Galvanic distortions of magnetotelluric (MT) data, such as the static-shift effect, are a known problem that can lead to incorrect estimation of resistivities and erroneous modelling of geometries with resulting misinterpretation of subsurface electrical resistivity structure. A wide variety of approaches have been proposed to account for these galvanic distortions, some depending on the target area, with varying degrees of success. The natural laboratory for our study is a hydraulically permeable volume of conductive sediment at depth, the internal resistivity structure of which can be used to estimate reservoir viability for geothermal purposes; however, static-shift correction is required in order to ensure robust and precise modelling accuracy.

We present here a possible method to employ frequency–domain electromagnetic data in order to correct static-shift effects, illustrated by a case study from Northern Ireland. In our survey area, airborne frequency domain electromagnetic (FDEM) data are regionally available with high spatial density. The spatial distributions of the derived static-shift corrections are analysed and applied to the uncorrected MT data prior to inversion. Two comparative inversion models are derived, one with and one without static-shift corrections, with instructive results. As expected from the one-dimensional analogy of static-shift correction, at shallow model depths, where the structure is controlled by a single local MT site, the correction of static-shift effects leads to vertical scaling of resistivity–thickness products in the model, with the corrected model showing improved correlation to existing borehole wireline resistivity data. In turn, as these vertical scalings are effectively independent of adjacent sites, lateral resistivity distributions are also affected, with up to half a decade of resistivity variation between the models estimated at depths down to 2000 m. Simple estimation of differences in bulk porosity, derived using Archie's Law, between the two models reinforces our conclusion that the suborder of magnitude resistivity contrasts induced by the correction of static shifts correspond to similar contrasts in estimated porosities, and hence, for purposes of reservoir investigation or similar cases requiring accurate absolute resistivity estimates, galvanic distortion correction, especially static-shift correction, is essential.

The electrical resistivity of a volume of rock is highly sensitive to the
presence of laterally and vertically varying amounts of electrically
conductive fluids connected via pore spaces or fluid conduits. Due to these
potentially strong resistivity contrasts between competent host rock and
fluid penetrated rock, electromagnetic (EM) methods, and in particular
magnetotellurics (MT), have been used with considerable success to image
conductive volumes at depth

As with all EM methods, MT data are highly sensitive to rock fluid content
and distribution (i.e. porosity and hydraulic permeability) and can be
related to other properties relevant to fluid movement. This has made the
method particularly interesting for the exploration of geothermal resources.
Indeed, geothermal research was the first commercial application of MT in the
late 1950s, though the interpretation of the corresponding conductive
structures is not always straightforward

Geological map of Rathlin Basin area, overlain with magnetotelluric
acquisition sites numbered and denoted by black crosses. Note the large areal
extent of the Antrim Lava Group basalts, with minimal surface expression of
the underlying sedimentary basin. Profiles A, B, and C denote the locations
corresponding to Figs.

The MT data set studied here was acquired in the context of a
multidisciplinary geothermal research program (IRETHERM), the overarching aim of which is to identify
and evaluate low-enthalpy geothermal resources within Ireland. One such
resource

The island of Ireland was formed during the Caledonian orogeny by the complex
accretion of several continental and island arc fragments during the closure
of the Iapetus Ocean between the Early Ordovician (485 Ma) and late Silurian
(423 Ma), resulting in seven identifiable terranes that comprise the
present-day basement across both Ireland and Great Britain

Regional shear and stress during the subsequent late-Paleozoic (350–250 Ma)
Variscan orogeny reactivated the Caledonian (490–390 Ma) Tow Valley Fault
(TVF), and the ensuing normal and dextral strike-slip faulting resulted in
the formation of a rift basin later filled by a succession of sediments to
form the Rathlin Basin. Although drilling in the adjacent Magilligan Basin
encountered Carboniferous formations at 1347 m total depth, the most basal formations
confirmed within the Rathlin Basin are the Permian Enler Group (EG)
sandstones and Early-Triassic Sherwood Sandstone Group sandstones (SSG). Both
formations are hydrocarbon reservoirs in the Irish Sea to the east

To date, two deep boreholes have been completed onshore in the Rathlin Basin,
namely the Port More 1 (PM1) and Ballinlea 1 (B1) boreholes, drilled in 1967
and 2008 respectively; however, only data from the former are available as
information from the latter is not yet in the public domain. The PM1 borehole
was drilled to a total depth of 1897 m and terminated in the EG sandstones,
with wireline log data acquired in two separate sections due to technical
difficulties

Modelling of regional gravity and magnetic data has been undertaken, with
results presented in

Stratigraphy encountered in the Port More 1 borehole (left), and measured normal resistivity data (right). Stratigraphy encountered includes Paleogene Antrim Lava Group of basalts and tuffs, Cretaceous Ulster White Limestone Formation, Jurassic Lower Lias sandstones, Late-to-Mid-Triassic Mercia Mudstone Group, Early-Triassic Sherwood Sandstone Group, and late-Permian Enler Group sandstones. Due to technical difficulties the resistivity data were acquired in three sections.

Density model from

Core samples of the EG and SSG sandstones successions gathered from the
Port More 1 borehole show promising reservoir properties, with fractional
porosities and hydraulic permeabilities ranging from 0.10 to 0.22 and
1–1000 mD respectively

The imaging of sub-basalt structures poses difficulties to other commonly
employed geophysical methods, particularly seismics

Due to the expected elevated hydraulic properties and saline pore fluids
(both factors that increase conductivity) of the proposed hydrothermal
aquifer within the basin, it was expected that MT data could be carefully
modelled to image the properties and distribution of the aquifer formations.
The increase in resistivity observed in wireline data from the MMG to the
underlying target sediments implies that, depending upon the thickness of
units beneath the MMG, MT may not be able to accurately estimate the units'
resistivities, as MT is primarily sensitive to a layer's conductance (i.e.
the ratio of a layer's thickness to resistivity), and thinner or less
conductive layers may be shielded by overlying conductors

The MT method samples the impedance transfer functions that relate the
electric and magnetic field components of EM plane waves that propagate into
the Earth. As these EM waves attenuate with dependency on the Earth's lateral
and vertical resistivity distribution, the observed MT responses can be
employed for estimating the underlying 3-D resistivity distribution

Though sensitive to conductive structures at depth, MT data are prone to
distortion, primarily of the electric field, due to the presence of galvanic
charges on the boundaries of shallow conductivity structures that are
unresolvable at the frequency range of the recorded data. One simple form of
this galvanic distortion is often easily identified by vertical offsets of
the logarithmic apparent resistivity curves and is referred to as the static-shift effect

Various methods have been proposed to quantify and correct for these static-shift effects, including continuous sampling and filtering of the electric
channels

Fortunately, in the case of the Rathlin Basin, broad-scale extrinsic
resistivity information is available. As part of the regional Tellus ground
and airborne geoscience mapping programme across both Northern Ireland and
the Republic of Ireland, airborne frequency domain electromagnetic (FDEM) data were gathered over the target area

As three-dimensional inversion of MT data is becoming a more common practice, the effects of static-shift correction on resulting resistivity distributions must be considered. This article focuses on the implementation of this correction scheme for MT data by comparing models found by independent 3-D MT inversion of the observed MT data and the static-shift-corrected MT data. In addition to comparing the model results, the statistical and spatial distribution of calculated static-shift corrections are examined and compared to previous works to verify their validity. Both the absolute resistivity and resistivity gradients are used to evaluate the differences between the two models, with the implications of the differences discussed in the context of the possible geothermal aquifer. Note that the approach presented here is primarily methodological in nature; the geological interpretation is brief and will be investigated at length in a future publication.

EM methods include a wide variety of techniques that
observe electromagnetic induction in the Earth and are most commonly used to
image the subsurface distribution of electrical resistivity

In a broader sense, electrical conductivity is a proxy measure of hydraulic
permeability rather than porosity, as the interconnection of conducting pathways
facilitates electric current flow. Due to this strong dependence on the
geometry of flow paths on the scale of interest, the relationship between
permeability and porosity is highly nonlinear

The MT method uses impedance transfer functions relating
the electric and magnetic field components of vertically propagating EM
source field plane waves to image the lateral and vertical resistivity
distribution within the Earth. MT signal waves are generated by two sources,
namely atmospheric electricity (generating signals of frequency > 10 Hz) and interactions of the Earth's magnetosphere with solar wind
(generating signals of frequency < 10 Hz). Recent detailed reviews
of MT methods, the underlying assumptions, and their application include

Resistivity information at a range of depths is inferred by considering
planar EM waves in the Earth at a range of frequencies, as their attenuation
at a given frequency is a function of the resistivity

The resistivity of a select volume of the Earth, as sampled by an EM wave of
frequency

The basic theory for AEM can be found in

AEM data take the form of ratios of the secondary magnetic fields (i.e.
formed by current systems in the ground) to the primary magnetic fields
(i.e. emitted by the transmitter coil), stated in parts-per-million. Both
inphase (i.e. no phase change) and quadrature (i.e. 90

Although multidimensional modelling and inversion methods are available

MT data were collected at 56 sites across part of the onshore Rathlin Basin
(site locations shown in Fig.

Visualisation of dimensionality of MT data, decomposed using the
“strike” analysis program

Robust estimates of the frequency domain MT transfer functions were
determined from the MT time series using commercial processing software from
Phoenix Geophysics that implements the technique described in

Although data were acquired at an array of sites with the intent of 3-D
inversion, as the data were expected to be predominantly 2-D in nature due to
the expected strong lateral contrast across the bounding Tow Valley Fault,
multisite, multi-frequency Groom and Bailey distortion analysis was applied
to the data on a cross-basinal profile basis using the “strike” analysis
tool

The MT responses were inverted for three-dimensional models using the ModEM
3-D MT inversion program

Inversion algorithms determine an appropriate model by iteratively adjusting
a resistivity model, computing its forward MT responses, and comparing these
responses to the observed data. Whereas the model steps vary depending on the
precise algorithm implemented, there are several key parameters that
influence an algorithm's behaviour, such as the data errors, type and degree
of regularisation, and initial starting and prior models. In particular, the
distance between data and model responses, i.e. the sum of the squared
residuals is used to measure the distance between the calculated and observed
responses. To meet the assumptions of least-squares theory, these residuals
must be standardised, i.e. scaled by the variance of the measurements in
order to make them normally distributed over

The regularisation of an inversion describes the weighting between minimising
the data residuals and some penalty function, commonly a roughness penalty
that enforces smoothness in order to stabilise the resulting model. ModEM
allows for the specification of separate regularisation parameters for the

The starting model for each inversion was a 30

Frequency domain airborne electromagnetic data in our MT survey area were
acquired as part of the regional Tellus survey described in

Flowchart illustrating the steps required to (a) find an original,
uncorrected resistivity model

The method proposed here for the correction of static-shift effects follows the
approach of

The approach used here is predicated upon certain key assumptions about the
near-surface geology and the induced galvanic distortion, and these
assumptions clearly show the limits of the approach. Firstly, as mentioned we
assume that the near-surface geology is 1-D in structure, i.e. we can treat
the off-diagonal impedance tensor elements

The first step of the implemented procedure is the inversion of the
uncorrected MT data to obtain a baseline resistivity model for comparison

Step 1: 3-D MT inversion of observed MT data

Step 2: Modelling of each four-frequency AEM sounding within the survey area as a single-layer structure (i.e. half-space) with
Airbeo

Step 3: Interpolation of AEM half-space models by inverse-distance-weighted (IDW)
averaging of log–resistivity values to populate the uppermost 200 m of an MT
forward modelling mesh with cells of 170

Step 4: 3-D solution of MT forward problem for the resistivity model found in Step 3 with ModEM, resulting in a set of high-frequency synthetic MT responses at six frequencies from 10 000 to 1000 Hz for each MT sounding location. The frequencies chosen coincide with those of the downsampled MT data.

Step 5: Multiplicative static-shift corrective factors

Step 6: The static-shift-corrected data are used as input for 3-D MT inversion with ModEM to obtain an improved resistivity model

Map of airborne FDEM half-space resistivity models, overlain with
geological boundaries (solid black lines, as in Fig.

Spatial distribution of static correction factors

Whereas multi-layered models that better reproduce the AEM data can also be
determined using Airbeo, they were not used in favour of the half-space
apparent resistivities for two principal reasons. Firstly, the interpolation of
the apparent resistivities to a 3-D MT mesh can be directly computed, whereas
multi-layered models require more advanced approaches to reconcile variation
in layer thicknesses unless these are explicitly set in the 1-D inversion to
facilitate interpolation. Secondly, the depth of sensitivity of the lowest
frequency of the AEM data (912 Hz

The statistical and spatial distributions of the static-shift multiplicative
corrective factors

Distribution of calculated static correction factors

From examination of the spatial and statistical distributions of

Statistical measures of the

Bivariate distribution of calculated static-shift corrections

Chart of frequency indices and values used in 3-D inversion process. Frequency spacings per decade were 2 (for 3000–1 Hz), 8 (for 1–0.01 Hz), and 4 (for 0.01–0.001 Hz).

Top row shows resistivity slices through the static-shift-corrected
model

Profile A taken along the axis of the concealed basin through the
static-shift-corrected resistivity model

Profile B taken across the static-shift-corrected resistivity model

Profile C taken across the static-shift-corrected resistivity model

Initial comparison of the two models, one with (

The resistivity structure of

We propose that this conductor primarily represents the conductive MMG, with
a clearly delineated upper boundary. The interpretation of the lower boundary
against the SSG (and equally, the boundary between the SSG and the EG
sandstones) is hindered by both the smoothing effects of the regularised
inversion approach used and the fact that inductive EM responses are intrinsically
sensitive to the tops of conductive units (and their integrated
conductivity) rather than to the bottoms of conductive units (i.e. the tops
of resistive units). The TVF, which forms the south-eastern boundary of the
basin, is clearly defined, although the angles of dip modelled are slightly
shallower than those modelled in

In order to demonstrate the lateral heterogeneity of the basin and
intra-basinal structures, Fig.

Representative histogram model of the portion of the static-shift-corrected model

Two diagnostic measures were used to assess the changes between

As the logarithmic resistivity difference

The NCG is largest where the gradient vectors
(i.e. resistivity changes) of the two models are orthogonal, such as
differences in structures and locations or similar structure but differing
magnitude of resistivity change (i.e. difference in the curvature of the model).
Both situations of elevated NCG are evident in the models, especially on
the zero-

Visualisation of the normalised residuals of the magnetotelluric
responses of

The closeness of MT model responses to the data is commonly judged by the
normalised root mean square error (nRMS), defined as

Regardless, the nRMS error remains a useful metric for comparing the relative
goodness of fit of a succession of model responses to the same data set. The
two models presented here reproduce the observed and corrected MT responses
to similar degrees with overall nRMS of 1.77 and 1.96 for

Although examining the misfits of a single model's responses to the data set used in its determination in such a granular fashion is useful in determining which data components are poorly fit and possibly why, taking a similar approach in order to compare two models is not valid in this case. Due to the application of individual static-shift corrections to each site's MT data, the gradients of the respective data spaces of the models are significantly altered. As most inversion algorithms (the nonlinear conjugate gradient method implemented in ModEM included) rely upon gradients within the data space to determine the direction of line searches as part of their optimisation, the static-shift corrections applied all but guarantee that the two inversions presented in this work are the products of different paths through their data spaces. Hence, although the overall mean nRMS estimates are similar, we cannot categorically state that any differences in misfit at the granular, individual datum level are not simply due to the different gradient progressions.

The key test of the two models lies in comparing the measured resistivity
values from the PM1 borehole to the vertical resistivity columns from

Left-hand panel shows the resistivity columns from both

The resistivity columns from the two models at the PM1 borehole site can also
be compared on the basis of integrated conductances, i.e. the ratio of a
layer's thickness and resistivity. In such a comparison, the LLG sediments
are represented as conductances of 31 (

Given the knowledge of the lithology and the measured borehole resistivities,
we conclude that

Changes in resistivity at depth from static-shift correction have strong
implications for the interpretation of the reservoir potential of the area.
Assuming Archie's Law holds and depending on the cementation exponent

The quasi-1-D correction of static-shift effects applied here affects the
resulting three-dimensional models to significantly greater depths than
expected, with differences between the corrected and uncorrected resistivity
models of up to half an order of magnitude present at depths of up to 2000 m
(see, for example, the constant depth slice at 2100 m depth in
Fig.

An approach for the correction of static-shift-type galvanic distortion in MT
data utilising airborne FDEM data has been tested that follows the use of
TDEM data in previous methods. The new approach was tested on an MT data set
from Northern Ireland, using a publicly available regional data set of
airborne frequency domain electromagnetic data to create a set of corrected
MT data. Three-dimensional inversion of each magnetotelluric data set
recovers structures with similar geometries; however, structures in the
near-surface show scaling of resistivity–thickness products proportional to
the static-shift correction applied. When compared to geophysical borehole
logs it is clear that the model from static-shift-corrected data reproduces
the observed resistivity with significantly greater fidelity. Significant
suborders of magnitude variations in resistivity are caused in the model by
the correction of the static-shift components of galvanic distortion, not only in
the near-surface but extending down to the target sediment depths
(

The model determined by the inversion of static-shift-corrected data was found to better recover the resistivity structure observed in a nearby borehole in comparison to the model from observed data. Based on these observations, we conclude that airborne FDEM data provide sufficiently accurate resistivity estimates to allow the correction of static-shift effects in MT data. Note that this approach as discussed here is valid only for locales where the near-surface resistivity distribution is approximately one-dimensional. Given the often regional acquisition and open availability of such AEM data, it is hoped that the approach demonstrated here could be further tested with other MT surveys. Pending further case studies, FDEM could in future be considered as another alternative method to evaluate and correct static-shift-type distortion. Additionally, whereas our approach assumes one-dimensional, single-layer models for the AEM data in deriving the static-shift corrections, future advances could investigate what effect more advanced AEM modelling (i.e. multiple layers or, where applicable due to AEM acquisition specifications, full 3-D modelling) would have on the computed forward MT responses and associated static-shift corrections.

Aside from the processing codes used to convert the
measured MT time series data to robust impedance data (implemented in
propriety programs from Phoenix Geophysics), codes used in this article are
available for academic and non-commercial purposes. The Airbeo program for
AEM modelling is part of the P223 software suite of Amira International,
assembled by CSIRO, and available from Amira International's website. The
“strike” program for distortion analysis of MT data can be obtained by
contacting A. G. Jones, the co-author of

Two types of geophysical data were modelled for this
article, namely airborne FDEM and MT data. The airborne FDEM data set is
publicly available under the Tellus project and accessible from the
project's website

The collection of the MT data, as part of the IRETHERM project, was funded by
Science Foundation Ireland; as a publicly funded project the data are
intended to be publicly available. IRETHERM data will be uploaded to the
European Plate Observing System (EPOS –

R. Delhaye, A. G. Jones, and M. R. Muller designed the MT acquisition plan, with contributions from D. Reay in terms of prior geological and geophysical knowledge. R. Delhaye and M. R. Muller carried out the acquisition, with the assistance of the acknowledged IRETHERM MT Team. MT data processing was done by R. Delhaye, under instruction from A. G. Jones and M. R. Muller. The workflow for AEM modelling and MT static-shift correction was planned and executed by R. Delhaye and V. Rath. MT inversions were performed by R. Delhaye, with instructive direction from A. G. Jones and V. Rath. The paper was prepared by R. Delhaye and V. Rath, with insightful comments and review from A. G. Jones and M. R. Muller.

The authors declare that they have no conflict of interest.

We would like to acknowledge Science Foundation of Ireland for the financial support for the IRETHERM project (10/IN.1/I3022) to A. G. Jones and particularly the student support to R. Delhaye. MT data acquisition was only possible with the assistance of the IRETHERM MT Team (S. Blake, T. Farrell, C. Hogg, J. Vozar, C. Yeomans). G. Egbert, A. Kelbert, and N. Meqbel are very gratefully thanked for making their ModEM code available to the community, especially N. Meqbel for installing it on our clusters and those of the Irish Centre for High-End Computing (ICHEC). The Geological Survey of Ireland and the Geological Survey of Northern Ireland are thanked for providing access to Tellus project data and other complementary information. M. Dessisa of the GSNI is especially thanked for his assistance with the latter. Amira International is thanked for providing open access to the P223 modelling suite. We also acknowledge the work of the Geological Survey of Ireland-funded project GSI-sc-04, “Spatially constrained Bayesian inversion of frequency and time domain airborne electromagnetic data from the Tellus projects” in advancing the available tools and utilities for the handling of Tellus project airborne data. ICHEC is thanked for providing the computational capability required for us to perform our inversions. Lastly, we gratefully thank A. Junge and an anonymous reviewer for their comments and suggestions for improving this paper. Edited by: C. Krawczyk Reviewed by: A. Junge and one anonymous referee