ISSN:
1365-246X
Quelle:
Blackwell Publishing Journal Backfiles 1879-2005
Thema:
Geologie und Paläontologie
Notizen:
Of particular importance in a non-unique geophysical inverse problem is the unique solution that yields extremal values of a model property of geophysical interest. In the 1-D magnetotelluric inverse problem, we choose the arithmetic average 〈inlineGraphic alt="inline image" href="urn:x-wiley:0956540X:GJI683:GJI_683_mu1" location="equation/GJI_683_mu1.gif"/〉(z1, z2) of the electrical conductivity σ(z) in a given depth range z1≤ z ≤ z2 as such a property, and determine the upper and lower bounds of 〈inlineGraphic alt="inline image" href="urn:x-wiley:0956540X:GJI683:GJI_683_mu2" location="equation/GJI_683_mu2.gif"/〉(z1, z2) such that σ(z) is compatible with given (noisy) complex impedances for M frequencies. In addition, we impose an a priori constraint on σ(z) such that σ−≤σ(z) ≤σ+, 0 ≤ z 〈 ∞, with pre-assigned bounds σ− and σ+.For a modest number of data, it is possible to derive the exact extremal models. In the one-frequency case (M = 1) the extremal models consist of a sequence of uniform layers with conductivities σ− and σ+ terminated by an infinite periodic sequence of layers with thicknesses π/2 times the local penetration depth (λ/4-plates). For M 〉 1, in addition to uniform layers, transitional layers with a continuous conductivity distribution occasionally occur, and the model structure at great depth asymptotically approaches the periodic structure of the lowest frequency. If a priori information is not incorporated (σ−= 0, σ+=∞), the extremal models consist—in the case of exact data—of at least M + 1 thin sheets separated by insulators. Therefore the exact extremal models are highly structured. The model structure for selected data sets is displayed in triangular (z1, z2)-diagrams, which for M 〉 1 clearly display the complexity of the underlying non-linear problem.As a by-product of the constrained one-frequency case, we determine the exact range of possible values of apparent conductivities and phases that can be obtained for given values of σ− and σ+.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1111/j.1365-246X.1995.tb06884.x
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