Depth profiling of the thermal diffusivity of an opaque solid: Formulation of the inverse problem based on perturbation theory

1999 ◽  
Author(s):  
J. F. Power ◽  
J. Karanicolas
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Thermal Diffusivity ◽  
Depth Profiling

Linearization of the eikonal equation

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1631-1632 ◽  
Author(s):  
David F. Aldridge
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Path Integral ◽  
Seismic Waves ◽  
Eikonal Equation ◽  
Nonlinear Inverse Problem ◽  
Nonlinear Functional ◽  
Arrival Times ◽  
Traveltime Tomography ◽  
Fermat's Principle

Seismic traveltime tomography is a nonlinear inverse problem wherein an unknown slowness model is inferred from the observed arrival times of seismic waves. Nonlinearity arises because the raypath connecting a given source and receiver depends on the slowness. Specifically, if L(s) designates a raypath through the slowness model s between two fixed endpoints, then the path integral for traveltime [Formula: see text] is a nonlinear functional of s because it does not, in general, satisfy the superposition condition (i.e., [Formula: see text] where [Formula: see text] and [Formula: see text] are two different slowness models). The tomographic inverse problem can be solved after linearizing the traveltime expression about a known slowness model [Formula: see text]. This linearized expression is usually obtained by appealing to Fermat’s principle (e.g., Nolet, 1987). Alternately, the required relation can be rigorously derived via ray‐perturbation theory (Snieder and Sambridge, 1992). The purpose of this note is to present a straightforward derivation of the same result by linearizing the eikonal equation for traveltimes. Wenzel (1988) adopts this approach, but his method of proof cannot be generalized to heterogeneous 3-D media. A full 3-D treatment is given here. The proof is remarkably simple, and thus it is quite possible that others have discovered it previously.

scholarly journals On a Spectral Inverse Problem in Perturbation Theory

2021 ◽  
Vol 17 (1) ◽  
pp. 95-115
Author(s):  
V.A. Marchenko ◽  
◽  
A.V. Marchenko ◽  
V.A. Zolotarev ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Spectral Inverse Problem

Thermal diffusivity measurement of insulating material using infrared thermography

2012 ◽  
Vol 20 (1) ◽  
Author(s):  
S. Chudzik
Keyword(s):  
Inverse Problem ◽  
Thermal Diffusivity ◽  
Three Dimensional ◽  
Infrared Camera ◽  
Test Method ◽  
Heat Diffusion ◽  
Three Dimensional Model ◽  
Thermal Diffusivity Measurement ◽  
Insulating Material ◽  
Thermal Insulating

AbstractThe article presents the results of research developing methods for determining the coefficient of thermal diffusivity of thermal insulating material. This method applies a periodic heating as an excitation and an infrared camera is used to measure the temperature distribution on the surface of tested material. In simulation study, the usefulness of known analytical solution of the inverse problem was examined using a three-dimensional model of the phenomenon of heat diffusion in the sample of tested material. To solve the coefficient inverse problem, an approach using artificial neural network is proposed. The measurements were performed on an experimental setup equipped with a ThermaCAM PM 595 infrared camera and frame grabber. The experiment allowed to verify the chosen 3D model of heat diffusion phenomenon and to determine suitability of the proposed test method.

scholarly journals Parameter identification and sensitivity analysis to a thermal diffusivity inverse problem

2015 ◽  
Vol 8 (3) ◽  
pp. 385-400
Author(s):  
Brian Leventhal ◽  
Xiaojing Fu ◽  
Kathleen Fowler ◽  
Owen Eslinger
Keyword(s):  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Thermal Diffusivity ◽  
Parameter Identification

scholarly journals INVERSE HEAT TRANSPORT PROBLEMS FOR COEFFICIENTS IN TWO‐LAYER DOMAINS AND METHODS FOR THEIR SOLUTION

2002 ◽  
Vol 7 (2) ◽  
pp. 217-228 ◽  
Author(s):  
S. Guseinov ◽  
A. Buikis
Keyword(s):  
Inverse Problem ◽  
Thermal Diffusivity ◽  
Inverse Problems ◽  
Heat Transport ◽  
Transport Process ◽  
Direct Problem ◽  
Piecewise Constant Function ◽  
Algebraic Equations ◽  
Heat Transport Process

In various fields of science and technology it is often necessary to solve inverse problems, where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infringement of the natural causal relationships can entail incorrectness of the mathematical stating of inverse problems. Therefore the development of efficient methods for solving such problems allows one to considerably simplify experimental research and to increase the accuracy and reliability of the obtained results due to certain complication of algorithms for processing the experimental data. The problem of determination of thermal diffusivity coefficients considering other known characteristics of heat transport process is among incorrect inverse problems. These inverse problems for coefficients are quite difficult even in the case of homogeneous media. In this paper it is supposed that the heat transport equation is non‐homogeneous and an algorithm for determination of the thermal diffusivity coefficients for both the media is proposed. At the first step, the non‐homogeneous inverse problem with piecewise‐constant function of non‐homogeneity is solved. For this auxiliary inverse problem, the proposed method allows one to determine both the coefficients of thermal diffusivity and to restore the heat transport process without any additional information, i.e. the algorithm also solves the direct problem. Then the initial non‐homogeneous inverse problem with a piecewise‐continuous function of non‐homogeneity is solved. The proposed method reduces the non‐homogeneous inverse problem for coefficients to a set of two transcendent algebraic equations. Finally, the analytical solution to direct problem is obtained using Green's function.

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