Topography and minimization of the standard deviation in one‐dimensional magnetotelluric modelling

Abstract

In one‐dimensional magnetotelluric modelling the standard deviation e is often used as an indicator of the degree of fit between the field measurements and the calculated model response. The topography of e in the space of the model parameters has been studied and found to be rather simpler than expected. The absolute minimum seems to be quite isolated from other minima. In general no such other local minima were found. To find the minimum it was not necessary, therefore, to look for a computing routine capable of jumping out of localized minima. But the search routine had to be capable of moving along a valley with an exceedingly level floor, as the minimum is often at large distances from the initial model. In this respect it was important to work with logarithmic coordinates. Since the absolute minimum εmin can be found, it often becomes possible to split emin into three separate components: (1) the scatter of the original field data, (2) the departure of these data from one‐dimensionality and (3) a component that will occur if one attempts to model the data with a structure comprising too few layers. Knowing this last contribution it becomes easy to decide which is the smallest number of layers necessary to model a given data Sci. Copyright © 1981, Wiley Blackwell. All rights reserved