# Index Geophysics

## Construction of conductance bounds from magnetotelluric impedances

### Item

#### Title (Dublin Core)

en-US Construction of conductance bounds from magnetotelluric impedances

#### Description (Dublin Core)

en-US Whereas any finite set of impedance data does not constrain the electrical conductivity σ (z) at a fixed level z in a 1D-model, the conductance function S (z2) as the depth-integrated conductivity from the surface to the depth z2 will be constrained. Assuming only the non-negativity of σ (z), it is shown that for a given depth z2 the models generating the lower and upper bound of S (z2) consist of a sequence of thin sheets. The determination of the positions of the thin sheets and their conductances leads to a system of nonlinear equations. As a limitation the present approach requires the existence of a model, which exactly fits the data. The structure of the extremal models as a function of z2 is discussed in examples with a small number of frequencies. Moreover, it is shown that any set of complex 1D impedances for M frequencies can be represented by a partial fraction expansion involving not more than 2M (positive) constants. For exactly 2M constants there are two complementary representations related to the lower and upper bound of S (z2). For the simple one-frequency case, a more general extremal problem is briefly considered, where the admitted conductivities are constrained by a priori bounds σ – (z) and σ + (z) such that σ – (z) ≤ σ (z) ≤ σ + (z). In this case, the extremal models for S (z2) consist of a sequence of sections with alternating conductivities&nbsp;σ – (z) and σ + (z). The sharpening of conductance bounds by incorporating a priori information is illustrated by an example.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ARK: https://n2t.net/ark:/88439/y078099
&nbsp;

Weidelt, P.

#### Subject (Dublin Core)

en-US Electromagnetic induction
en-US Inverse problem
en-US Extremal models
en-US Methods

#### Publisher (Dublin Core)

en-US Journal of Geophysics

1985-08-29

#### Type (Dublin Core)

info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
en-US Peer-reviewed Article

application/pdf

#### Identifier (Dublin Core)

https://journal.geophysicsjournal.com/JofG/article/view/237

#### Source (Dublin Core)

en-US Journal of Geophysics; Vol 57 No 1 (1985): Journal of Geophysics; 191-206
2643-2986
2643-9271

eng

#### Relation (Dublin Core)

https://journal.geophysicsjournal.com/JofG/article/view/237/197