Technique of construction of a 1D inhomogeneous elastic model of the Earth’s crust

Category: 14-3
I.P. Dobrovolsky


UDC 550.340



I.P. Dobrovolsky


Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia



The homogeneous system of equations of the linear elasticity theory for the isotropic media with 1D continuous heterogeneity is considered. When applied to problems for half-space, double Fourier transform reduces the problem to ordinary differential equations. For some types of heterogeneity it is possible to receive solutions of these equations in a finite form. Generally differential equations are transformed to integral ones. Solutions of specific problems are given.

Keywords: continuous heterogeneity, stratified medium, double Fourier transformation.



Bateman H., Erdélyi A., Higher transcendental functions, vol. 1, Moscow: Nauka, 1973, 296 p. [in Russ].

Bateman H., Erdélyi A., Higher transcendental functions, vol. 2, Moscow: Nauka, 1973, 296 p. [in Russ].

Dobrovolskiy, I.P., Matematicheskaya teoriya podgotovki i prognoza tektonicheskogo zemletryaseniya (Mathematical theory of tectonic earthquake preparation and prediction), Moscow: Fizmatlit, 2009, 240 p.

Dobrovolsky, I.P., A piecewise homogeneous medium with plane-parallel boundaries, Geophysical Research Journal, 2012, vol. 13, no. 4, pp. 60–69.

Elsgolts, L.E., Differentsialnye uravneniya i variatsionnoye ischisleniye (Differential equations and calculus of variations), Moscow: Nauka, 1969, 424 p.

Gelfand, I.M. and Shilov, G.E., Obobshchennyie funktsii I deistviya nad nimi (Generalized functions and operations on them), Moscow: GIFML, 1959, 470 p.

Gradshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, sum, ryadov i proizvedeniy (Tables of integrals, sums, ranges and products), 4th edition, Moscow: GIFML, 1963, 1100 p.

Kamke, E., Spravochnik po obyknovennym differentsialnym uravneniyam (Ordinary differential equations: Reference book), Moscow: Nauka, 1976, 576 p.

Lomakin, V.A., Teoriya uprugosti neodnorodnyh tel (Elasticity theory of inhomogeneous bodies, Moscow: Izd-vo MGU, 1976, 368 p.

Naimark, M.A., Lineynyie differetsialnyie operatory (Linear differential operators), Moscow: GITTL, 1954, 352 p. 

Verlan A.F. and Sizikov V.S., Metody resheniya integralnyh uravneniy s programmami dlia EVM. Spravochnoye posobiye (Methods of solving integral equations with numeric codes. Reference book), Kiev: Nauk. dumka, 1978, 292 p.