Reply to “Three-dimensional galvanic distortion of three-dimensional regional conductivity structures: Comment on Three-dimensional joint inversion for magnetotelluric resistivity and static shift distributions in complex media” by A. G. Jones

Abstract

[1] Static shift and spatial aliasing are the bane of magnetotelluric exploration and Jones [2011] provides two useful comments on the issue of accounting for static shift in 3-D inversion, one concerning Sasaki and Meju [2006] and another concerning Zhdanov et al. [2011]. This is followed by an overview of well-known impedance tensor relationships in magnetotelluric data analysis (equations (1)–(9)), on which he based his comments. The main tenet of his discussion is that in a fully 3-D situation, all the elements of the impedance tensor (Zxy, Zxx, Zyx and Zyy) are nonzero and should be considered in any 3-D inversion approach. In practice, for geological interpretation, we commonly define apparent resistivities and phases using Zxy and Zyx, which permit an assessment of whether they are influenced by galvanic distortion (i.e., static shift) from their expected background levels especially by comparison with data from coincident alternative EM soundings which are less affected by small size near-surface heterogeneities such as the transient EM method [e.g., Sternberg et al., 1988; Meju, 1996, 2005]. There are other ways of determining and removing static shifts using only MT data as mentioned by Jones [2011] and these have their strengths and weaknesses. Whatever the adopted approach, for a long time, static shift is commonly identified on apparent resistivity sounding curves while the phase curves are assumed to be unaffected, even though Jones [2011] use physical arguments to suggest that phase mixing rather than geometric amplitude shifts obtains in complex 3-D environments at all spatial scales. Regional galvanic distortions are fully accounted for in 3-D inversions within the accuracy of the forward modeling unless the model discretization is inadequate. However, there is one type of galvanic distortions that cannot be handled in the conventional 3-D MT inversion. That is the distortions due to near-surface inhomogeneities located just below the receiver sites, because such inhomogeneities cannot be accurately represented by the given model discretization in the inversion. These include random conductive weathered patches (model A of Sasaki and Meju [2006]), elongate conductors such ancient stream channels (model B of Sasaki and Meju [2006]) and covered waste dump sites, all common in real life. The Sasaki and Meju [2006] approach to removing static shifts was introduced to tackle this type of galvanic distortions, assuming that the distortions can be represented by static shifts (and it was shown in Figures 3 and 5 that the phases are unaffected for model A and are partially affected at higher frequencies for model B). [3] It is important to stress that the purpose of inversion is to find a model that explains the observed data quantitatively. In the first experiment in our paper (model A), we show that joint estimation of resistivities and static shifts improve the inversion image in the presence of surficial inhomogeneities that are too small to be recovered by the conventional 3-D inversion. In the next experiment (model B), we show that our method is still effective in recovering resistivity distribution even if the effects of near-surface structure include frequency-dependent shifts. The necessary constraint, which serves as a form of a priori information, is provided by the assumption of a Gaussian or a zero-sum distribution of static shifts (justified by numerous alternative EM field measurements) in our inverse problem formulation (i.e., the β2S term in equation (1) above), not by the assumption that the MT phase is unaffected by static shift. While we put emphasis on static shifts arising from the weathered surficial layer, deeper structures may yield static effects if the period range starts at, say, 10 s. This is just a matter of the spatial scale of operation. Our 3-D algorithm is full domain and can handle such a situation. It should also be borne in mind that the mathematical representations of the complex subsurface process on which Jones [2011] based his comments are necessarily simple approximations of physical reality.