Comment on: ‘One‐dimensional magnetotelluric inversion using an adaptation of Zohdy's resistivity method’ by B.A. Hobbs and C.C. Dumitrescu

Abstract

The principle of Zohdy’s (1989) algorithm has been applied by Hobbs and Dumitrescu (1997) to magnetotelluric (MT) data, yielding a layered resistivity model with the number of layers corresponding to the number of discretely measured frequencies. A similar approach was used earlier by Xu and Liu (1995). Both Hobbs and Dumitrescu (1997) and Xu and Liu (1995) expand the concept of Zohdy’s (1989) algorithm into the MT inverse problem, and use the same resistivity refinement formulae to adjust the model parameters, namely equation (23) of Hobbs and Dumitrescu (1997) and equation (8) of Xu and Liu (1995). The advantages of their procedures are obvious, as mentioned by Hobbs and Dumitrescu (1997), i.e. that no extraneous information has to be provided and that this scheme produces a gradation of resistivity with depth, differing from the smooth model of Occam’s inversion (Constable, Parker and Constable 1987). When applying Zohdy’s (1989) method to magnetotelluric data, a transformation from the conventional frequency scale to a length scale is a prerequisite. Hobbs and Dumitrescu (1997), as well as Xu and Liu (1995), suggested using the Bostick (1977) or the Schmucker (1970) transformations to construct suitable initial model depths and resistivities in their procedures. After constructing an initial model, the depth scale is first changed by a multiplicative factor, through minimization of the x 2 misfit. However, we do not believe that it is always true that these transformations produce the appropriate depths of the model. We present an example where these transformations provide a misleading estimation of model depths, and where a model with an unsatisfactory fit is produced by these procedures. Hence this scheme does not provide a high enough confidence in the inverse model parameters. The COPROD data (Fig. 1) from an MT site in Scotland obtained by Jones and Hutton (1979) were widely distributed for the purpose of comparing one-dimensional inversions (e.g. Constable, Parker and Constable 1987; Parker and Booker 1996; Zhang and Paulson 1997). A significant feature of the COPROD MT data is the upward bias from 458 in the phase at the five early periods. Although the large error bars in the phase show a great uncertainty at 28.5 and 38.5 s, the extrapolated phase values of these two periods from the three later phase data, i.e. at the periods of 52.1,