Search results for "seismologia"
showing 2 items of 2 documents
Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in Cartesian coordinates
2018
With a Hamilton–Jacobi equation in Cartesian coordinates as a starting point, it is common to use a system of ordinary differential equations describing the continuation of first-order derivatives of phase-space perturbations along a reference ray. Such derivatives can be exploited for calculating geometrical spreading on the reference ray and for establishing a framework for second-order extrapolation of traveltime to points outside the reference ray. The continuation of first-order derivatives of phase-space perturbations has historically been referred to as dynamic ray tracing. The reason for this is its importance in the process of calculating amplitudes along the reference ray. We exte…
Kinemaattinen inversio-ongelma pallosymmetrisellä monistolla
2017
Tutkielman pääaiheena on maanjäristysaaltoihin ja Maan sisärakenteen tutkimiseen liittyvä käänteinen kinemaattinen ongelma. Maapalloa mallinnetaan kolmiulotteisella kompaktilla reunallisella monistolla \(\bar{B}^3(0, R)\), jonka säde normitetaan ykköseksi \(R=1\). Aaltorintamat kulkevat pitkin geodeeseja, jotka sijaitsevat kokonaan avoimessa pallossa \(B^3(0, 1)\) lukuun ottamatta päätepisteitä, jotka ovat reunalla \(S^2(0, 1)\). Symmetrioiden nojalla tarkastelu voidaan siirtää tasoon \(\mathbb{R}^2\), jossa riittää tutkia kiekon \(\bar{B}^2(0, 1)\) geodeeseja. Äänennopeus \(v=v(r)\) oletetaan isotrooppiseksi ja aidosti positiiviseksi \(C^{1,1}([0, 1])\)-funktioksi, jolle \(v^{\prime}(0)=0\…