3D analysis of the MT data for resistivity structure beneath the Ashute geothermal site, Central Main Ethiopian Rift (CMER)

Abstract

The Ashute geothermal field (around Butajira) is located near the western rift escarpment of the Central Main Ethiopian Rift (CMER), about 5–10 km west of the axial part of the Silti Debre Zeit fault zone (SDFZ). Several active volcanoes and caldera edifices are hosted in the CMER. Most of the geothermal occurrences in the region are often associated with these active volcanoes. The magnetotelluric (MT) method has become the most widely used geophysical technique for the characterization of geothermal systems. It enables the determination of the subsurface electrical resistivity distribution at depth. The high resistivity under the conductive clay products of hydrothermal alteration related to the geothermal reservoir is the main target in the geothermal system. The subsurface electrical structure of the Ashute geothermal site was analyzed using the 3D inversion model of MT data, and the results are endorsed in this work. The ModEM inversion code was used to recover the 3D model of subsurface electrical resistivity distribution. According to the 3D inversion resistivity model, the subsurface directly beneath the Ashute geothermal site can be represented by three major geoelectric horizons. On top, a relatively thin resistive layer (>100 Ωm) represents the unaltered volcanic rocks at shallow depths. This is underlain by a conductive body (< 10 Ωm), possibly associated with the presence of clay horizon (smectite and illite/chlorite zones), resulting from the alteration of volcanic rocks within the shallow subsurface. In the third bottom geoelectric layer, the subsurface electrical resistivity gradually increases to an intermediate range (10–46 Ωm). This could be related to the formation of high-temperature alteration minerals such as chlorite and epidote at depth, suggesting the presence of a heat source. As in a typical geothermal system, the rise in electrical resistivity under the conductive clay bed (products of hydrothermal alteration) may indicate the presence of a geothermal reservoir. Otherwise, no exceptional low resistivity (high conductivity) anomaly is detected at depth.

Highlights

• •The magnetotelluric (MT) approach was utilized to determine the Earth's resistivity structure and identify hydrothermal alteration zones.
• •The dimensionality analysis of the Ashute geothermal field indicates that at shallow depths 1-D and 2-D structures, and deeper depths show 3-D structures.
• •The identified notable structures of the 3-D distribution of resistivity cross-section of the Ashute geothermal field were very high resistivity (>100 Ω m) mixed with the low resistivity body, followed by a conductive layer below 10 Ω m overlay of the moderately resistive layer with resistivity values (10–46 Ω m), at deeper depths.

1. Introduction

The Main Ethiopian Rift (MER) is one of the East Africa Rift Systems (EARS), which is a seismically and volcanically active portion that runs northeast through the Ethiopian plateau [1–3]. The Central MER (CMER) is a component of the MER that spans from Lake Koka to Lake Awasa and has boundary faults that run roughly N30°E–N35°E on average [2,3]. Several active volcanoes and caldera edifices are hosted in the CMER [4]. Geothermal resources are often associated with these active volcanoes [5,6]. The Ashute (around Butajira) geothermal field is found closer to the western rift escarpment in the CMER, where thermal manifestations like mud pools and hot springs are aligned NNE-SSW [7].

For the investigation of geothermal systems, including the analysis of altered rocks, and faults and conducting geothermal fluids filled with fractures, electromagnetic (EM) tools have become industry standards [8]. It's also utilized to find accumulated magma zones beneath active volcanoes, which are associated with high conductive anomalies [9]. According to Muñoz [8], subsurface electrical conductivity is a vital parameter for the description and detection of geothermal settings. Conducting electrolytes arise in geothermal systems in fault zones and conductive fluids filled with fractures that can hold substantial quantities of dissolved salts [10]. Temperature, Water content, porosity, fractures, permeability, and the concentration of dissolved solids are the key factors that affect resistivity values and rock matrix (to a minor level), and the host rocks have less conductivity than the geothermal system [11,12]. Clay mineral alteration has a high conductivity signature produced by hydrothermal processes in geothermal systems [12]. The MT method has been recognized for a long time as the best method for geothermal exploration due to its numerous advantages in delineating high resistivity zones associated with high-temperature effects and its deeper depth of investigation effectively [13]. Many MT studies have been conducted in recent years in the major tectono-volcanic regimes of the Ethiopian rift to explore, delineate, and characterize the 3D electrical resistivity model of the geothermal systems [14–17]. The previous geophysical study in the CMER revealed that the high conductivity region was obtained using magnetotelluric data beneath the SDFZ [14,18]. This region is consistent with the low seismic velocity region [19]. However, the Ashute geothermal site is located within the CMER near the SDFZ, has not previously been studied in sufficient detail, and requires additional data. Accordingly, MT measurements proved the most effective method for detecting the highly conductive “clay cap” and the deep geothermal reservoir. Therefore, cautious data gathering, processing, modeling, and interpretation in terms of mapping large kilometers required for some geothermal fields make a valuable contribution to geothermal exploration and exploitation [12].

In this regard, the 3D MT inverse modeling and data analysis of a comprehensive MT study of the geothermal field of the Ashute area near the SDFZ were the main focus of this study. The 3D inversion model was performed using ModEM inversion codes [20–22] and an open-source python program (MTpy) for a given dataset [23]. The approach could provide information on the subsurface geoelectrical structures in order to detect hydrothermal alteration zones, delineate and explore geothermal resources for further implementation and determine the 3D resistivity distribution of the study area. In addition, the Ashute MT data were analyzed in order to determine its geoelectrical dimensionality, directionality, and phase tensor properties in the subsurface. Therefore, the main objective of this research is to generate a 3-D electrical resistivity model of the subsurface to delineate and characterize the geothermal structures of the Ashute geothermal field.

2. Tectonics and geologic setting

The EARS is a typical location for studying the evolution of continental extension, lithospheric plate rupture, and the dynamics through which distributed continental deformation is progressively concentrated at oceanic spreading centers [24]. The Main Ethiopian Rift (MER) is the portion of the EARS that connects the Afar triple junction to the north and the Kenya Rift to the south. The opening of the Ethiopian rift has been established by the unrest of at least two mantle plumes, currently found beneath the Afar depression to the north of MER and the Gregory Rift in Kenya. The Southern Ethiopia Eocene-Oligocene magmatism arose from the earlier Kenyan plume, which drifted southward when the African plate moved northward [25]. The Afar plume is supposed to be younger, and it is considered to be the source of the majority of central Ethiopia and the Afar region magmatism [26,27]. Uplift of mantle plume activity produces uplift of rift shoulders and dome development in the escarpments of both rifts, resulting in the current relief of Ethiopia [7,28,29]. The main scarp between the northern flanking and plateaus of southern Ethiopia and the rift floor is built by dextrally stepped northeast striking normal border faults, with height differences reaching up to 2000 m [14,24,30]. The occurrence of high enthalpy geothermal prospects and active magmatism in the MER is due to plume interaction [7,31]. The tectonic-magmatic activity throughout the Cenozoic era was significant in the formation of the Ethiopian rift valley that is active today.

The most notable volcano-tectonic event in the CMER is the copious flows of ignimbrites that formed due to the collapse of the Early Pliocene's extremely large calderas [32–34]. From the Early Pleistocene until the present, the Silti Debre Zeit Fault Zone (SDFZ) to the west and the Wonji Fault Belt (WFB) to the east have been the epicenters of tectonic and volcanic activity [32,[35], [36], [37], [38]].

The rift valley is noticeable by long rift escarpments on both the eastern and western borders. The boundary faults have an N30°E average trend (Fig. 1). The ESE-dipping and N25°E–N35°E-trending Guraghe and Fonko faults form the western boundary, while the WNW-dipping and N30°E-trending Asela–Langano fault system forms the eastern boundary (Fig. 1). On the western boundary of the CMER, bands of a few off-axis Quaternary volcanism can be detected, for example, in the SDFZ, which contains the Bishoftu and Butajira volcanic chains on the west side of Aluto. The SDFZ was initially estimated to be 100 km long and 2–5 km wide, but its exact size is still under debate [14,33].

Fig. 1.

The map illustrates the tectonic setting and location of the Ashute geothermal field in the CMER. The ERS includes a zone of tectonically active regions between two expanding African plates, the Somalian and Nubian (modified from Ref. [39]).

Modest transversal structures and locally complicated geometries are common characteristics of segmented and articulated border fault systems. The NE–SW-trending border faults near the Lake Langano curve acquire a local NW–SE trend, and the main S or Z-shaped pattern of the Langano Rhomboidal fault system is formed by the interaction between these two intersecting trends [3,[40], [41], [42]]. Fault-slip measurements on the two rift borders in the CMER reveal a stress field characterized by an ESE–WNW extension trend, with slight changes between NW–SE and E–W [3,41,[43], [44], [45], [46]].

In the central part of MER, the Lakes region is located on the basin floor and is covered by Holocene lacustrine deposits. These lake sediments are accompanied by micro-organic deposits (diatomite). However, WFB, on the other hand, cuts those sediments in some places and creates step-like terrain. The placement of Lake Abijata and Lake Langano is controlled by the influence of such faults, whereas Lake Shalla is a caldera-created lake through a volcanic eruption [47]. On the western side of the CMER, the SDFZ is dominated by Quaternary core volcanoes, and basaltic lava flows, as well as associated scoria cones, and lava flows with phreatomagmatic deposits [48]. Several intermittent amalgamating nested scoria cones have been positioned parallel to the Guraghe escarpment near the SDFZ [33]. Around the study area, scoria, highly vesicular basalt, rhyolite, layered pumice, crystalline ignimbrite, and deposits of pyroclastic flow with extreme differences in textural features are highly weathered and covered with 0.5-m thick soil. The study area (Ashute), is typically covered by lacustrine sediment deposits (see Fig. 2).

Fig. 2.

The map depicts the geology of CMER (Adopted and modified from the Geological Survey of Ethiopia, 1996).

3. Magnetotelluric method

The Magnetotelluric method (MT) is a part of studies of Electromagnetic (EM) induction, built on measurements of natural transient electromagnetic fields at an observation point on the surface of the earth, providing through defining the subsurface distribution of electrical resistivity. Natural signal EM-induction studies are mainly carried out through two well-established techniques, the MT method and the Geomagnetic Depth Sounding (GDS). A technique in applied Geophysics, the MT method was initially recognized and outlined by Tikhonov [49] and then by Cagniard [50]. A broadband depth sounding ranging in frequency from > 0.0001 Hz to < 10,000 Hz can be employed for shallow and deep structural investigations. The natural MT fields of frequencies from 0.0001 to 1 Hz are generally produced by geomagnetic micro pulsations. At frequencies from 1 to 10,000 Hz, most of the signal is due to the current system of worldwide lightning activity.

For MT study, the usual components measured at a single site are time variations of the three orthogonal magnetic fields $\left({\mathrm{H}}_{\mathrm{x}},{\mathrm{H}}_{\mathrm{y}},{\mathrm{H}}_{\mathrm{z}}\right)$ and two electric fields simultaneously measured on the surface of the earth in MT surveying [49–51].

Magnetotelluric transfer functions, often known as the responses of MT, are functions that connect the observed components of the electromagnetic fields at different frequencies. Provided that the source fields can be as consented to as plane waves, these functions depend on the material's electrical characteristics and frequency, not on the EM sources. As a result, according to the observed frequency, this characterizes the materials underlying the resistivity distribution. The most commonly used transfer functions of MT data are the impedance tensor and geomagnetic transfer function (tipper vector). The impedance tensor, Z, is the typical MT transfer function, and it signifies the direct relationship between the variations of electromagnetic fields in the horizontal direction at a particular location. It is a frequency-dependent, complex second-rank matrix (Equation (1)) that defines the interaction between orthogonal components of electric $\left({\mathrm{E}}_{\mathrm{x}},{\mathrm{E}}_{\mathrm{y}}\right)$ and magnetic fields $\left({\mathrm{H}}_{\mathrm{x}},{\mathrm{H}}_{\mathrm{y}}\mathrm{o}\mathrm{r}\frac{{\mathrm{B}}_{\mathrm{x}}}{\mu },\frac{{\mathrm{B}}_{\mathrm{y}}}{\mu }\right)$ $\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{y}$ at a specified frequency.

$$\mathrm{E}=\mathrm{Z}\mathrm{H}\mathrm{o}\mathrm{r}\left(\begin{array}{c}{\mathrm{E}}_{\mathrm{x}}\\ {\mathrm{E}}_{\mathrm{y}}\end{array}\right)=\left(\begin{array}{cc}{\mathrm{Z}}_{\mathrm{x}\mathrm{x}}& {\mathrm{Z}}_{\mathrm{x}\mathrm{y}}\\ {\mathrm{Z}}_{\mathrm{y}\mathrm{x}}& {\mathrm{Z}}_{\mathrm{y}\mathrm{y}}\end{array}\right)\left(\begin{array}{c}{\mathrm{H}}_{\mathrm{x}}\\ {\mathrm{H}}_{\mathrm{y}}\end{array}\right)$$ (1)

or the EM field spectra are linearly related by way of:

$${\mathrm{E}}_{\mathrm{x}}\left(\omega \right)={\mathrm{Z}}_{\mathrm{x}\mathrm{x}}\left(\omega \right){\mathrm{H}}_{\mathrm{x}}\left(\omega \right)+{\mathrm{Z}}_{\mathrm{x}\mathrm{y}}\left(\omega \right){\mathrm{H}}_{\mathrm{y}}\left(\omega \right)$$ (2)

$${\mathrm{E}}_{\mathrm{y}}\left(\omega \right)={\mathrm{Z}}_{\mathrm{y}\mathrm{x}}\left(\omega \right){\mathrm{H}}_{\mathrm{x}}\left(\omega \right)+{\mathrm{Z}}_{\mathrm{y}\mathrm{y}}\left(\omega \right){\mathrm{H}}_{\mathrm{y}}\left(\omega \right)$$ (3)

where ${\mathrm{Z}}_{\mathrm{x}\mathrm{y}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{Z}}_{\mathrm{y}\mathrm{x}}$ are called the principal impedances while ${\mathrm{Z}}_{\mathrm{x}\mathrm{x}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{Z}}_{\mathrm{y}\mathrm{y}}$ are the supplementary as shown in Equation (2), and (3).

The MT tensor (M) was first coined by Weaver et al. [52], which is a similar portrayal of the transfer function but uses the B field as an alternative to the H field (e.g., Equation (4)):

$$\mathrm{E}=\mathrm{M}\mathrm{B}\mathrm{o}\mathrm{r}\left(\begin{array}{c}{\mathrm{E}}_{\mathrm{x}}\\ {\mathrm{E}}_{\mathrm{y}}\end{array}\right)=\left(\begin{array}{cc}{\mathrm{M}}_{\mathrm{x}\mathrm{x}}& {\mathrm{M}}_{\mathrm{x}\mathrm{y}}\\ {\mathrm{M}}_{\mathrm{y}\mathrm{x}}& {\mathrm{M}}_{\mathrm{y}\mathrm{y}}\end{array}\right)\left(\begin{array}{c}{\mathrm{B}}_{\mathrm{x}}\\ {\mathrm{B}}_{\mathrm{y}}\end{array}\right)$$ (4)

Every matrix member has both real and imaginary parts, signifying that each component has both a magnitude and a phase because both tensors (Z and M) are complex integers.

In a 3D earth model (see Fig. 11), conductivity varies in all three directions (x, y, z). The general form of the impedance tensor in a 3D earth model (Equation (5)) is

$${\mathrm{Z}}_{3\mathrm{D}}=\left(\begin{array}{cc}{\mathrm{Z}}_{\mathrm{x}\mathrm{x}}& {\mathrm{Z}}_{\mathrm{x}\mathrm{y}}\\ {\mathrm{Z}}_{\mathrm{y}\mathrm{x}}& {\mathrm{Z}}_{\mathrm{y}\mathrm{y}}\end{array}\right)$$ (5)

where ${\mathrm{Z}}_{\mathrm{x}\mathrm{x}}\ne {\mathrm{Z}}_{\mathrm{y}\mathrm{y}}\ne 0\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{Z}}_{\mathrm{x}\mathrm{y}}\ne {\mathrm{Z}}_{\mathrm{y}\mathrm{x}}$. There is no mechanism to rotate the impedance tensor such that on-diagonal elements on Z become zero.

Fig. 11.

The recovered 3-D inversion of resistivity model of Ashute geothermal area.

The interpretation must take into account each component of the tensor. The diagonal elements of the impedance tensor and any part of the tipper vector are all non-zero elements and do not vanish in any direction. For the 3D earth, the full impedance tensor with four complex elements for each frequency can be used to calculate different forms of apparent resistivity.

Apparent resistivity $\left(\rho \right)$, and phase ($\mathrm{\phi }$) (see Equations (6), and (7), respectively) of the Earth response functions in MT surveys are often used. An equivalent uniform half-space average resistivity is used to calculate the apparent resistivity of a layered earth model.

$${\rho }_{\mathrm{i}\mathrm{j}}\left(\omega \right)={\left|{\mathrm{C}}_{\mathrm{i}\mathrm{j}}\left(\omega \right)\right|}^2\mu \omega \left(\mathrm{\Omega }\mathrm{m}\right)$$ (6)

The response functions $\mathrm{C}=\frac{1}{\mathrm{K}}=\frac{{\mathrm{E}}_{\mathrm{x}}}{\mathrm{i}\omega \mu {\mathrm{H}}_{\mathrm{y}}}=\frac{-{\mathrm{E}}_{\mathrm{y}}}{\mathrm{i}\omega \mu {\mathrm{H}}_{\mathrm{x}}}$, is complex and has a phase lag known as an impedance phase, and in the case of 1- D layered half-space:

$${\mathrm{\phi }}_{\mathrm{i}\mathrm{j}}=\mathrm{Arg}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}}\right)={\tan }^{-1}\left(\frac{{\mathrm{E}}_{\mathrm{i}}}{{\mathrm{B}}_{\mathrm{j}}}\right)$$ (7)

The tippers that developed as described by a forward model were seen and placed restrictions on the possibility of melting within MER [14]. The MT method had been long known as the preferred method in geothermal exploration due to its great investigation depth and its effectiveness in delineating low conductivity zones associated with high-temperature effects, e.g., alteration [53]. The hydrothermal alteration mineralogy and the presence of reservoir fluids in fractured rocks play a significant role in controlling the distributions of electrical resistivities in geothermal systems, especially in high-temperature fields [8,16,54].

3.1. Data acquisition and processing

The natural time variations of the electrical and magnetic fields of 30 MT sites were measured in a period range of 0.00313–2941.17 s, over a 32 km² rectangular grid with an interstation spacing of 1 km on average, and gathered within two months, utilizing (MTU-5A/MTU-5/V5) a V5 System 2000 MTU Phoenix Geophysics at local and remote stations. It was carried out in 2017 under the supervision of GSE geophysical personnel. The distance between stations varies, but it is roughly 1 km on average. A five-component MT unit typically consists of five non-polarized electrodes, four of which measure two perpendicular electric field components $\left({\mathrm{E}}_{\mathrm{x}},{\mathrm{E}}_{\mathrm{y}}\right)$ in the horizontal directions, i.e., along with the N–S and E–W directions, while the fifth electrode serves to ground the MTU data logger in the center. These electrodes are usually comprised of a porous pot that contains metal interacting with a solution, which connects to the ground via porous materials, commonly $\mathrm{C}\mathrm{U}{\mathrm{S}\mathrm{O}}_4$ or $\mathrm{P}\mathrm{b}{\mathrm{C}\mathrm{l}}_2$. Three induction coils were used for measuring the magnetic field, two of which measured the horizontal orthogonal components (${\mathrm{H}}_{\mathrm{x}},{\mathrm{H}}_{\mathrm{y}}$) and the rest measured the vertical component (Hz), as illustrated in Fig. 3. Magnetic sensors (induction coils) measure the horizontal and vertical magnetic field components on the earth's surface. In order to minimize noise and the effect of everyday temperature variations, the two magnetic coils were buried. The magnetic field in the vertical direction, Hz, was measured by burying the induction coil as much as possible vertically, 90° into the ground.

Fig. 3.

Schematic diagram showing the field setup for MT data acquisition.

The data logger serves as the MT measuring system's central controller unit. It manages the acquisition process and signals from amplifier sensors before sending them to an AD converter for conversion to digital format. As a stable power source, a standard 12-V car battery was used. The field configuration shown in Fig. 3 is as follows.

The GPS time signals were used to obtain timing at each MT station. To remove electromagnetic noise (cultural noise) induced by artificial electrical sources, vibrations, and electromagnetic signals from other sources at each measuring station, a remote reference was located 15 km NW of the Ashute Geothermal field was chosen for the entire duration. The coils and wires were buried in the ground to reduce wind noise, with the added benefit of lowering heat impacts on the induction coils. At most of the sites, the devices were deployed and running for more than 24 h.

During the data processing stage, the time series data were utilized to estimate both the impedance tensor and tipper after the data were acquired. Prior to data analysis and inversion, we used the processed data (spectral data) in this investigation.

3.2. A dimensionality analysis

The dimensionality analysis of MT data is a key approach to determine whether the site's impedance tensors and tippers are compatible with structures of 1D or 2D or show more complex 3D structures. Many methodologies have been developed to investigate the dimensionality of MT data at various times. The most commonly used methods include the skew parameter of Swift [55], ellipticity [56], Groom and Bailey decomposition [57], Bahr's phase-sensitive skew [58,59], rotational invariants, and WAL [60,61], and the phase tensor [62]. Bohr's phase-sensitive skew [59], and Phase tensor [62], were utilized for the dimensionality analysis of the Ashuite MT data. The dimensionality analysis of the Ashute geothermal field indicates 1D and 2D structures at shallow depths, and 3D structures at deeper depths.

The parameters and approaches used for dimensionality analysis of the Ashuite MT data and results are explained in further depth in the following sections.

3.2.1. Bahr's phase-sensitive skew, η

Bahr [58] suggested phase-sensitive skew, a rotationally invariant parameter, as the first modern dimensionality tool (see Equation (8)). It measures the skew of the impedance tensor's phases and is provided by:

$$\eta =\frac{{\left|\left[{\mathrm{D}}_1,{\mathrm{S}}_2\right]-\left[{\mathrm{S}}_1,{\mathrm{D}}_2\right]\right|}^{\frac{1}{2}}}{\left|{\mathrm{D}}_2\right|}$$ (8)

where the D (difference) and S (sum) impedances (Equations (9), and (10), respectively) are recognized as modified impedances [59] given by

$${\mathrm{D}}_1={\mathrm{Z}}_{\mathrm{x}\mathrm{x}}-{\mathrm{Z}}_{\mathrm{y}\mathrm{y}},{\mathrm{D}}_2={\mathrm{Z}}_{\mathrm{x}\mathrm{y}}-{\mathrm{Z}}_{\mathrm{y}\mathrm{x}}$$ (9)

$${\mathrm{S}}_1={\mathrm{Z}}_{\mathrm{x}\mathrm{x}}+{\mathrm{Z}}_{\mathrm{y}\mathrm{y}},{\mathrm{S}}_2={\mathrm{Z}}_{\mathrm{x}\mathrm{y}}+{\mathrm{Z}}_{\mathrm{y}\mathrm{x}}$$ (10)

According to the criteria of Bahr [58,59], for interpreting η based on its value of distorted 2D (3D/2D), or 1D, 2D examples are indicated by the skews value of phase-sensitive smaller than 0.1 while 3D data is represented by the skew parameters of 'phase sensitive', with values of η greater than 0.3. A modified dataset of 3D/2D with values between 0.1 and 0.3 (0.1 < η < 0.3) is regarded to be suggestive [51].

As demonstrated in Fig. 4, Bahr's phase-sensitive skew was presented for the entire MT stations in the Ashute geothermal region.

Fig. 5.

An elliptical illustration of the MT phase tensor graphically. The lengths of the semi-major and semi-minor axes of the ellipse are proportional to the principal values ${\mathbf{\phi }}_{\mathbf{max}},\mathbf{a}\mathbf{n}\mathbf{d}{\mathbf{\phi }}_{\mathbf{min}}$ . The skew angle is a third coordinate invariant used to characterize a non-symmetric tensor. The observer's reference frame $\left({\mathbf{X}}_{\mathbf{1}},{\mathbf{X}}_{\mathbf{2}}\right)$ is used to calculate the tensor's relationship. The angle $\left(\mathbf{\alpha }-\mathbf{\beta }\right)$, determines the direction of the ellipse's principal axis [62].

Fig. 4.

The Bahr's phase-sensitive skew plot of the Ashute geothermal field for all stations.

The result of η indicates low values close to zero below 0.3 at periods (< 50 s), implying 1D, a 2D character at shallow depths for the majority of MT stations. The high values above the threshold for longer periods (> 50 s) indicate 3D dimensionality at deeper depths. The expectation value η estimator for the 1D, 2D, and 3D/2D cases is biased. η value increases as the noise level increases and decreases for low noise levels. η value is dependent on the noise level [51].

3.2.2. Phase tensor analysis

The phase tensor analysis method was created by Ref. [62] as a tool for getting information on the regional dimensionality structure when it doesn't suffer from galvanic distortion. It can be graphically represented as ellipses [63]. The phase tensor $\left(\mathrm{\phi }\right)$ is defined as the ratio of the real (X) to imaginary (Y) sections of the complex tensor of impedance, Z, and is expressed as follows in Equations (11) and (12):

$$\mathrm{\phi }={\mathrm{X}}^{-1}\mathrm{Y}$$ (11)

$$\mathrm{Z}=\mathrm{X}+\mathrm{i}\mathrm{Y}$$ (12)

The observed impedance $\mathrm{Z}=\mathrm{C}{\mathrm{Z}}_{\mathrm{R}}$, if galvanic distortion is present, where C is the distortion tensor, and ${\mathrm{Z}}_{\mathrm{R}}={\mathrm{X}}_{\mathrm{R}}+\mathrm{i}{\mathrm{Y}}_{\mathrm{R}}$ is the regional impedance. As a result, the distorted real part $\mathrm{X}=\mathrm{C}{\mathrm{X}}_{\mathrm{R},}$ and the distorted imaginary part as $\mathrm{Y}=\mathrm{C}{\mathrm{Y}}_{\mathrm{R}}$ can be written. The regional and observed phase tensors are the same (Equation (13)) and free of galvanic distortion, according to the following correlations:

$$\mathrm{\phi }={{\mathrm{X}}_{\mathrm{R}}}^{-1}\mathrm{Y}={\left({\mathrm{C}\mathrm{X}}_{\mathrm{R}}\right)}^{-1}\left({\mathrm{C}\mathrm{Y}}_{\mathrm{R}}\right)={{\mathrm{X}}_{\mathrm{R}}}^{-1}{\mathrm{C}}^{-1}\mathrm{C}{\mathrm{Y}}_{\mathrm{R}}={{\mathrm{X}}_{\mathrm{R}}}^{-1}{\mathrm{Y}}_{\mathrm{R}}={\mathrm{\phi }}_{\mathrm{R}}$$ (13)

The principal or singular values of, $\mathrm{\Phi }$, β, and β, which describe the phase tensor, can be represented as expressed by ${\mathrm{\phi }}_{\max }\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{\phi }}_{\min }$ are given by:

$$\mathrm{\phi }={\mathrm{R}}^{\mathrm{T}}\left(\alpha -\beta \right)\left[\begin{array}{cc}{\mathrm{\phi }}_{\max }& 0\\ 0& {\mathrm{\phi }}_{\min }\end{array}\right]\mathrm{R}\left(\alpha +\beta \right)$$ (14)

Here ${\mathrm{R}}^{\mathrm{T}}$ represents the transposed or inverse of the rotation matrix, while $\mathrm{R}\left(\alpha +\beta \right)$ represents the rotation matrix.

Bibby et al. (2005) defined ellipticity ($\mathbf{\lambda }$) expressed in Equation (15) as a dimensionality metric as follows:

$$\lambda =\frac{{\left[{\left({\mathrm{\phi }}_{\mathrm{x}\mathrm{x}}-{\mathrm{\phi }}_{\mathrm{y}\mathrm{y}}\right)}^2+{\left({\mathrm{\phi }}_{\mathrm{x}\mathrm{y}}+{\mathrm{\phi }}_{\mathrm{y}\mathrm{x}}\right)}^2\right]}^{1/2}}{{\left[{\left({\mathrm{\phi }}_{\mathrm{x}\mathrm{x}}+{\mathrm{\phi }}_{\mathrm{y}\mathrm{y}}\right)}^2+{\left({\mathrm{\phi }}_{\mathrm{x}\mathrm{y}}-{\mathrm{\phi }}_{\mathrm{y}\mathrm{x}}\right)}^2\right]}^{1/2}}$$ (15)

The principal values of the phase tensor are identical to its eigenvalues if the phase tensor is symmetric (β = 0), implying that the regional conductivity distribution is mirror-symmetric [62]. This occurs for 1D or 2D regional distribution. The phase tensor of the 1D structure has a circular shape $\left({\mathrm{\phi }}_{\max }={\mathrm{\phi }}_{\min }\right)$ with the values $\beta =0$, and $\lambda =0$. The phase tensor is depicted as an ellipse that is lower to extremely small, approaches zero (β = ± 3°), and the principal values of a 2D regional structure of resistivity are usually unique $\left(\mathrm{i}.\mathrm{e}{\mathrm{\phi }}_{\max }\ne {\mathrm{\phi }}_{\min }\right)$. The phase tensor ellipse, on the other hand, has part of its principal axes in the direction of the strike. Whereas the non-symmetric phase tensor has a considerable skew angle (β). An alternative sign of a 3D structure is a quick lateral variation in the major axis when a 3D structure is present. As a result, all of the invariants, namely, $\beta \ne 0,{\lambda \ne 0,\mathrm{\phi }}_{\max }\ne 0\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{\phi }}_{\min }\ne 0$, are non-zero when assuming a 3D structure.

Figs. 6–8 depict phase tensor maps at various frequencies in the Ashute geothermal field that indicate the dimensionality of MT data. The 1D symbol occurs at 320, 50, and 9.4 Hz, and has a small skew angle (−3 3) the phase tensor is circular, as illustrated in Fig. 6. Fig. 7 shows that 2D structures viewed near or less than 0.02 Hz have a small skew angle and an elliptical phase tensor. The phase tensor analysis result, as shown in Fig. 8, reveals 3D. At 0.0088, 0.00275, and 0.0011 Hz are indicated as the deeper structures with large skew angles. Consequently, the phase tensor analysis at shallow depths shows dimensionality of 1D and 2D, and high skew angles at deeper depths described 3D effects below 0.011 Hz.

Fig. 6.

The maps depict the phase tensors of all stations at 320, 50, and 9.4 Hz frequencies from left to right, respectively, and tipper vectors and phase tensor ellipses (plotted according to the Parkinson convention).

Fig. 8.

The maps depict the phase tensor of all stations at 0.0088, 0.00275, and 0.0011 Hz frequencies from left to right, respectively, and tipper vectors and phase tensor ellipses (plotted according to the Parkinson convention).

Fig. 7.

The maps depict the phase tensor of all stations at 1.02, 0.2, and 0.011 Hz frequencies from left to right, respectively, and tipper vectors and phase tensor ellipses (plotted according to the Parkinson convention).

4. Three-dimensional MT inversion

There are many 3D inversion algorithms developed and available for use [21,22,[64], [65], [66], [67], [68], [69], [70], [71]]. For academic purposes, ModEM and WSINV3DMT Inversion codes are freely available. In this study, the ModEM inversion tool [20–22] was utilized to perform 3D MT inverse modeling with a full impedance tensor as input data elements. For electromagnetic data inversions, the ModEM program (Kelbert et al., 2014) was written in Fortran 90 and developed at Oregon State University by Naser Meqbel, Gary Egbert, and Anna Kelbert. The inversion process is established on Non-Linear Conjugate Gradients (NLCG), and the finite difference method (FDM) was utilized to solve the 3D forward problem. This approach requires extremely little memory since it keeps away from storing the Jacobian matrix and instead directly computes it. The line search strategy iteratively updates the original model, ${\mathrm{m}}_0$. The ModEM3DMT algorithm seeks the optimal model to minimize the objective function (see Equation (16)), which comprises model regularization and a data regularization term in the 3D magnetotelluric inversion process [22]:

$$\mathrm{\Phi }\left(\mathrm{m},\mathrm{d}\right)={\left(\mathrm{d}-\mathrm{f}\left(\mathrm{m}\right)\right)}^{\mathrm{T}}{{\mathrm{C}}_{\mathrm{d}}}^{-1}\left(\mathrm{d}-\mathrm{f}\left(\mathrm{m}\right)\right)+\lambda {\left(\mathrm{m}-{\mathrm{m}}_0\right)}^{\mathrm{T}}{{\mathrm{C}}_{\mathrm{m}}}^{-1}\left(\mathrm{m}-{\mathrm{m}}_0\right)$$ (16)

where d represents the observed data, $\mathrm{f}\left(\mathrm{m}\right)$ represents the forward response, m represents the conductivity model, ${\mathrm{C}}_{\mathrm{d}}$ represents the covariance of data, ${\mathrm{C}}_{\mathrm{m}}$ represents the covariance of the model, ${\mathrm{m}}_{\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r}}\left({\mathrm{m}}_0\right)$ represents the prior model, and a trade-off parameter (λ).

For 3D inversion, the initial model used consists of 54 × 34 × 45 cells in the x, y, and z directions, respectively. The total number of cells is 82, 6200 as shown in Fig. 16. Poor-quality (large error bars) data with wide scatter were recognized and removed manually from the input data, and the data was carefully selected. The data includes the full impedance tensor. It enhances the recovery of the actual resistivity structure and makes the previous model less reliant [72]. The inner grid in the model's central component (core) has a grid cell size of 200 × 200 m in the x and y directions, respectively, with 7 padding cells rising by a factor of 1.3 in each direction. There are a total of 45 layers in the vertical direction, with the first layer thickness of 15 m increasing by a factor of 1.1 for the successive layers (Fig. 9).

Fig. 16.

The elevation of the Ashute geothermal field, and the locations of the MT stations and water sample sites, are depicted on a map.

Fig. 9.

The map illustrates the model grid that was used for the 3D inversion of the Ashuite geothermal field data.

For each iteration, the root mean square misfit (RMS) as expressed in Equation (17) and residuals ${\mathrm{r}}_{\mathrm{i}}$ distribution (Equation (18)) were analyzed to assess the final recovery model's quality. The overall RMS is presented in ModEM, which is calculated as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}=\sqrt{\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\frac{{\left({{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{o}\mathrm{b}\mathrm{s}}-{{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}\right)}^2}{{{\mathrm{e}}_{\mathrm{i}}}^2}}$$ (17)

where ${{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{o}\mathrm{b}\mathrm{s}}$ and ${{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}$ are represents the observed and predicted responses, respectively, and ${\mathrm{e}}_{\mathrm{i}}$ is observed response errors, and N is the number of responses at all sites and times evaluated. The residuals are calculated as follows:

$${\mathrm{r}}_{\mathrm{i}}=\frac{{{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{o}\mathrm{b}\mathrm{s}}-{{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{p}\mathrm{r}\mathrm{e}}}{{{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{o}\mathrm{b}\mathrm{s}}}$$ (18)

The recovered models are deemed suitable if the residuals have a mean value of zero and little variation, or are at least equally distributed. In this investigation, the initial RMS for the 3D inversion model was 40.6 at the start of the inversion and decreased to 1.69 after 94 iterations. The background resistivity of the initial model was set to 100 Ωm. In general, the resulting model's data misfit is reasonable, with only a few under or over-fitted data portions (Fig. 10).

Fig. 15.

RMS misfit, calculated for the preferred model at each iteration number.

Fig. 10.

The results of a 3D inversion of measured and computed curve fitness of apparent resistivity and phase for a few selected stations. Red represents TE mode (${\mathrm{Z}}_{\mathrm{x}\mathrm{y}}$) and blue represents TM mode ($Z_{yx}$). The dotted lines represent the measured data, while the solid lines represent the computed response.

5. Result and discussion

The dimensionality analysis result obtained from the phase-based tools of the Ashute MT data are consistent, and the MT dataset revealed that, at higher periodicity, the geoelectric subsurface structure is 3D in nature, implying the need for a 3D model. The identified notable structures of the 3D distribution of resistivity cross-section of the Ashute geothermal field were very high resistivity (> 100 Ωm) mixed with the low resistivity body, followed by a conductive layer below 10 Ωm overlay of the moderately resistive layer with resistivity values (10–46 Ωm), at deeper depths as shown in Fig. 11. In the Ashute geothermal field at shallow depths, the geoelectrical structure is complex because of the non-uniform horizontal resistivity distribution of unconsolidated sediments and unaltered volcanic products exposed in the Ashuite site. At these depths, the layer has a high resistivity value with a thickness of roughly 300 m, whereas conductive layers have a thickness that extends up to 1500 m. In most of the study area, low resistivity appears at around 300 m, while at some spots in the area, it begins at the surface and discontinues. Resistivity gradually increases with depth below the conductive zone. Figs. 13 and 14 show the cross-sections of resistivity in the directions of N–S and E–W for the recovered 3D MT model. These sections of resistivity described the main characteristics of the Ashute subsurface formations. A 3D inversion model of the Ashute area indicates there are no substantial conductive features at deeper depths since the vertical slices are depicted up to a maximum depth of 5 km for simplicity and in order to obtain a better resolution map. However, we tried to make a 3D inversion model up to 10.8 km depth. The vertical Slice of the 3D model only along sections with good site coverage denoted as AA’, BB’, CC’, DD’, EE, and FF’ were used in order to avoid misinterpretations as shown in Figs. 13 and 14. The vertical slice along the N–S is represented by profiles AA’, BB’, and CC’ which are shown in Fig. 13. Due to the effect of altered lacustrine sediment, the vertical slice along AA’ indicates a low resistive zone (ρ < 5 Ωm) and (ρ < 10 Ωm) observed on the top layer at a depth down to 50 m. The presence of conductive clay minerals in the central region of the profile (1.6 < x < 6.4 km) at a depth between 30 m and 1500 m, the high resistivity (ρ ≥ 100 Ωm) of the upper few hundred meters of the shallow layers extend down to 200 m, whereas for profiles BB’ and CC’ have similar resistivity distribution as AA’, but the thickness of conductive clay minerals of them are smaller than it. At greater depths resistivity increases step by step from a resistivity value of 10–46 Ωm to maximum values of ρ > 100 Ωm. The upper few hundred meters shallow resistive layers is a resistive (ρ ≥ 100 Ωm) that is exposed on the surface at (6.4 km < x < 8 km) on the profile BB’.

Fig. 13.

The vertical cross-sections drawn from the 3D inversion resistivity model of the Ashute geothermal site on the profiles AA', BB', and CC' in the direction of N–S, as shown in Fig. 12.

Fig. 14.

The vertical cross-sections drawn from the 3D inversion resistivity model of the Ashute geothermal site on the profiles DD', EE', and FF' in the direction of E–W, as shown in Fig. 12.

The vertical slice along the E–W is represented by profiles DD’, EE’, and FF’ which are shown in Fig. 14. The E–W slice along DD' in the north of the Ashuite reveals a shallow, thin high resistive zone (ρ ≥ 100 Ωm) started from the surface observed in the central region between 1 and 2.4 km in the east, which is only about the thickness of 300 m, whereas underlay this high resistivity body the low resistivity (ρ < 10 Ωm) also extends down between 400 m and 800 m in the central region between 0.6 and 2.4 km in the east. At greater depths resistivity gradually increases from a resistivity value of 10–46 Ωm to maximum values of ρ > 100 Ωm. The E–W slice along with EE’, and FF'in the central and south of the Ashute is shown in Fig. 12. The high resistivity of the central and south of the Ashute overlays the low resistivity with almost the same thickness as DD' on the top layer for each slice exposed with low and high resistivity body interpreted as altered lacustrine sediment and unaltered volcanic material. For both vertical slices N–S and E–W, the zone of high resistivity (ρ ≥ 100 Ωm) extends a depth down to 400 m and almost below 3 km, with a conductivity zone overlying a moderately resistive core (reservoir). At depths below and above 10.8 km, the recovered model shows no significant high conductive structure. The result of the resistivity pattern in this study is very similar to the previous magnetotelluric study at Aluto Langano geothermal field in CMER [14,15]. However, the only known structure coming into question as a potential conductor is the SDFZ, located 40 km west of Aluto at the western rift margin [14].

Fig. 12.

A Horizontal slice was obtained from the ground with Z = 142 m. A white dot indicates an MT station. The initial subsurface layer without topography corresponds to the horizontal slice's depth. Figs. 13 and 14 show resistivity cross-sections taken in N–S and E–W directions along with Lines AA’, BB, CC’ DD’, EE’, and FF’.

In the western side of the study area, the Geological Survey of Ethiopia (GSE) collected and analyzed water samples from five sites from hot springs, mud pools, and a Crater Lake in 2017 (see. Fig. 1). The thermal manifestations around the study area show a better permeable zone and high CO2 flux [7,73]. Hot springs were taken into account because of their high flow rates and high discharge temperatures. The standard method was used to analyze the water samples' chemical composition. The results of water samples in the Ashuite area (Fig. 16) with codes of 0.01, 0.02, and 0.04 have a low ratio of Na/K and a high ratio of Na/Mg. These results revealed that the materials within the water samples had originated from the source of a deep reservoir. Water sample sites with codes 0.01, 0.03, and 0.05 have similar Cl/SO4 ratios, which suggests that the materials have the same geological context and originated from the same source [74]. The heat source of Ashute (Butajira) geothermal fluids is derived mainly from the crust because the expected value of the helium isotope ratio 3He/4He is smaller than that of mantle plumes. Because of interactions with crustal minerals, the helium isotope ratio can drop to as low as 2.3 Ra [7].

According to the silica geothermometers, sample code 0.03, which has a subsurface temperature of about 158.86 °C, is the hottest spring in the Ashute area, followed by sample code 0.01, which has a subsurface temperature of about 151.8 °C. The Na–K and K–Ca ratios for codes 0.01, 0.02, and 0.03 are 208 °C, 754 °C, 206 °C, and 287.9 °C, 374.5 °C, 311.5 °C, respectively. However, the values of the silica geothermometer are less than those of the Na–K and K–Ca geothermometers. These results are inconsistent with those obtained using Na–K geothermometers, which showed in the Haro Shetan water samples (with sample code 0.02) were the hottest. The difference in these geothermometers' results could indicate an effect of meteoric waters, which comprise dissolved constituents that differ from those found in the geological environment (shallow conditions mixing with groundwater). According to Gebrewold [74], the discharge temperature of the hot springs in the study region (Ashute hot springs) ranges from 77.5 °C to 91.06 °C, with pH values ranging from 7.0 to 8.92, indicating that they are closer to neutrality and some extent alkaline in nature.

The enthalpy, which is used to express the heat content of the fluids and acts as the carrier transferring heat from deep heated rocks to the surface, is often used to classify geothermal resources. The Ashute geothermal potential region, which uses a hinge on silica and the molecular ratio of geothermometers, is obtained from intermediate to high enthalpy resources [74]. According to a consequence of the geothermometer results, mud pools and some manifested hot springs have substantial heat-generating capabilities, indicating that more research is needed to determine their appropriateness for energy generation.

The recovered 3D inversion model of the resistivity of the Ashute area was interpreted to correlate with the conceptual model of a high-enthalpy geothermal system as explained by Johnston et al. [75], Samrock et al. [14], and Cherkose & Mizunaga [15]. The alteration mineralogy is primarily responsible for the high-temperature subsurface resistivity distribution [8,15,54,67]. In the Ashute area, the resistivity cross-section of the model indicates three distinct anomalies: the very resistive top layer of approximately 300 m maximum thickness from the surface in the limited area; and the low resistive zone, which starts in the south of the survey area as a result of the unconsolidated sediment in the swampy area, followed by the altered zones of low resistivity. The presence of smectite, which has a low resistivity (< 5 Ωm) and a thickness of 750 m, distinguishes the upper smectite zone (alteration zone). The illite/chlorite zone, the second alteration zone, has a resistivity of < 10 Ωm, and a thickness of 250 m. The creation of alteration minerals has high temperatures and is mainly comprised of minerals like chlorite and epidote with resistivity (10–46 Ωm), which has resulted in the establishment of the last moderately resistant core (reservoir) zone underneath the conductive region as a source of heat. The up-flow zone is a region of the reservoir where the flow of fluid is mainly in the vertical direction and the distribution of temperature with depth has a low vertical gradient. The conductive clay cap typically increases close to the surface because of the comparative increment minerals in the layer, which have higher resistivity minerals with different resistivities above the up-flow zone. Chlorite, epidote, smectite, calcite, and quartz are the most common alteration minerals in the major stages. We didn't obtain a low resistivity structure in a deep, active magmatic system under Ashute. However, a forward model was developed to explain the tippers indicating the possibility of melting located about 5–10 km southeast of the Ashute geothermal zone. Samrock et al. [14] used MT data analysis of forward modelling tipper results for the Aluto geothermal area along the SDFZ to predict the high-conductive region. This high conductive zone corresponds to the previous study of the low seismic velocity region [19] and the high conductive anomaly from the MT study [18,76]. Therefore, the presence of a strong conductor under the SDFZ is approximately 5–10 km SE of Ashute Geothermal Field or 40 km NW of Aluto at lower crustal depths.

6. Conclusions

The magnetotelluric method, which determines the subsurface electrical resistivity distribution, is a frequently used technique for geothermal exploration. The dimensionality analysis of the Ashute MT data at shallow depths indicates 1D and 2D structures, and deeper depths show 3D structures, suggesting the requirement for 3D inversion to image the complicated structure of the subsurface. The inversion program used for the recovered 3D resistivity model was ModEM. For the 3D inversion, 30 sites of MT data covering a total of 80 frequencies over a period range of 0.001–1000 s were utilized for the inversion process. The recovered 3D inversion of the resistivity model of the Ashute geothermal site was interpreted to correlate with the conceptual model of a high-enthalpy geothermal system. It is immensely reliant on subsurface alteration mineralogy. The identified notable structures of the 3D distribution of resistivity cross-section of the Ashute geothermal field, were very high resistivity (> 100 Ωm) mixed with the low resistivity body at the top layer, followed by a conductive layer below 10 Ωm overlays of the moderately resistive layer with values of resistivity (10–46 Ωm), at deeper depths. The low resistivity zones are categorized into two parts with a resistivity value of less than 5 Ωm and less than 10 Ωm. The low resistivity begins to appear at 500 m, becoming dominant in the area and, in some areas, extending from the surface to 1500 m. As you go deeper below the conductive zone, the resistance gradually increases. The recovered 3D inversion model did not disclose an extremely low deep resistivity structure under the Ashute site. Thus, based on these findings, we conclude that the existence of a hot extended magma reservoir beneath the Ashute geothermal field is doubtful and that the source of unrest is most likely due to changes in the hydrothermal system rather than an active magmatic system. The results of tipper forward modelling show a conducting region found about 5 km SE of Ashute along the SDFZ. A regional extremely conductive zone was identified 40 km west of Aluto, closer to the SDFZ, in a previous study [14,76]. However, the Ashute geothermal field could not exist in the deep extended high conductive body because it is found some 45–50 km away from the Aluto geothermal field.

Author contribution statement

Aklilu Abossie: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools, or data; Wrote the paper.

Dr. Shimeles Fisseha (Associate professor) and Pro. Bekele Abebe: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data, and supervision.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

The data that has been used is confidential.

Additional information

No additional information is available for this paper.

Declaration of competing interest

The authors declare no conflict of interest.