Discrete frequency inequalities for magnetotelluric impedances of one-dimensional conductors

For the one-dimensional magnetotelluric inverse problem the ties between the impedances at neighbouring frequencies, reflecting the analytical properties of the transfer function, are expressed in terms of inequalities between the data. After the derivation of some elementary necessary constraints for data sets with two or three frequencies, a set of necessary and sufficient conditions warranting the existence of a one-dimensional conductivity model in the general M-frequency case is given. This set of constraints characterizes a 1-D data set by the signs of 2M determinants derived from the data.           ARK: https://n2t.net/ark:/88439/y087338 Permalink: https://geophysicsjournal.com/article/228 &nbsp

On mapping seafloor mineral deposits with central loop transient electromagnetics

Electromagnetic methods are commonly employed in exploration for land-based mineral deposits. A suite of airborne, land, and borehole electromagnetic techniques consisting of different coil and dipole configurations have been developed over the last few decades for this purpose. In contrast, although the commercial value of marine mineral deposits has been recognized for decades, the development of suitable marine electromagnetic methods for mineral exploration at sea is still in its infancy. One particularly interesting electromagnetic method, which could be used to image a mineral deposit on the ocean floor, is the central loop configuration. Central loop systems consist of concentric transmitting and receiving loops of wire. While these types of systems are frequently used in land-based or airborne surveys, to our knowledge neither system has been used for marine mineral exploration. The advantages of using central loop systems at sea are twofold: (1) simplified navigation, because the transmitter and receiver are concentric, and (2) simplified operation because only one compact unit must be deployed. We produced layered seafloor type curves for two particular types of central loop methods: the in-loop and coincident loop configurations. In particular, we consider models inspired by real marine mineral exploration scenarios consisting of overburdens 0 to 5 m thick overlying a conductive ore body 5 to 30 m thick. Modeling and resolution analyses showed that, using a 50 m(2) transmitting loop with 20 A of current, these two configurations are useful tools to determine the overburden depth to a conductive ore deposit and its thickness. In the most extreme case, absolute voltage errors on the order of 10 nV are required to resolve the base of a 30 m thick ore deposit. Whether such noise floors can be achieved in real marine environments remains to be seen

Construction of conductance bounds from magnetotelluric impedances

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 σ – (z) and σ + (z). The sharpening of conductance bounds by incorporating a priori information is illustrated by an example.           ARK: https://n2t.net/ark:/88439/y078099 Permalink: https://geophysicsjournal.com/article/237 &nbsp