Two-dimensional, regularised inversion of VLF data

Abstract

Very low frequency electromagnetic (EM) methods using VLF transmitters have found many applications in subsurface geophysical investigations. Surface measurements involving both the vertical component of the magnetic field (VLF-EM or VLF-Z) and of the apparent resistivity (VLF-R) are increasingly common. Although extensive VLF data sets have been successfully used for mapping purposes, modelling and interpretation techniques which assess the third (i.e. depth) dimension appear limited. Given a profile of VLF-R measurements the main purpose of the present study is to demonstrate an automatic method for the construction of a resistivity cross-section. The technique used is one of a new generation of regularised inversion methods. These techniques attempt to overcome the problem of equivalence/non-uniqueness in EM sounding data by constructing the resistivity distribution with the minimum amount of structure that fits the data. VLF data represent a special case of plane-wave EM sounding in that they conform, in practice, to a single-frequency technique. This fact imposes a limitation in the amount of vertical resolution that we can expect using such data. In the case of two-dimensional modelling and inversion, resolution through the cross-section is a resultant attribute from both vertical and lateral resistivity gradients within the subsurface. In order to provide insight into the practical application of regularised inversion techniques to VLF data, both synthetic and field examples are considered. Both sets of examples are primarily concerned with VLF data applied to near-surface fault mapping where the main aim is to assess the location, dip and depth extent of conductive subsurface features.2

Quantitative 2D VLF data interpretation

“…General resolution features of both modes include the fact that the upper surfaces of concealed zones are better resolved than their lower surfaces (see also Beamish, 1994). Resolution of detailed subsurface features such as that examplified by the rotated 'L' shaped body is not possible using regularised (smooth model) inversion schemes.…”

“…The algorithm implements firstderivative smoothing and includes a regularisation parameter () that controls the degree of model smoothness/roughness (often a trade-off with misfit). VLF studies using the former method were described by Beamish (1994). The latter method is used in the present study since it readily permits the use of a regular subsurface finitedifference grid comprising in excess of 100x100 1 m cells.…”

“…As discussed by Fischer et al (1983) and Beamish (1994) in order to ensure consistency with a 2-D approach, the directional VLF data must conform to one of the two principal modes of 2-D induction. The assumption of infinite strike (which defines the 2-D case) provides two decoupled modes involving separate combinations of the field components.…”

Three-dimensional modelling of VLF data

“…1. When VLF measurements can be obtained in one, or both, of these modes, interpretation can proceed in a straightforward manner, and 2D forward modelling and inversion becomes possible (Beamish, 1994). An important consideration in a 2D context is the joint information provided by VLF-R and VLF-Z measurements.…”

“…This applies both to mapping applications (e.g., Guerin et al, 1994) and the determination of the 2D resistivity distribution along profiles (e.g., Beamish, 1994). The frequency bandwidth of VLF has been extended to higher-frequency transmitters (to 240 kHz) and the multi-frequency method is referred to as radiomagnetotellurics (Turberg et al, 1994;Zacher et al, 1996).…”