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Constable, SC, Parker RL, Constable CG.  1987.  Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics. 52:289-300.   10.1190/1.1442303   AbstractWebsite

The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models. To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model. Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric‐resistivity inversion, demonstrate the method and show it to have practical application.

Farrell, WE, McKenzie DP, Parker RL.  1969.  On the note emitted from a mug while mixing instant coffee. Proceedings of the Cambridge Philosophical Society-Mathematical and Physical Sciences. 65:365-367. AbstractWebsite
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Parker, RL, Booker JR.  1996.  Optimal one-dimensional inversion and bounding of magnetotelluric apparent resistivity and phase measurements. Physics of the Earth and Planetary Interiors. 98:269-282.   10.1016/s0031-9201(96)03191-3   AbstractWebsite

The properties of the log of the admittance in the complex frequency plane lead to an integral representation for one-dimensional magnetotelluric (MT) apparent resistivity and impedance phase similar to that found 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 instance, the one-dimensional conductivity model that minimizes the chi(2) misfit statistic for noisy apparent resistivity and phase is a series of delta functions. One of the most important applications of the delta function solution to the inverse problem for complex admittance has been answering the question of whether or not a given set of measurements is consistent with the modeling assumption of one-dimensionality. The 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 polarization in which the electric field is perpendicular to the strike of two-dimensional structure, This greatly magnifies the utility of the consistency test. The new solution also allows one to compute the upper and lower bounds permitted on phase or apparent resistivity at any frequency given a collection of MT data, Applications include testing the mutual consistency of apparent resistivity and phase data and placing bounds on missing phase or resistivity data, Examples presented demonstrate 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 electromagnetic profiling data.