OPTIMAL ONE-DIMENSIONAL INVERSION AND BOUNDING OF MAGNETOTELLURIC APPARENT RESISTIVITY AND PHASE MEASUREMENTS

The properties of the log of the admittance in the complex frequency p lane lead to an integral representation for one-dimensional magnetotel luric (MT) apparent resistivity and impedance phase similar to that fo und previously for complex admittance. The inverse problem of finding a one-dimensional model for MT data can then be solved using the same techniques as for complex admittance, with similar results. For instan ce, the one-dimensional conductivity model that minimizes the chi(2) m isfit statistic for noisy apparent resistivity and phase is a series o f delta functions. One of the most important applications of the delta function solution to the inverse problem for complex admittance has b een answering the question of whether or not a given set of measuremen ts is consistent with the modeling assumption of one-dimensionality. T he new solution allows this test to be performed directly on standard MT data, Recently, it has been shown that induction data must pass the same one-dimensional consistency test if they correspond to the polar ization in which the electric field is perpendicular to the strike of two-dimensional structure, This greatly magnifies the utility of the c onsistency test. The new solution also allows one to compute the upper and lower bounds permitted on phase or apparent resistivity at any fr equency given a collection of MT data, Applications include testing th e mutual consistency of apparent resistivity and phase data and placin g bounds on missing phase or resistivity data, Examples presented demo nstrate detection and correction of equipment and processing problems and verification of compatibility with two-dimensional B-polarization for MT data after impedance tensor decomposition and for continuous el ectromagnetic profiling data.