu sebye E.S. [Aki et al, 1977], defi ning the relative correction to an a priori 1D reference model of velocity or slowness (the inverse value to the velocity); 2) the second approach represents the ideas related to the inversion of common travel-time fields, namely localization of velocity heterogeneities, and which represents the solution in the true velocities (the method of Taylor's approximation proposed by V.S.…”

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confidence: 99%

The deep structure of the Zagros mountain system according to Taylor approximation seismic tomography data

Tsvetkova,

Gintov,

Bugaienko

et al. 2023

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The seismic tomographic model obtained by the Taylor approximation method provides new constraints on the Earth’s crust and mantle structure beneath the Zagros mountain system at depths of 50—850 km. Based on structural geology and seismic tomography data, we divide the Zagros into Northwestern (Kirkuk, Lurestan, and Dezful regions) and Central (Kazerun and Fars regions) parts. The Central Zagros was formed due to subduction-collision tectonics, and the Northwestern Zagros was formed due to a collision-shear (transpression) tectonic process. Based on the 3D P-velocity model of the Zagros and its surrounding mantle, a high-velocity distal southeastern part of the Arabian Plate was established, subducting under the Central Zagros and the Iranian Plate, following the subduction of the Neotethys. This slab covers an area of 23—32°NL — 49—58°EL, i.e., the Bay of Bengal, the Central Zagros, and the southern part of the Iranian Plate. The maximum horizontal extent of the submerging part of the Arabian slab is 800—1100 km, and the maximum submersion depth is 450—500 km. A number of projections on the horizontal plane of the lines of intersection of the surface of the subducting Arabian Plate with horizontal sections of 50, 100, 200, 300, and 400 km were constructed. We obtained the direction of plate plunging, which in different areas varies from northern to northeastern 30—45°. In the Northwestern Zagros, according to the model, traces of subduction do not appear; however, right-lateral strike-slip deformations along the Main Recent Fault are visible and continue now in the crust. The difference in the types of deformation of the Northwestern and Central Zagros is most likely due to the features of the outlines of the eastern edge of the Arabian Plate and the complex nature of its movements. Analysis of earthquake mechanisms in 1977—2001 shows that the movement of the Arabian Plate could have occurred with frequent alternation in the S-N and N-E directions due to the alternation of spreading processes in the Gulf of Aden and the southeastern part of the Red Sea.

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