The magnetotelluric method is a passive electrical method for geophysical exploration that uses temporal fluctuations of the Earth’s electromagnetic (EM) field to remotely sense the electrical properties of the subsurface ([8]). Two electric field components ( E x , E y ) and three magnetic field components ( H x , H y , H z ) are measured at each MT station. The frequency-dependent impedance tensor (Z), which is the ratio of orthogonal electric and magnetic components measured at the Earth’s surface, can be used to determine the electrical properties of the subsurface as a function of depth ([6]):

where Z x x , Z x y , Z y x and Z y y are elements of the impedance tensor Z and are also complex magnitudes.

The complex impedance tensor with real and imaginary parts in the frequency domain can be expressed in terms of the apparent resistivity and phase:

where the subscripts i and j are indexes for the rows and columns of the impedance tensor. The apparent resistivity represents the average resistivity of the subsurface at a particular frequency. The phase in degrees describes the phase difference between the electric and magnetic field giving additional information on resistivity structure ([33]):

The MT data used in this study were acquired by a team from Geothermal Development Company (GDC) between 2011 and 2022. A total of 81 MT sounding datasets, shown as green dots in Figure 3 were used for this study. The stations were selected to provide coverage across the western, central and eastern parts of the Korosi geothermal field, while accounting for terrain accessibility and avoiding sources of cultural and electromagnetic noise. The nearest neighbor station spacing ranged from approximately 0.06 to 1.26 km, with denser coverage in the central part of the field and comparatively wider spacing towards the margins where access was more limited. This distribution provided sufficient spatial coverage for evaluating lateral resistivity variations across the principal parts of the geothermal field.

Data were acquired using Phoenix MTU-5A 24-bit data logger, non-polarizing porous pot electrodes and three induction coils. At each sounding station, five channels of data were recorded simultaneously: two orthogonal horizontal electric field components ( E x , E y ) and three magnetic field components ( H x , H y , H z ). The electric field was measured using two 60 meter electrodes configured in a cross layout, oriented to magnetic north-south and east-west, with non-polarizing electrodes buried in shallow pits to ensure stable electrical contact with the subsurface. The magnetic field component was measured using three induction coils; the horizontal coils ( H x , H y ) were aligned with the electrodes, while the vertical coil ( H z ) was vertically buried in the ground. At each station, data were recorded for approximately 18 hours to provide sufficient time for resolving long period MT responses and to include nighttime intervals, when cultural electromagnetic noise is generally reduced and natural field signal quality may improve.

The raw time-series data were subsequently processed using the SSMT2000 software manufactured by Phoenix Geophysics, which utilizes robust Fourier transformation techniques to convert time-domain signals into the frequency domain, ultimately yielding apparent resistivity and impedance phase curves. Following robust processing in SSMT2000, the MT plot files were imported into Phoenix MT Editor for quality control. Apparent resistivity and phase curves were examined together with the individual cross-powers that are used to calculate each point on the curves. Automatic editing was initially applied and subsequently refined through manual inspection. Cross-powers affected by excessive scatter, poor coherence, cultural interference or inconsistent behavior were excluded, while reliable estimates were retained or restored. The edited responses were exported in Electronic Data Interchange (EDI) format for dimensionality analysis and three dimensional inversion. No complete station or continuous frequency band was rejected, only individual unreliable cross-powers or frequency estimates were excluded and all 81 stations were retained for dimensionality analysis and three-dimensional inversion. The final inversion dataset contained 80 frequencies covering 0.001 - 320 Hz.

Figure 3.Profiles overlain of the Korosi geothermal field with the location of MT data stations on DEM map. The profile lines used to extract vertical sections from the three dimensional resistivity model are also shown.

Although the measurements were collected during several survey campaigns between 2011 and 2022, the datasets were prepared using a common coordinate convention and were converted to a consistent impedance format before inversion. Electrode and magnetic coil orientations, impedance signs, frequency sampling and units were checked during compilation. Instrument calibration information contained in the original datasets was retained during processing. This enabled the different survey campaigns to be incorporated into one internally consistent dataset.

Prior to MT modelling, dimensionality analysis was performed to evaluate whether the computed impedance tensors, apparent resistivities and phases from observed data at selected frequencies reflect one dimensional (1D), two dimensional (2D) or three dimensional (3D) geoelectrical structures.

It also enables the identification and quantitative assessment of galvanic and inductive distortions ([15]; [22]) and allows the recovery of subsurface strike directions ([21]). This step is essential for selecting the most representative modelling approach for a given MT dataset. In this study, we applied the phase tensor technique ([7]; [5]) to determine if the local geo-electric environment is best characterized by a 1D, 2D, or 3D resistivity model.

Figure 4.The phase tensor plotted graphically as an ellipse. The major and minor axes of the ellipse depict the principal axes and values of the tensor with the orientation of the major axis specified by the angle α-β.

As an essential tool for assessing subsurface geoelectric dimensionality, the phase tensor enables the visualization of lateral changes in the regional conductivity structure at different depths via frequency-dependent ellipse maps and remaining entirely unaffected by galvanic distortion caused by small-scale, unresolvable surface structures ([2]; [5]; [7]).

Mathematically defined as the product of the inverse real and the imaginary matrix of the impedance tensor, the phase tensor captures the regional-scale inductive response without requiring prior assumptions about the nature of the subsurface conductivity distribution. It is applicable where both the heterogeneity and the regional conductivity structures are 3D.

Graphically, the tensor is represented as an ellipse characterized by its maximum ( Φ max ) and minimum ( Φ min ) axes representing the principal axes of the tensor as shown in Figure 4. The third coordinate invariant, the skew angle (β), quantifies the degree of asymmetry in the phase tensor and it is the primary indicator used to distinguish between 2D and 3D subsurface structures ([7]). If the skew angle is small (<3˚) and has low ellipticity (circular) this indicates 1D or 2D geoelectric structures whereas large skew angles indicate the presence of a 3D regional structure.

The objective of a 3D MT inversion is to produce a 3D resistivity model consistent with MT data that require it ([20]). The 3D MT data inversion was carried out using the 3D ModEM code ([13]; [17]; [23]). The use of 3D inversion is particularly important in structurally complex geothermal systems, where 1D and 2D assumptions may oversimplify resistivity boundaries and reservoir geometry ([34]; [29]).

ModEM code for 3D inversion is based on the minimization of the problem of penalty function effect by the parallelized nonlinear conjugate gradient represented by Equation (4).

The first term in Equation (4) represents the data misfit between the measured ( d ) and model response F ( m ) . m and m 0 are the initial and estimated model, respectively. C d and C m are the data and model covariances whereas λ is a trade-off parameter between data misfit and model structure. The initial model, m 0 is updated iteratively by line search strategy and the 3D forward scheme is based on finite differences, and the inverse scheme exploits the nonlinear conjugate gradient method.

A total of 81 MT data soundings were used for 3D inversion and a starting model of 50 Ωm half-space was applied for the inversion. In the vertical z direction, 48 layers were used with the first layer thickness of 10 m subjected to an increasing factor of 1.1. The x direction was padded with four cells with an increasing factor of 1.1. The y direction was also padded with five cells with an increasing factor of 1.1. The resultant model was 9.6 km in depth with 68 × 85 × 48 cells in x, y and z direction. The 3D inversion process used all four components of the impedance tensor data with error floors of 5% of ( | Z x y × Z y x | ) for all components for all sites. The inversion reduced the normalized root-mean square (RMS) misfit from 21.4 to 4.07 after 34 iterations.

Surface topography was not explicitly incorporated into the inversion mesh and the model therefore employed a flat surface approximation. Lake Baringo was also not represented as a separate conductive water body or included explicitly in the model boundary conditions. Consequently, shallow resistivity variations near areas of pronounced relief and towards the Lake Baringo margin may partly reflect simplifications associated with the model geometry. Interpretation in these areas was therefore undertaken cautiously, with greater emphasis placed on laterally persistent and deeper resistivity structures.

The overall complexity of the subsurface structure beneath Korosi geothermal area was evaluated using MT phase tensor at different periods shown in Figures 5-7 in which the phase tensor ellipses are colored by their skew angles. These specific period intervals were targeted to optimize resolution across the reservoir zone, as they successfully capture the transition into more pronounced 3D geoelectric behavior. The dimensionality of the subsurface structures can be inferred from the shapes of the phase tensor and skew angle. Figure 5 shows ellipses at short periods (0.1 s) and a significant amount of the ellipses in the survey area are quite generally circular, yellow in color and show relatively small skew angles (−3˚ < β > 3˚) exhibiting a 1D characteristic, whereas some few stations indicate 2D (elliptical with β < 3˚) implying structures at shallow depths mostly have 1D and 2D characteristics.

The phase tensor analysis at period 1 second in Figure 6, shows that most of the stations exhibit a more complex aspect that points to 3D effect characterized by a high skew angle (elliptical with β > 3˚) whereas some few stations indicate 2D (elliptical with β < 3˚) dimensionality. For longer periods in Figure 7, clear characteristics of the 3D structure are shown (elliptical with β > 3˚). Generally, the phase tensor analysis shows a complex scenario in which 1D and 2D dimensionality effects are prominent at shallow depth whereas 3D characteristics are detected at deeper levels.

At different depths, the directions of the observed induction arrows, in Parkinson convention ([30]), are heterogeneous, implying complexity in the distribution of the conductive structures. The phase tensor results clearly show that the subsurface is complex electrically and therefore 3D data inversion is needed.

Figure 5. Phase tensor ellipses in the Parkinson convention for a period of 0.1 seconds.

Figure 6.Phase tensor in the Parkinson convention for a period of 1 second.

Figure 7. Phase tensor ellipses in the Parkinson convention for a period of 10 seconds.

Figure 8.Comparison of measured and predicted MT responses at stations K36 and K158. Dots represent measured data and continuous lines represent responses predicted from the final ModEM model. The upper panels show apparent resistivity and the lower panels show impedance phase.

The quality of the final inversion was assessed by comparing the measured impedance responses with the responses predicted by the recovered three dimensional resistivity model. Figure 8 presents representative apparent resistivity and phase fits for stations K36 and K158. The predicted responses reproduce the principal trends in the measured apparent resistivity and phase, particularly at short and intermediate periods. Some discrepancies occur at longer periods and vary among stations and impedance components, indicating reduced model fit for parts of the deeper response. Overall, the comparison demonstrates that the final 3D model captures the main resistivity structure of the Korosi geothermal field.

Three west-east resistivity cross-sections extracted from the final 3D inversion model are presented in Figures 9-11. Slices are shown to a maximum depth of 5 kilometers, since there are no significant structures towards greater depths and they image the resistivity distribution beneath the Korosi geothermal field. Although each profile exhibits local variations in geometry, all three display a similar resistivity architecture consisting of a shallow resistive layer, an extensive conductive zone and a deeper resistive body. Conductive (C) and resistive (R) anomalies are labelled independently in each profile for ease of description.

Figure 9.3D resistivity model through Profile 1.

Profile 1 crosses the northern part of the study area as shown in Figure 9. A thin resistive uppermost layer (R1) occupies the near-surface throughout the profile with resistivity values generally exceeding 100 Ωm. The uppermost layer is underlain by a broad conductive anomaly (C1) with resistivity values below approximately 10 Ωm occupying the entire length of the profile. The conductor reaches its greatest thickness beneath the western part of the section, extending to approximately 2200 m below sea level (b.s.l) before gradually thinning eastward. Underlying C1 is a large resistive body (R2) with resistivity values exceeding 100 Ωm. The resistive body deepens toward the western part of the profile but rises progressively toward the east, where its upper boundary becomes significantly shallower beneath the eastern side of the profile.

Figure 10 shows Profile 2 and it comprises a thin near-surface resistive layer (R3), two conductive anomalies (C2 and C3) and a deep resistive body (R4). Conductor C2 occupies the western portion of the profile and extends from the near surface to approximately 2,300 m b.s.l. A second conductor (C3) occurs beneath the eastern part of the profile and is separated from C2 by a zone of relatively higher resistivity. The deep resistive body R4 underlies both conductive anomalies and occupies most of the lower half of the profile. The upper surface of R4 rises gradually toward the eastern part of the section.

Figure 10. 3D resistivity model along Profile 2.

Profile 3, the southernmost profile, is presented in Figure 11. A thin, laterally continuous high-resistivity layer (R5) occurs near the surface throughout the profile, with resistivity values generally exceeding 100 Ωm. A conductor (C4) with resistivity values generally below 10 Ωm extends from near the surface to approximately 1800 m b.s.l. Exploration well KW-02 is situated close to the eastern boundary of conductive anomaly C4. Conductive anomaly C5 occurs in the eastern part of the profile where it extends from near the surface to depths of approximately 1800 m b.s.l. C5 is separated from the western conductor (C4) by a resistive zone occupying the central part of the profile. The lower part of the profile is dominated by a large high-resistivity body (R6) occupying depths from approximately 1800 m b.s.l.

Figure 11. 3D resistivity model along Profile 3 cutting through Korosi well KW-02.

The 3D MT inversion model of the Korosi geothermal field images a broadly consistent three layer resistivity structure across the three west-east profiles. This consists of a thin, near-surface high resistivity layer (>100 Ωm), a laterally extensive conductive zone with resistivity values generally below 10 Ωm, and a deeper resistive body with resistivity values commonly exceeding 100 Ωm. Similar resistivity patterns are widely reported in volcanic hosted geothermal systems, where a conductive clay cap overlies a more resistive deeper zone ([20]; [19]; [35]).

The thin, laterally continuous near surface resistive layer imaged at the top of all three profiles is interpreted as relatively unaltered, dry or weakly altered volcanic rocks above the main hydrothermal alteration zone. At Korosi, this layer is likely associated with recent, well drained tuffs and lava units that form part of the volcanic edifice. Its high resistivity is consistent with limited clay alteration and reduced pore fluid connectivity in the shallow subsurface ([12]; [18]).

The conductive bodies C1 - C5, with resistivity values generally below 10 Ωm, are interpreted as components of the hydrothermal clay cap. This low resistivity zone is most likely produced by smectite- and zeolite-rich alteration of tuffs and other permeable volcanic units. Such alteration is common in the lower temperature parts of volcanic geothermal systems, where smectite and mixed-layer clays strongly reduce bulk resistivity. With increasing temperature and depth, smectite-rich assemblages are commonly replaced by more resistive illite, chlorite and locally epidote-bearing alteration minerals, producing a transition from the conductive clay cap into a more resistive deeper zone ([32]; [31]; [14]).

The western conductors C1, C2 and C4 form the most laterally persistent conductive feature in the model, suggesting that the clay alteration zone is continuous along the western part of the field. Their repeated occurrence across the three profiles indicates that this conductive zone is unlikely to be an isolated anomaly, but rather a coherent hydrothermal alteration feature. Where eastern conductors are imaged, particularly C3 on Profile 2 and C5 on Profile 3, they are separated from the western conductive zone by a relatively resistive central block. This geometry suggests lateral compartmentalization of the alteration system, possibly controlled by structural or lithological variations. However, the presence of separate conductive zones should not be interpreted directly as evidence for separate reservoirs without supporting temperature, permeability and geochemical data.

A relatively resistive zone is imaged beneath the conductive clay cap in all three MT profiles. The deeper resistive bodies R2, R4 and R6 therefore represent key features of the inversion model, although their geological meaning remains non-unique. In volcanic geothermal systems, the transition from a conductive clay cap to a deeper resistive zone is commonly associated with increasing temperature and the replacement of smectite-rich alteration by illite, chlorite and locally epidote-bearing assemblages. Such a transition may indicate reservoir level conditions. However, high resistivity at depth does not necessarily confirm the presence of a productive geothermal reservoir, because similar resistive signatures may also result from dense intrusive rocks, low-porosity lava units, relict alteration zones or basement lithologies ([10]; [19]).

The KW-02 well provides an important qualitative constraint on the Profile 3. Its position near the eastern margin of conductor C4, close to the central resistive block between C4 and C5, allows comparison between the MT model and available drilling observations. Although the well indicates the presence of permeable zones, the available temperature information does not confirm high-temperature reservoir conditions at the drilled location. Therefore, the C4 resistive transition should be interpreted as a permeable but not necessarily high temperature zone, at least where it is intersected by KW-02.