Non-linear inverse geothermal problems

Name: Non-linear inverse geothermal problems
Rating: 5 (1 reviews)

Dennis Wokiyi

nov. 2017 · Linköping Studies in Science and Technology. Thesis Bok 10 · Linköping University Electronic Press

5,0

1 anmeldelse

E-bok

Sider

Vurderinger og anmeldelser blir ikke kontrollert Finn ut mer

Om denne e-boken

The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard’s definition of well-posedness.

We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces.

Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well- posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.

Vurderinger og anmeldelser

5,0

1 anmeldelse

Vurder denne e-boken

Fortell oss hva du mener.

Hvordan lese innhold

Smarttelefoner og nettbrett

Installer Google Play Bøker-appen for Android og iPad/iPhone. Den synkroniseres automatisk med kontoen din og lar deg lese både med og uten nett – uansett hvor du er.

Datamaskiner

Du kan lytte til lydbøker du har kjøpt på Google Play, i nettleseren på datamaskinen din.

Lesebrett og andre enheter

For å lese på lesebrett som Kobo eReader må du laste ned en fil og overføre den til enheten din. Følg den detaljerte veiledningen i brukerstøtten for å overføre filene til støttede lesebrett.

Rapporter ulovlig innhold