# Stochastic Inversion Method for Modeling the Electrical Conductivity Distribution within the Earth´s Mantle

**Author(s):**Jóźwiak W.

**Volume:**327

**Series:**C-78

The gist of the study of the Earth's interior is to make observations of natural physical processes at the surface and then to construct such models of the structure that would explain the observations in the best way. It is only in the case of the crust and partly the upper mantle that we are able to artificially generate phenomena to get information about their structure. Thus, unlike in other natural sciences, we cannot use repeatable experiments designed to study the nature of a specific phenomenon. Moreover, attempts to make laboratory investigations of physical parameters of the matter (conductivity, density, velocity of seismic waves, and the like) are also very diffcult, because it is impossible to reproduce natural conditions existing in the Earth's interior (very high pressures and temperatures). At the end it is worth to point out the temporal scale of some phenomena (e.g., secular changes), which is also a hindrance in making accurate and complete observations. Because of all the above factors, our knowledge is still incomplete and in some cases uncertain.

MONOGRAPHIC VOLUME

CONTENTS

1. Introduction, ...3

2. Structure of the Earth´s interior, ...5

2.1 The crust, ...6

2.2 The mantle, ...7

2.3 The core, ...8

2.4 Results of seismic tomography, ...9

3. Review of methods for constructing numerical models of conductivity distribution within the Earth, ...12

3.1 The beginnings of electromagnetic investigations of the Earth, ...12

3.2 Forward modeling, ...14

3.3 Inversion methods, ...15

4. Stochastic inversion method for deep geomagnetic soundings, ...20

4.1 Electromagnetic induction problem in a spherical-symmetric Earth, ...20

4.2 The stochastic method, ...32

4.3 The maximum likelihood method, ...33

4.4 Description of the program to realize the proposed method, ...36

5. Methods of experimental data treatment, ...39

5.1 Classical spherical-harmonic analysis method, ...39

5.2 Methods for regional transfer function determination, ...40

6. Review of the models of electrical conductivity distribution within the Earth, ...45

7. Examples of application of the stochastic method, ...55

7.1 Experimental data, ...55

7.2 Results of the inversion, ...57

8. Summary, ...64

References, ...67

Stochastyczna metoda inwersyjna w zastosowaniu do modelowania rozkładu przewodnictwa elektrycznego w płaszczu Ziemi

(streszczenie), ...74