theadvantages$of$complementingmt$profilesin$36d...

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The advantages of complementing MT profiles in 3-‐D environments with 2

geomagnetic transfer function and inter-‐station horizontal magnetic transfer 3

function data: Results from a synthetic case study 4

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Joan Campanyà1, Xènia Ogaya1, Alan G. Jones1,2, Volker Rath1, Jan Vozar1 & Naser 7

Meqbel3 8

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1Dublin Institute for Advanced Studies (DIAS), Ireland 10

2Now at: Complete MT Solutions, Ottawa, Canada 11

3GFZ German Research Centre For Geosciences, Potsdam, Germany 12

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E-mail: [email protected] 17

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SUMMARY 27

As a consequence of measuring time variations of the electric and the magnetic field, 28

which are related to current flow and charge distribution, magnetotelluric (MT) data in 29

two dimensional (2-D) and three dimensional (3-D) environments are not only sensitive 30

to the geoelectrical structures below the measuring points but also to any lateral 31

anomalies surrounding the acquisition site. This behaviour complicates the 32

characterisation of the electrical resistivity distribution of the subsurface, particularly in 33

complex areas. In this manuscript we assess the main advantages of complementing the 34

standard MT impedance tensor (Z) data with inter-station horizontal magnetic tensor (H) 35

and geomagnetic transfer function (T) data in constraining the subsurface in a 3-D 36

environment beneath a MT profile. Our analysis was performed using synthetic 37

responses with added normally distributed and scattered random noise. The sensitivity of 38

each type of data to different resistivity anomalies is evaluated, showing that the degree 39

to which each site and each period is affected by the same anomaly depends on the type 40

of data. A dimensionality analysis, using Z, H and T data, identifies the presence of the 41

3-D anomalies close to the profile, suggesting a 3-D approach for recovering the 42

electrical resistivity values of the subsurface. Finally, the capacity for recovering the 43

geoelectrical structures of the subsurface is evaluated by performing joint inversion 44

using different data combinations, quantifying the differences between the true synthetic 45

model and the models from inversion process. Four main improvements are observed 46

when performing joint inversion of Z, H and T data: (1) superior precision and accuracy 47

at characterising the electrical resistivity values of the anomalies below and outside the 48

profile; (2) the potential to recover high electrical resistivity anomalies that are poorly 49

recovered using Z data alone; (3) improvement in the characterization of the bottom and 50

lateral boundaries of the anomalies with low electrical resistivity; and (4) superior 51

of 63Geophysical Journal International

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imaging of the horizontal continuity of structures with low electrical resistivity. These 52

advantages offer new opportunities for the MT method by making the results from an 53

MT profile in a 3-D environment more convincing, supporting the possibility of high-54

resolution studies in 3-D areas without expending a large amount of economical and 55

computational resources, and also offering better resolution of targets with high 56

electrical resistivity. 57

58

1. INTRODUCTION 59

Over the last thirty years theoretical and technological developments have justified and 60

established the use of the magnetotelluric (MT) method in many regions with widely 61

differing objectives, by adjusting it to the specific requirements of each area of study 62

(e.g., Chave & Jones, 2012). Thanks to this relatively rapid progress, MT studies have 63

been undertaken from the deepest seas (e.g. Heinson et al., 2000; Baba et al., 2006; 64

Seama et al., 2007) to the highest mountain ranges on Earth (e.g., Le Pape et al., 2012; 65

Kühn et al., 2014), characterizing the geoelectrical subsurface in a large variety of 66

regions and for both academic and commercial applications (e.g., Heinson et al., 2006; 67

Tuncer et al., 2006; Falgàs et al., 2009; Jones et al., 2009; Campanyà et al., 2011; La 68

Terra & Menezes, 2012; Ogaya et al., 2014; Piña-Varas et al., 2014). However, 69

limitations of the MT method still exist and there is ample room for improvement. 70

One of the main issues hindering high resolution of the subsurface using MT is that in 3-71

D environments the data can be strongly affected by geoelectrical structures located 72

some distance away from the sites where the data are acquired, affecting most data sets 73

to at least some degree (e.g. Brasse et al., 2002), and potentially leading to inaccurate 74

characterization of the subsurface below the study area (e.g. Jones & Garcia, 2003). In 75

recent years, the availability of 3-D forward and inversion codes (e.g. Farquharson et al. 76


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2002; Siripunvaraporn et al. 2005a; Avdeev & Avdeeva, 2009; Egbert & Kelbert 2012; 77

Kelbert et al., 2014; Grayver, 2015; Usui, 2015) has improved the characterization of the 78

subsurface in these situations, and 3-D inversion has become a more routine procedure 79

for the EM community, although more experience is needed before it becomes as firmly 80

established as is 2-D inversion (e.g., Miensopust et al., 2013; Tietze & Ritter, 2013; 81

Kiyan et al., 2014). 82

However, difficulties associated with logistics, acquisition costs and instrumentation 83

availability still often require MT field specialists to acquire data predominantly along 2-84

D profiles, even when the study is performed in a 3-D environment. Jones (1983), 85

Wanamaker et al. (1984), Berdichevsky et al. (1998), Park & Mackie (2000), Ledo et al. 86

(2002) and Ledo (2005) studied the limitations of 2-D interpretation of 3-D MT data and 87

made various recommendations, showing some situations where 2-D inversion of 3-D 88

data can properly reproduce the geoelectrical subsurface when the content in the 2-D 89

modes is appropriately chosen for inversion. Siripunvaraporn et al. (2005b) suggest that 90

if the data are 3-D in nature but collected along a profile rather than on a grid, the results 91

from the 3-D inversion of the MT profile are superior to the results obtained by 92

performing 2-D inversion of the same data, even with the far coarser mesh employed in 93

3-D as compared to 2-D inversion. Following this idea, several publications recommend 94

inverting all four components of the MT impedance tensor (Z), e.g. Siripunvaraporn et 95

al. (2005b), Tietze & Ritter (2013) and Kiyan et al. (2014), instead of the approach of 96

inverting only the off-diagonal components (Zo) (e.g. Sasaki, 2004; Sasaki & Meju, 97

2006). However, the presence of anthropogenic noise can strongly reduce the quality of 98

the Z data, in particular the quality of the diagonal components, making it sometimes 99

worthless to use all components of the Z tensor for the inversion process because of 100

scatter and/or extremely large errors in the diagonal components of Z. 101


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Inter-station horizontal magnetic transfer function (H) and the geomagnetic transfer 102

function (T) data, which are not affected by electric field effects caused by galvanic 103

distortion from charges on conductivity boundaries or gradients on small-scale 104

structures, have been used to improve MT results and constrain the subsurface using 2-D 105

or 3-D inversion (e.g. Soyer & Brasse, 2001, 2-D H only of field data; Gabàs & 106

Marcuello, 2003, 2-D Z + T theoretical study; Siripunvaraporn & Egbert, 2009, 3-D Z, T 107

and Z+T of synthetic and field data; Berdichevsky et al., 2010a, 2-D Z + T of field data; 108

Habibian et al., 2010, 2-D Z + T of field data; Tietze & Ritter, 2013), 3-D Z, T and Z+T 109

of synthetic and field data, Habibian & Oskooi, 2014, 2-D H cf. T theoretical study, 110

Meqbel et al., 2014, Z, T and Z+T of field data, Rao et al., 2014, Z and Z+T of field 111

data; Yang et al., 2015, Z and Z+T of field data; Varentsov, 2015a,b, performing 2D, 112

2D+ and quasi 3-D inversion using Z, T and H with theoretical and field data), but no-113

one has yet undertaken an examination of the advantages of including H and T , 114

simultaneously, when performing 3-D inversion of Z data (Z+H+T in 3-D). It should be 115

noted that the magnetic effects caused by galvanic distortion charges do affect Z, H and 116

T (e.g., Chave & Smith, 1994; Chave & Jones, 1997), however, these effects rapidly 117

decrease with increasing period due to the square root dependence of their sensitivity on 118

frequency, and can effectively be ignored over broad frequency bands. This rapid 119

decrease is true for pure galvanic distortion but not in other situations as for example in 120

the case of presence of current channelling caused by thin-long structures (e.g. Lezaeta 121

and Haak, 2003; Campanyà et al., 2012). 122

Another area for improvement for the MT geophysical technique is its issue with 123

recovering high electrical resistivity anomalies in areas with contrasting low electrical 124

resistivity values, or areas beneath strong low resistivity anomalies (e.g. Vozoff, 1991; 125

Berdichevsky et al., 1998; Bedrosian, 2007; Berdichevsky & Dmitriev, 2008; Chave & 126


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Jones, 2012; Miensopust et al., 2013). The capacity at recovering low electrical 127

resistivity structures is a particular strength of the MT method as a geophysical 128

technique when characterizing geoelectrical structures from the first few metres to the 129

asthenosphere (e.g. Jones, 1999; Ledo et al., 2011; Rosell et al., 2011; Campanyà et al., 130

2012; Ogaya et al., 2013; Dong et al., 2014; Muñoz, 2014). However, issues in 131

recovering high electrical resistivity anomalies are somewhat of a limitation for the MT 132

method in certain resource exploration applications, for example where resistive 133

hydrocarbons are present (e.g. Simpson & Bahr, 2005; Unsworth et al., 2005) and very 134

high quality data are required. 135

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The aim of this paper is to evaluate and highlight, from numerical experiments, the 137

advantages in combining Z (full tensor) or Zo (off-diagonal components only) responses 138

with H and T responses when characterizing and modelling the subsurface below a MT 139

profile in a 3-D environment, and to evaluate if the sensitivity and resolution issues 140

discussed above can be addressed. 141

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2. EXPERIMENTAL DESIGN 143

The numerical experiment consisted of calculating the forward responses of a defined 144

synthetic model with embedded 3-D anomalies. These responses were used for a 145

sensitivity test, evaluating the effects of each anomaly on the different types of data, Z or 146

Zo, H and T. Dimensionality analyses and inversions were also performed characterising 147

the 3-D behaviour of the responses and recovering the electrical resistivity structures of 148

the subsurface by performing 3-D joint inversion with different combinations of Z, H 149

and T. The fit of the data and the accuracy for recovering the electrical resistivity 150


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distribution of the subsurface was quantified with the aim of providing a robust support 151

to the conclusions extracted from the experiment. 152

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2.1 Synthetic Model 154

The background structure of the synthetic model (Fig. 1) is a 1-D layered Earth 155

comprised of four layers: (1) a resistivity of 100 Ωm between 0 m (the surface) and 90 m 156

depth; (2) a resistivity of 400 Ωm between 90 m and 1500 m depth; (3) a low-resistive 157

layer of 10 Ωm between 1500 m and 2000 m depth; and (4) a layer from 2000 m to 90 158

km depth with a resistivity of 200 Ωm. A half space of 20 Ωm at 90 km depth was added 159

at the bottom of the model to ensure that the EM fields at the adopted periods do not 160

penetrate away from the utilized mesh, also creating a more common response for the 161

longest periods simulating the existence of a hypothetical asthenosphere. This 1-D 162

layered background was used to simulate a more realistic and complex situation than a 163

homogeneous background, and at the same time to highlight the inherent deficiencies of 164

H and T data for resolving laterally uniform structures. 165

Within this layered background structure there are three 3-D resistivity bodies; two low 166

resistivity structures (L1 and L2) and a high resistivity body (H1) (Fig. 1). Both low and 167

high resistivity anomalies have been added to highlight the resolution differences 168

between these two types of anomalies when characterising the subsurface. L1 and L2 are 169

located between 500 m and 1000 m depth and have a resistivity value of 3 Ωm. H1 is 170

located between 1500 m and 2000 m depth, with a resistivity value of 400 Ωm. L1 and 171

H1 cross the single north-south MT profile whereas the L2 structure lies completely 172

outside the simulated linear acquisition profile to its west; this geometry was chosen 173

with the aim of evaluating the capacity of the various inversions in determining 174

structures outside the profile and to appraise if unexpected artefacts associated with L2 175


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may be artificially created below the profile. Due to the importance of the role of H and 176

T responses in characterizing the conducting 10 Ωm layer between 1500 m and 2000 m 177

depth, this layer has been labelled as target body L3. 178

179

The forward response of the synthetic model at the 28 sites located along the north-south 180

profile, covering a range of periods between 0.0001 and 1000 s (frequencies of 10000 – 181

0.001 Hz), was calculated using the ModEM code (Egbert & Kelbert 2012, Kelbert et 182

al., 2014), modified for inclusion on H responses (see supplementary material, S1, for 183

more details), with a large 3-D mesh that comprised 222 x 182 x 132 cells in the north-184

south, east-west and vertical directions, respectively. The core of the mesh comprised 185

162 x 112 x 132 cells with a horizontal cell size of 120 m x 120 m, while the distance 186

between sites was 600 m. The lateral size of the padding cells increased by a factor of 187

1.3 from the edges of the core outward to the boundaries. The thickness of the top layer 188

was 10 m, with an increasing factor of 1.048 for the subsequent layers in the z-direction, 189

ensuring that the thickness of each cell within the depth of interest, namely the first 3 190

km, is smaller than the horizontal cell size. 191

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2.2 Response types 193

As mentioned above, three different EM tensor relationships were studied in our 194

numerical experiment: (1) the standard MT impedance tensor (Z) (Eq. 1); (2) the 195

geomagnetic transfer function (T) (Eq. 2); and (3) the inter-station horizontal magnetic 196

transfer function (H) (Eq. 3). 197

𝒆! = 𝒁𝒉! (1)

ℎ!! = 𝑻𝒉! (2)

𝒉! = 𝑯!"𝒉! (3)


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198

where 𝒉! and 𝒉! are two component vectors comprising the horizontal magnetic 199

components at the local site l ℎ!! , ℎ!! and the neighbouring reference site n ℎ!!, ℎ!! , 200

respectively. The neighbouring reference site is the site used to relate the horizontal 201

magnetic fields of all the studied sites (local sites) with the horizontal magnetic fields of 202

this site (neighbouring reference site). 𝒆! is a two component vector comprising the 203

horizontal electric components at the local site l 𝑒!! , 𝑒!! and ℎ!! is the vertical component 204

of the magnetic field recorded at the local site l. 𝒁 and 𝑯!" are 2x2 complex matrices 205

and 𝑻 is a 1x2 complex vector. In all cases dependence on frequency is assumed. 206

The H transfer function relates the horizontal magnetic field between two different sites 207

(one of the local sites and the neighbouring reference site), characterizing the differences 208

associated with the electrical resistivity distribution below the two sites. This requires 209

that the structures below the neighbouring reference site should also be characterised 210

(e.g. Soyer, 2002), which can be achieved by having the neighbouring reference site 211

within the area of study. 212

213

Note that, in case the neighbouring reference site used to acquire and process the data is 214

outside the study area, for the inversion process the H data can be rearranged using as a 215

neighbouring reference site any of the sites in the study area, even if the data at this site 216

were not acquired during the whole survey. This can be achieved following steps 217

analogous to the ones used in the ELICIT methodology to process MT data (Campanyà 218

et al., 2014), in which inputs and outputs related by the transfer functions do not need to 219

be acquired simultaneously. 220

221


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For the experiment presented in this paper, site 26 (identified with a green arrow in Fig. 222

1) has been chosen as a neighbouring reference site for all of the H responses as there 223

are no prescribed anomalies below it and thereby facilitating simple evaluation of the 224

properties of the H responses. 225

226

2.3. Sensitivity Analysis 227

A non-linear sensitivity test was performed to identify the sites and periods responsive to 228

the geoelectrical anomalies and to characterize and quantify the effects of those 229

anomalies on the Z, H and T responses, individually and collectively. The sensitivity test 230

consisted of calculating the differences between the forward responses of the 1-D 231

layered model with the studied anomalies included (L1, L2 and H1) and the forward 232

responses of the background 1-D layered model without any anomalies. The differences 233

between the model responses were divided by the adopted error, thus highlighting how 234

sensitive the responses are to the anomalies with respect to the errors in the data. 235

Impedance error bounds were set to 5 % of |𝑍𝑖𝑗| for diagonal and off-diagonal 236

impedance tensor elements, in combination with an error floor of 5 % of 𝑍!" ∗ 𝑍!"!! 237

for the diagonal elements. Error floor was added to avoid the extremely small error 238

values associated with the periods of the Zxx and Zyy components not affected by the 3-239

D anomalies. For the T and the H responses we used constant error bounds of 0.02. 240

These errors were chosen consistent with the errors assumed in other publications with 241

both real and synthetic data (e.g. Soyer, 2002; Habibian et al., 2010; Egbert & Kelbert, 242

2012; Tietze & Ritter, 2013). Figures 2, 3, 4 and 5 show the effects of the L1, L2, H1 243

and L1+L2+H1 anomalies, respectively, individually and collectively as contoured 244

pseudo-sections, with distance along the profile on the abscissa and period, on a decadic 245

logarithm scale, along the ordinate. Differences within the assumed errors, values 246


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between -1 and 1, are white in colour and show the periods for the various components 247

at the sites that are insensitive to the anomalies. Therefore, for these periods the 248

anomalies cannot be resolved within the assumed precision. Dark blue and dark red 249

areas show periods at the sites that are highly sensitive to the anomaly, with anomalous 250

responses of four or more standard deviations of the assumed errors. Note the somewhat 251

simplicity of anomalous response for single features (Figs. 2-4), but the complexity of 252

the response when all features are included (Fig. 5). The total summed effect of each 253

anomaly on the responses is quantified in Fig. 6. In this figure, the sensitivities of Zo 254

(off-diagonal components of Z) are also shown, as the off-diagonal components have 255

been often used as a data type, although most practitioners now invert the full impedance 256

tensor Z. These pseudo-sections show the sensitivity of each period at each site, with 257

respect to the adopted error, between the responses of the 1-D layered model with the 258

studied anomaly and the responses of the 1-D layered model without any anomaly. The 259

sensitivity values for each period and site were calculated following equation 5: 260

261

𝑆 = 1+ (𝑎𝑏𝑠 !"#$% !"#$%&#"!!"#"!""#"

− 1) ∀ !"#$% !"#$%&#"!!"#"!""#"

> 1 (5) 262

263

where S is the sensitivity per each period and site. Note that this equation has the 264

condition that each component of the analysed tensor relationship, for each period and 265

site, is included in the summand only if difference between model response and data is 266

greater than the assumed error, which means is sensitive to the analysed anomaly. 267

268

Four main conclusions can be drawn from the sensitivity tests: 269

(1) The influence of each anomaly at a given site and at a given period depends upon the 270

types of responses used. Whereas the Z and H responses are more sensitive at the sites 271


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directly above the anomalies, the T responses are more sensitive at the sites located at 272

the edge of the anomalies. This can be understood as a consequence of the physics of 273

induction. For a uniform source field there is no vertical field above a laterally uniform 274

Earth, the greatest effects in T are off to the side of the anomaly (see, e.g., Jones, 1986). 275

(2) The anomalies affect a narrower range of periods for H and T responses than for Z 276

responses. For the Z responses, the anomalous effect extends to longer periods without 277

seeing the end of the effect of the anomalies for the analysed periods. This is because the 278

galvanic charges on the boundaries of conductivity contrasts, once imposed, remain in 279

place at all longer periods. There are both magnetic and electric effects of the charges 280

(see, e.g. Chave & Smith, 1994; Chave and Jones, 1997; Jones 2012) but the magnetic 281

effects drop off very quickly with increasing period for isolated anomalies. 282

(3) For the H and T responses the influence of anomaly L1 is stronger than for 283

anomalies L2 and H1, though the difference is not as large as for Z and Zo responses 284

(Fig. 6). This is because MT is primarily sensitive to elongated conductors, and in our 285

numerical experiment L1 is the longest and most conducting of the three anomalies. This 286

could result in the inversion modelling of the Zo and Z responses naturally focussing 287

more on fitting data responding to the L1 structure than to the other anomalies, as this 288

will lead to the greatest overall misfit reduction, whereas for the H and T responses the 289

L1, L2 and H1 anomalies will have similar weight during the inversion process. 290

(4) With the 3-D geoelectrical structures (L1, L2 and H1) orientated perpendicular to the 291

MT profile, the presence of sensitive periods for the Zxx, Zyy, Hxy, Hyx, Hyy and Ty 292

components implies that the analysed responses are sensitive to the 3-D nature of the 293

anomalies (Berdichevsky & Dmitriev, 2008). However, in this numerical experiment, 294

the effect of the L1 anomaly on the y component of the T responses is smaller than the 295


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assumed error (Fig. 2c), which means that in this situation the T responses “see” the L1 296

anomaly as a 2-D structure within the precision of the responses. 297

298

The different influences of each anomaly in relation to the examined types of responses 299

suggest that the use of H and T responses as an accompaniment to the commonly used 300

Zo and Z responses will introduce complementary information that enhances resolution 301

and restricts acceptable model space, whilst simultaneously increasing the weight to the 302

L2 and H1 anomalies during the inversion process. 303

304

2.4. Dimensionality analysis 305

The dimensionality of the synthetic model was analysed using the Z, H and T responses 306

separately (Fig. 7). Normally distributed scattered random noise was added to the 307

responses in a manner consistent with the errors assumed for the sensitivity test. In 308

particular, the added noise at each site and frequency was derived by generating random 309

numbers from the normal distribution with mean parameter (0) and standard deviation 310

(1) and multiplying this number by the data error of the responses. The same errors as 311

those assumed for the sensitivity test were assumed for the distorted responses. 312

For the Z responses, dimensionality analysis was performed using the phase tensor 313

(Caldwell et al., 2004), as this method is routinely used for evaluating the dimensionality 314

of the study area without being affected by galvanic distortion. To assess the presence of 315

3-D structures, a variant of the β criterion was used. Typically β is used to justify 2-D/3-316

D interpretation based on a threshold value (see e.g. Caldwell et al., 2004; Thiel et al. 317

2009; Booker, 2014). In this case we took into account the errors of the data, as 318

suggested by Booker (2014), interpreting all deviations from zero that are above the 319

error in determining β as a 3-D. The ellipses are each filled with a colour associated with 320


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the magnitude of β divided by this error. Values greater than one require the presence of 321

3-D structures (Fig. 7a). The error in β was calculated by computing a thousand β values 322

using different values of the Z components (Zxx, Zxy, Zyx and Zyy, real and imaginary) 323

randomly distributed within the total range of the assumed error. 324

For the H responses dimensionality analysis was performed following similar criteria to 325

that used by Berdichevsky et al. (2010b), plotting the variations of the H responses: H-I, 326

where I is the identity matrix. In this case 1-D structures are represented by dots 327

(Phi_max = Phi_min = 0), 2-D structures by lines (Phi_max > Phi_min = 0) and 3-D 328

structures by ellipses (Phi_max ≥ Phi_min ≠ 0). The colour represents the magnitude of 329

Phi_min divided by the error of Phi_min. Only values greater than one require the 330

presence of 3-D structures to explain the observed responses (Fig. 7b). Error in Phi_min 331

values were derived following equivalent steps to that the calculation of the error in β. 332

333

Finally, induction arrows (Schmucker, 1970), following the Parkinson criteria (i.e., the 334

real arrows generally point towards current concentrations in conducting anomalies, 335

Jones, 1986), were used to study the dimensionality of the area using the T responses 336

(Fig. 7c). For the T responses, the presence of real and imaginary arrows pointing in 337

non-parallel directions at the same period and site is associated with a 3-D structure, as 338

the imaginary induction arrow is approximately parallel to the difference between two 339

real induction arrows at consecutive periods at the same site (Marcuello et al., 2005). 340

The coloured circles show the differences between the angle of the real and the 341

imaginary arrows, for each period and site, divided by the error at constraining the angle 342

difference. Note that to define the angle difference between real and imaginary arrows 343

we computed the differences using the same and opposite directions of the real and 344

imaginary arrows, and selected the minimum angle difference value. Values greater than 345


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one at dividing the angle difference by the error at determining the angle difference 346

suggest the presence of 3-D structures (Fig. 7c). Errors at defining the angle difference 347

between real and imaginary arrows were derived following equivalent steps to that the 348

calculation of the error in β. 349

350

Comparing the results in Fig. 7 between all sites and periods, differences between the 351

angles of the phase tensor ellipses (removing the 90º ambiguity), the directions of the 352

arrows (T responses) and the angles of Phi_max (H responses), all of them are also 353

related to a 3-D environment. Note that for structures crossing the MT profile (L1 and 354

H1), the phase tensor and the induction arrows appear to characterize the 3-D behaviour 355

at the sites located at the edges of the anomalies, whereas looking at the variations of H, 356

sites located above of the anomalies seems to be more affected by the 3-D effect of the 357

anomalies. 358

359

2.5. 3-D Inversion of the MT Profile 360

Nine inversions were performed using different combinations of Z, Zo, H and T 361

responses employing the ModEM algorithm (Egbert & Kelbert 2012, Kelbert et al., 362

2014) modified for inclusion on H responses, (see supplementary material, S1, for more 363

details). In all cases, the same inversion parameters were used to avoid differences 364

associated with inversion set-up parameters and thus focusing only on the differences 365

related to the investigated data types. 366

367

2.5.1 Inversion parameters 368

The 3-D solution mesh, purposely chosen with a lower resolution than the forward mesh 369

described above, comprised 137 x 120 x 99 cells in the north-south, east-west and 370


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vertical directions, respectively. The centre of the mesh comprised 99 x 62 x 99 cells 371

with a horizontal cell size of 200 m x 200 m, while the distance between sites was 600 372

m, thus ensuring the presence of free cells between the sites. The lateral extent of the 373

padding cells increased by a factor of 1.3. The thickness of the top layer was 10 m, 374

increasing by a factor of 1.069 for the subsequent layers in the z-direction. The same 375

responses studied in the dimensionality analysis, with added noise, were used for the 376

inversion process, but only for periods between 0.0001 s (frequency of 10000 Hz) and 377

31.62 s (frequency of 0.0316 Hz), focusing on the periods affected by the anomalies and 378

avoiding the periods affected by the assumed hypothetical asthenosphere at 90 km depth. 379

380

Several tests were executed to choose the initial electrical resistivity model and the 381

smoothing parameters. The starting model was chosen after inverting the Z responses, 382

which are sensitive to lateral-vertical variations and to the actual resistivity of the 383

subsurface, with seven different half-space starting models of 80, 100, 120, 150, 200 and 384

400 Ωm, respectively. Inversion results starting with a half-space model of 120 Ωm 385

recovered the most similar electrical resistivity values to the synthetic model used to 386

generate the synthetic data, having a lower average distance between the final inversion 387

result and the original synthetic model. For all the inversions a similar nRMS was 388

obtained regardless of the different starting models. The smoothing values used for this 389

test were 0.3 in all directions. As shown below, these smoothing values do not differ 390

significantly from the smoothing values finally used during the inversion problem. 391

392

It is well known that regularization, necessary in any ill-posed inverse problem, has a 393

large influence on the results of the inversion and particularly on resolution. In the case 394

of the ModEM code we have to choose horizontal and vertical smoothing parameters. 395


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To take care of that, we performed additional tests to determine the appropriate 396

regularization parameters, being aware that different data types may react differently to 397

the same smoothing parameters. Inverting Z and Z+T+H several combinations of 398

horizontal and vertical smoothing parameters were executed using smoothing values 399

between 0.1 and 0.6 (always assuming the same smoothing values for north-south and 400

east-west directions). Searching for the simplest model that can fit the data, the largest 401

smoothing parameters were chosen that adequately recover the synthetic model while 402

still allowing the inversion processes to fit the data within the error bars. Based on these 403

tests, the chosen starting model for all the inversions presented in this manuscript was a 404

homogeneous half-space of 120 Ωm, and the smoothing values for all the inversions 405

were 0.4 for north-south and east-west directions, and 0.3 for the vertical direction. Note 406

that despite a smoothing of 0.5 for the north-south and east-west direction was also 407

appropriate to fit Z data, it was not appropriate when inverting the combined Z+T+H 408

responses, suggesting that the joint inversion process including all possible data requires 409

more detail in the model to fit the data. No outstanding differences were observed when 410

using 0.5 or 0.4 smoothing parameter for north-south and east-west directions when 411

performing the inversion process with Z data. In the presented inversions, the a priori 412

model was the same as the initial model (both are homogeneous), assuming that there is 413

no prior information about the electrical resistivity values of the subsurface.” 414

415

An additional test was performed to evaluate if the choose neighbouring reference site 416

for the H responses in the sensitivity test was adequate for the inversion process. Four 417

inversions with Z and H responses were performed using four different reference sites 418

for the H responses: (1) using a site close to the L2 anomaly; (2) on top of the L1 419

anomaly; (3) on top of the H1 anomaly; (4) as in the sensitivity test, on top of a non-420


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complex environment (almost 1-D). Results from the inversion process (Fig. 8a) show 421

that locating the reference site on top of a non-complex environment, such as the one 422

used for the sensitivity test, facilitate convergence of the inversion process (lower 423

nRMS) also obtaining the model that better recovers the original synthetic model. Figure 424

8b shows the nRMS of each inversion for each site and data type. From the results of 425

this test, it is strongly recommended not to use a reference site on top of anomalies (L1 426

and H1 in our case), in particular on top of a strong conductive anomaly such as L1. In 427

this experiment, the inversion process using a reference site on top of L1 was not able to 428

fit the data and the obtained model was the one that recovered the original synthetic 429

model worst of all (Fig. 8). The inversion process using a neighbouring reference site 430

close to L2 also does not converge to an nRMS lower than 1.2 but the model from the 431

inversion process is superior to the two cases where the neighbouring reference site was 432

on top of L1 and H1 anomalies. Note that the nRMS for the H response associated with 433

the neighbouring reference site is always close to 1 in all cases. This is because the H 434

responses compare the signal between two sites, and the signal between the 435

neighbouring site with itself is the same. The fact that it is one and not zero is because of 436

the noise we added in the responses. For the following inversions presented in this 437

manuscript, the same site as the one used in the sensitivity test was used as a reference 438

site for the H responses. 439

440

For the numerical experiment, four inversions were performed to examine and highlight 441

the improvements that can be made by complementing the Zo and Z responses with the T 442

and H responses, whilst also evaluating the necessity of using diagonal components of Z 443

in these situations. The final inversions were (1) Zo, (2) Z, (3) Zo+H+T, and (4) Z+H+T. 444

Four additional inversions, (5) Zo+H, (6) Zo+T, (7) Z+H and (8) Z+T were performed to 445


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differentiate the contributions of the H and T responses independently. Finally, the 446

capacity of the H and T responses to characterize the subsurface by themselves was 447

considered in inversion (9) H+T. This latter one is interesting as no electric fields are 448

involved, thus there should be primary sensitivity to lateral conductivity variations rather 449

than to the absolute values of the conductivities themselves. 450

451

2.5.2. Results 452

The results are displayed showing a north-south section of the obtained electrical 453

resistivity models beneath the MT profile and with horizontal slices of the models at 650 454

and 1550 m depths. Figure 9 shows the results of inversion (1) Zo, (2) Z, (3) Zo+H+T 455

and (4) Z+H+T, highlighting the advantages of complementing Z or Zo with H and T. 456

Figure 10 displays the results of inversions (5) Zo+T, (6) Zo+H, (7) Z+T, (8) Z+H and 457

(9) H+T demonstrating the consequences of different contributions of H and T 458

responses. The same colour scale was used in all figures. White dashed lines indicate the 459

positions of the main resistivity structures, L1, L2, L3 and H1, to facilitate the 460

comparison of the obtained inversion results with the original synthetic model. 461

2.5.2.1 Fit of the data 462

The fit of the data of each inversion process is shown in Fig. 11 plotting the summed 463

normalized root mean square (nRMS) as calculated in the ModEM code (Egbert & 464

Kelbert 2012, Kelbert et al., 2014) for each site, type of response and for each type of 465

inversion, providing valuable information on how data misfit distributes along the 466

profile for different inversions and different response types. Different colours were used 467

for each type of response: red for Zo responses, black for Z responses, blue for T 468

responses, and green for H responses. No systematic problems related to over-fitting 469

were observed with a particular response type or site locations, although some of the 470


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sites positioned at the edges of the profile have slightly larger nRMS than the ones 471

located within the profile. Note that the nRMSes associated with Z and Zo responses are 472

similar when only Z or Zo were used in the inversion process or when they were 473

combined with T and H responses during the inversion process. This result shows that 474

all datasets are fit to a similar level and that no remarkable decrease in resolution of a 475

particular type of response is observed when other responses are used during the 476

inversion process. 477

478

More detailed information about the fit of the data can be found in Fig. S2 479

(Supplementary Material), where differences between data and model responses divided 480

by the error were plotted for each type of inversion, component of the data, site and 481

period in a pseudo-section format. Grey areas are periods with differences lower than the 482

error; red and blue areas are periods with differences larger than the errors. 483

484

2.5.2.2 Electrical resistivity model beneath the MT profile 485

Models resulting from inversion of the Zo or Z responses (Figs. 9a1, 9a2) show the 486

existence and presence of the main anomalies but do not resolve or characterize them 487

well; in particular the resistivity values directly below L1 are poorly resolved due to the 488

shielding effects of L1. These two models appear to be unable to differentiate between 489

anomaly L1 and the conducting anomalous layer L3 that underlies L1, implying a 490

continuous horst-like structure with the L3 getting shallow to the depths of L1 in the 491

middle of the profile. Additionally, the high electrical resistivity anomaly H1 is inferred 492

but not well recovered, showing resistivity values around 80 Ωm, which are almost an 493

order of magnitude lower than the correct value (400 Ωm). Note that these values (∼80 494

Ωm) are also lower than the initial half-space model used for the inversion process (120 495


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Ωm). The use of the H and T responses as complements to the Zo or Z responses (Figs. 496

9a3, 9a4) significantly improves resolution of all targets, conductive and resistive, 497

showing L1 and L3 structures as disconnected (Z+H+T) or almost disconnected 498

(Zo+H+T), thus better constraining the bottom of anomaly L1 and clearly recovering 499

anomaly H1 in the northern part of the profile. The use of the H and T responses also 500

better defines the north and south boundaries of anomalies L1 and H1. By 501

complementing the Zo or Z responses with the H responses, the continuity of the low 502

resistivity layer (L3) is better defined, although in none of the models is the continuity of 503

L3 correctly recovered below L1 due to the electromagnetic shielding effects of L1 to 504

any structure immediately below it. 505

506

2.5.2.3 Horizontal slices at 650 m and 1550 m depth 507

The horizontal slices through the various 3-D resistivity models at 650 m depth are 508

shown in Fig. 9b. If only the Zo responses are inverted, the model is symmetrical on both 509

sides of the profile, thus characterizing the anomalies to extend outside of the profile but 510

without indicating on which side the anomalies are located. This illustrates and 511

emphasizes that the off-diagonal components contain no directional information for off-512

profile structures. The use of diagonal components in inversion of the full Z responses 513

characterizes the dimensionality of the structures whilst locating L2 to be west of the 514

MT profile and inferring the westerly extension of L1 (compare Fig. 9b1 with Fig. 9b2). 515

From Figs. 9b3 and 9b4 it is clear that by complementing the Zo or Z responses with H 516

and T responses the correct dimensionality of the structures is recovered in both cases, 517

showing in particular a remarkable improvement when Zo responses are complemented 518

with H and T responses. Fairly equivalent models are obtained from the Zo+H+T and 519

Z+H+T responses, but with slightly improved resolution, closer to the original synthetic 520


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model, when using Z+H+T. The use of the H and T responses also improves the 521

characterization of L2 by showing more reliable low resistivity values than when only 522

using Zo or Z responses, even if the resistivity values are still higher than in the original 523

synthetic model. Additionally, the north and south boundaries and the east and west 524

propagation of L1 are better defined when complementing the Zo or Z responses with the 525

H and T ones. 526

527

Figure 9c shows the horizontal slices of the final 3-D models at 1550 m depth. At this 528

depth the synthetic model is a uniform 10 Ωm conducting layer (defined as anomaly L3) 529

within which a 400 Ωm resistive anomaly (H1) is embedded. Models from the 530

conventional MT, Zo and Z, responses (Figs. 9c1, 9c2), exhibit a more complex situation 531

than might be expected from the original synthetic model, somewhat suggesting the 532

presence of the H1 anomaly with the highest electrical resistivity values (∼ 100 Ωm) 533

either directly below or outside of the profile, which is still lower than the 120 Ωm of 534

the starting model used for the inversion process. By carrying out joint inversion 535

including the H and T responses, the models better define the L3 layer and more 536

accurately recover H1 below and outside the MT profile, with electrical resistivity 537

values of around 250 Ωm, which is greater than the 120 Ωm of the starting model used 538

for the inversion process (Figs. 9c3, 9c4) and closer to the 400 Ωm of the original 539

synthetic model (Fig. 9c5). 540

541

2.5.2.4 Contribution of H and T 542

Figure 10 shows the results of the inversion process combining Zo and Z responses with 543

either T or H responses separately. From Fig. 10a, results below the profile, it can be 544

seen that the inclusion of the H responses is responsible for superior differentiation 545


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between L1 and L3. This differentiation also occurs when inverting Z+T but not when 546

Zo is complemented with T responses (Zo+T). i.e., the use of diagonal terms of the 547

impedance tensor is key to resolving the lack of interconnection between L1 and L3. In 548

addition, the H responses contribute to better defining the continuity of the low electrical 549

resistivity L3 layer. The main improvement gained by using the T responses is superior 550

definition of the north and south boundaries of L1. 551

Figure 10b shows the results at 650 m depth when inverting the H or T responses as a 552

complement to the Zo and Z responses. In all cases, comparing with the results in Figs. 553

9b1 and 9b2, the resolution and characterization of the anomalies are improved, 554

especially in defining the L2 anomaly. The main differences between complementing 555

with either the H or T responses are observed when characterizing the propagation of 556

anomaly L1 to the west, which is constrained by the H and Z responses but not by the T 557

responses, as expected from our sensitivity tests above. Figure 10c displays the model 558

slices at 1550 m depth, showing the contribution of including the H and T responses 559

separately from each other (cf. Figs. 9c). In all cases, the use of either or both the H and 560

T responses lead to superior recovery of the H1 anomaly and show its propagation to the 561

east. Figure 10c also shows that by using the H responses as a complement to the Z and 562

Zo responses, the models better reproduce the electrical resistivity values of the original 563

synthetic model off-profile. 564

565

Figures 10a5, 10b5 and 10c5 show that the magnetic-field only H and T responses alone 566

are insufficient to characterize the subsurface by themselves. The associated models 567

locate the anomalies along the north-south and east-west directions, but have no 568

resolution in the vertical direction and do not recover the electrical resistivity values. 569

This is because the magnetic field is sensitive to lateral resistivity contrasts (both 570


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amplitude and position), but is insensitive to 1-D layering and to the actual resistivity 571

values of the synthetic model 572

573

2.5.2.5 Accuracy of the models 574

One way to quantify how well the models obtained from the inversion process reproduce 575

the synthetic model is to calculate the differences between them in model space. We 576

have calculated these differences with a focus on the structures below the profile, where 577

we expect to obtain higher resolution. Figure 12 shows the differences between the 578

synthetic model and the models obtained from the inversion process, using decadic 579

logarithm electrical resistivity values. Blue colours indicate results from the inversion 580

process that are more resistive than the synthetic model, red colours indicate results 581

more conductive than the synthetic model, and white colours indicate an almost-perfect 582

fit between the inversion process model and the synthetic model. Note that the colour 583

scale indicates differences between the two models that are greater than ±0.023; this 584

value is equivalent to a difference of approx. ±0.5 Ωm for electrical resistivity values of 585

10 Ωm, and a difference of approx. ±50 Ωm for electrical resistivity values of 1000 Ωm. 586

The average differences for each type of inversion are shown in Table 1. 587

588

Table 1. Average differences between the final inversion models and the original 589 synthetic model. Differences calculated using log10 electrical resistivity values. 590 Inverted

Data Zo Z Zo+H+T Z+H+T Zo+T Zo+H Z+T Z+H H+T

Difference 0.151 0.149 0.133 0.134 0.144 0.141 0.134 0.138 0.214

591

These results indicate the superior performance when reproducing the electrical 592

resistivity values of the synthetic model when the Z or Zo responses are combined with T 593


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and H responses. The results also corroborate that the electrical resistivity values 594

obtained when using only the T and H responses are not correctly reproduced. 595

596

By conducting a more detailed analysis of Fig. 12, the following important points 597

associated with the recovering of each anomaly become apparent: 598

1) Structure L1: The edges and bottom are better recovered when T and H responses are 599

each or both involved in the inversion process. Despite the electrical resistivity values 600

always remaining more conductive than in the synthetic true model, they are better 601

recovered when the H responses are included in the inversion process; 602

2) Structure H1: In all the inversion processes the electrical resistivity values associated 603

with H1 are less resistive than in the synthetic model, however, recovery of these 604

resistivity values, and the geometry of the anomaly, is always improved when the H and 605

T responses are each or both involved in the inversion process. 606

3) Structure L3: The electrical resistivity values are improved when the H responses are 607

included in the inversion process. Note that when the T responses are used in the 608

inversion process, the top of the anomaly is also better characterized, particularly in the 609

southern part of the profile. 610

4) Background 1-D model: Results from the inversion processes complementing Z or Zo 611

with the H responses are the ones that best recover the electrical resistivity values of the 612

background 1-D resistivity model; not only do the results show smaller differences with 613

respect to the original synthetic model, but they also show a more homogeneous (less 614

blobby) resistivity model than the other inversion results. 615

616

3. DISCUSSION 617

Focusing on the recovery of electrical resistivity structures in 3-D areas, the use of the 618

full impedance tensor responses (Z), instead of using only the off-diagonal elements 619


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(Zo), is highly recommended for all 3-D inversions because of the far superior capacity 620

to reproduce the dimensionality of the geoelectrical structures in the subsurface. It 621

reaffirms and further validates the conclusions drawn and emphasized previously by 622

Siripunvaraporn et al. (2005b), Tietze & Ritter (2013), and Kiyan et al. (2014). 623

However, it is not always possible to use all of the components of the MT impedance 624

tensor because diagonal components, being of lower amplitude, are far more affected by 625

the presence of noise. This requires the necessity of including robust complementary 626

information in these situations. Siripunvaraporn & Egbert (2009) highlighted the 627

advantages of using Z+T data during the 3-D inversion process, suggesting that 628

resistivity values, geometry of the anomalies, and depths are all better characterized. 629

However, not all of the studies show major advantages when performing joint inversion 630

of Z+T responses in a 3-D environment. Tietze & Ritter (2013) present a situation where 631

results from Z responses alone are more reliable than the results from Z+T responses. In 632

previous synthetic studies working with T and H responses, Habibian and Oskooi (2014) 633

show that inversion processes using either or both T and H responses have vertical 634

resolution and are able to recover the correct electrical resistivity values of the 635

subsurface, which does not happen in the experiment shown in this manuscript (Fig. 10). 636

However, in the previous study the background structure was homogeneous with 637

uniform resistivity and the same as the one used for the starting model for the inversion. 638

This configuration masks the incapacity of the H and T responses on their own to 639

recover vertical anomalies or the correct electrical resistivity values. The numerical 640

experiment design in this manuscript, using a 1-D layered model as a background, 641

highlight this deficiency of the H and T responses, showing that vertical resolution or 642

the obtained electrical resistivity values from an inversion using either or both T and H 643

responses are only reliable if additional information defining the background structures 644


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of the study area is added. However, complementing Z and Zo responses, T and H aids 645

superior determination of the electrical resistivity values of the subsurface, including the 646

characterisation of the absolute electrical resistivity values (see Table 1 and Fig. 12). 647

Results from Varentsov (2015a,b) combining Z, H and T responses using 2-D, 2-D+ and 648

a quasi 3-D approaches encourage the use of H responses for the inversion process, 649

improving the accuracy of the results, and better separating close spaced conductors in 650

complex geoelectrical situations. 651

652

In this work, the advantages of using T and H responses as a complement to Z or Zo 653

responses in a 3-D environment are evaluated from the results of a numerical 654

experiment. Starting with the sensitivity of each response type to the studied anomalies, 655

the results of our numerical experiment exhibit that both the H and T responses are also 656

sensitive to the dimensionality of the structures and can be used to successfully 657

reproduce the dimensionality of the anomalies when complementing Zo or Z responses 658

(Figs. 9 and 10). The sensitivity tests performed (Fig. 6) demonstrate that the Zo and Z 659

responses are intrinsically more sensitive to the existence of the anomalies than are the 660

H and T responses. However, the dimensionality analysis (Fig. 7) and the capacity for 661

recovering the detail of the geoelectrical structures (Figs. 9, 10 and 12) are remarkably 662

improved when the Zo or Z responses are complemented with either, and especially both, 663

the H and T responses. Each response type has a specific behaviour when characterizing 664

the dimensionality of the structures and consistency between all of them will support the 665

ultimately adopted dimensionality of the study area. The use of the T and H responses 666

can also improve the dimensionality analysis in situations where the phase tensor is not a 667

strong tool; see for example the results close to the L2 and H1 anomalies (Fig. 7). In that 668

case the phase tensors do not correctly define the presence of 3-D structures having no 669


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periods showing absolute values of the β angle divided by the associated error greater 670

than 1. However, by using the H and T responses the characterisation of 3-D structures 671

of these areas is significantly improved. Comparing the dimensionality analysis from the 672

H and T responses close to resistive anomaly H1, induction arrows clearly point in 673

different directions than the direction of Phi_max from the H responses, which is also 674

suggestive of a 3-D situation. 675

676

Focusing now on the ability of recovering the correct electrical resistivity distribution of 677

the subsurface, the observed improvements are associated with the use of different types 678

of responses that better restrict the model space than if any are used individually. More 679

specifically, this phenomenon occurs because the Z responses are far more sensitive to 680

the L1 anomaly than to the L2 and H1 anomalies, whereas for our model the T and H 681

responses have similar sensitivity to all of the anomalies (Fig. 6). Such sensitivity means 682

that the inversion of the Zo or Z responses focuses mainly on L1, with less importance 683

placed upon the L2 and H1 anomalies. Results from the sensitivity tests (Figs. 2, 3, 4 684

and 5) can also be used to understand how inclusion of the H and T responses improves 685

the characterization of the subsurface. 686

687

Inspecting the resolved structures beneath the MT profile (Figs. 9, 10 and 12), four main 688

improvements are apparent when performing joint inversion of the Zo or Z responses 689

with H and T ones: 690

(1) Characterization of the bottom of the L1 anomaly with better differentiation between 691

the L1 and L3 structures; 692

(2) The possibility of recovering the high resistivity anomaly, H1, surrounded by low 693

resistivity values, L3, that are poorly recovered when using only Zo or Z responses; 694


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(3) Better resolution in determining the resistivity values of the subsurface, obtaining 695

results more similar to the original synthetic model; 696

(4) Superior definition of the shape of the anomalies in the north-south direction, i.e. 697

along profile, with a better fit inside the white dashed lines in the figures. 698

699

Despite all these advantages, we would like to point out that in all models the location of 700

the L3 layer at the edges of the profile is somewhat shallower than what it should be. 701

This problem is not properly corrected when complementing Z or Zo with T and H 702

responses, although results with T responses seem to slightly improve the depth of the 703

conductive layer L3 (Figs. 9, 10 and 12). 704

705

Looking outside the line of the profile (Figs. 9b, 9c and 10b, 10c), L2 and H1 are better 706

recovered when the inversion is complemented with H and T responses. However, 707

although the characterization of the off-profile anomalies is improved when 708

complementing the Z responses with the H and T ones, the shape of the anomalies and 709

the electrical resistivity values are still not properly constrained, probably as a 710

consequence of a combination of (i) the non-uniqueness of the MT method, and (ii) 711

scatter and error. 712

713

Inspecting the results obtained from the T responses, the main signal associated with the 714

anomalies is located at the edge of the structures (Figs. 2, 3, 4, 5, 6), making the T 715

responses a good type of data to define boundaries of the structures along the MT 716

profile. Note that from Fig. 6d this edge-detection is more precise for low resistivity 717

anomalies (L1) than for high resistivity anomalies (H1). This can also be observed when 718

recovering the anomalies from the inversion process (Figs. 9 and 10) where the north 719


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and south boundaries of L1 and H1 are improved when the T responses are included. 720

This result, highlighting the capacity of the T responses characterising the edges of the 721

anomalies, is consistent with previous results, such as Siripunvaraporn & Egbert (2009) 722

and Habibian and Oskooi (2014). In addition, the top of the low electrical resistivity 723

layer L3 is improved when the inversion of Z or Zo data is complemented with T data 724

(Figs. 10a1, 10a3, 12c and 12d). This makes T data a good complement to improve the 725

definition in recovering the edges and shape of the anomalies below a profile located in 726

a 3-D environment, in agreement with results suggested by Siripunvaraporn & Egbert 727

(2009). Note that, apart from the H1 anomaly, no major improvement associated with 728

the use of T responses has been observed in defining the electrical resistivity values of 729

the anomalies or the background 1-D model (Figs. 12c, 12d). Results from Fig. 10 730

shows that, although the use of T data as a complement of Zo provides an improvement 731

in characterizing the subsurface, the results are remarkably better when Z and T 732

responses are both used in the inversion process. 733

734

Examining the results from the H responses, the major advantage is that their use makes 735

the resistivity model more consistent as a whole as all the sites are related to the 736

neighbouring reference site and the intensity of the anomalies tend to be consistent along 737

the whole profile. This effect is also observed in the sensitivity test (Figs. 4b and 6c). In 738

this case the neighbouring reference site is located close to H1 and is affected by its 739

presence, which is why the effect of H1 can be seen at sites south of the profile. This 740

property of H responses increases the consistency of the model as a whole for shallow 741

and deep structures independently of the extension of the area of the study. This level of 742

consistency is not required when using the Zo, Z or T responses, where each site is 743

mostly focused on the anomalies nearby but without any explicit link to anomalies that 744


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are located far away along the study area, where the periods of the site are insensitive. 745

The consequences of this property in the inversion process can be seen in Fig. 12, where 746

the models including the H responses obtain electrical resistivity values of the anomalies 747

and the background 1-D resistivity model closer to the original synthetic model. Note 748

that from Fig. 10, although results are better quality when Z+H are used in the inversion 749

process, instead of Zo+H, differences are not as remarkable as the differences observed 750

between Z+T and Zo+T, having similar results from both types of inversion. Note also 751

that, from the performed test shown in Fig. 8, to facilitate and improve the results from 752

the inversion process using H responses it is recommended to use a neighbouring 753

reference site located on top of a non-complex geoelectrical area. Results from the 754

dimensionality analysis or from prior inversions using Z alone or Z+T can be used to 755

choose the optimum neighbouring reference site for Z+H or Z+T+H inversion. 756

757

4. CONCLUSIONS 758

759

The use of the H and T responses is demonstrated to be a crucial complement to the Zo 760

or Z ones in order to better resolve and characterize the structures beneath MT profiles 761

in 3-D environments. For the synthetic model considered here, large differences were 762

seen whether the diagonal components of Z were used or not, having far better results 763

when the diagonal components were included. These differences were reduced when 764

including the H and T responses in the inversion process, although results using the 765

diagonal components of Z still recover the subsurface better than when the diagonal 766

components are not used. From the results of this experiment, four main improvements 767

are observed when carrying out joint inversion of the Zo or Z responses with the H and T 768

ones: 769


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

(1) More accurate characterization of the electrical resistivity values of the studied 770

anomalies and also of the background resistivity model; 771

(2) Superior capability for recovering high electrical resistivity anomalies than by using 772

the Zo or Z responses alone; 773

(3) Improved definition of the bottom of low electrical resistivity anomalies and the 774

north, south, east and west boundaries of the anomalies beneath and outside the MT 775

profile; and 776

(4) Superior imaging of the horizontal continuity of low electrical resistivity anomalies. 777

Additionally, note that the use of the H responses increases the reliability of the 778

resistivity model as a whole, reducing the possibility for the inverse problem to generate 779

spurious anomalies if the anomaly is not consistent with the data acquired at the 780

neighbouring reference site. Although any site could be used as a neighbouring reference 781

site, as far as the structures below the neighbouring reference site are properly 782

constrained, it is recommended to use a site located on top of a simple geoelectrical area 783

and it is particularly strongly recommended not to use a site on top of a strong anomaly. 784

785

All of these advantages incentivise the use of H and T responses as complements Z or Zo 786

responses, in particular when characterizing the subsurface beneath a MT profile in a 3-787

D environment. This supports the possibility of high-resolution studies in 3-D 788

environments without expending large amounts of economical and computational 789

resources, and also opening the door for the achievement of targets with high electrical 790

resistivity values. 791

792

5. ACKNOWLEDGMENTS 793


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We would like to acknowledge the financial support to JC and XO from the IRECCSEM 794

project (www.ireccsem.ie) funded by a Science Foundation of Ireland Investigator 795

Project Award (SFI: 12/IP/1313) to AGJ. Gary Egbert, Anna Kelbert and Naser Meqbel 796

are very gratefully thanked for making their ModEM code available to the community. 797

The authors wish to acknowledge Irish Centre for High-End Computing (ICHEC) for the 798

computing facilities provided. Finally, the authors would like to thank Stephan Thiel, the 799

two anonymous reviewers, and the Associate Editors Mark Everett and Ute Weckmann 800

for their very helpful suggestions and comments on our submitted versions that 801

improved our final paper. 802

803

804

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responses of three-dimensional bodies in layered earths, Geophysics, 49, 1517–1023

1533. 1024

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electrical resistivity of the north-central USA from EarthScope long period 1026

magnetotelluric data. Earth and Planetary Science Letters, 422, 87–93. 1027

1028

1029

FIGURE CAPTIONS: 1030

1031

Figure 1: Synthetic geoelectrical model composed of four layers: (1) Between 0 m and 1032

90 m depth with an electrical resistivity of 100 Ωm; (2) Between 90 m and 1500 m depth 1033

with an electrical resistivity of 400 Ωm; (3) Between 1500 m and 2000 m depth with an 1034

electrical resistivity of 10 Ωm; (4) Layer from 2000 m to 90 km depth with an electrical 1035

resistivity of 200 Ωm. Two low electrical resistivity structures (L1 and L2) and a high 1036

electrical resistivity body (H1) are also present. L1 and L2 are located between 500 m 1037

and 1000 m depth and have an electrical resistivity value of 3 Ωm. H1 is located 1038

between 1500 m and 2000 m depth with electrical resistivity values of 400 Ωm. The 1039

green arrows points to site 26, which is used as a neighbouring reference site for H 1040

responses. 1041

1042

Figure 2: Results of the sensitivity test for the L1 anomaly. Values obtained by 1043

calculating the differences between the forward responses of the 1-D layered model 1044

containing L1 anomaly and the forward responses of the background 1-D layered model 1045

without anomalies. The differences are divided by the assumed error, thus showing how 1046

sensitive the responses are to the anomaly with respect to the errors. White areas are 1047


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

periods that are non-sensitive to L1 (differences smaller than the assumed error). Red 1048

and blue areas are periods that are sensitive to L1. 1049

1050

Figure 3: Results of the sensitivity test for the L2 anomaly. Values obtained by 1051


containing L2 anomaly and the forward responses of the background 1-D layered model 1053



periods that are non-sensitive to L2 (differences smaller than the assumed error). Red 1056

and blue areas are periods that are sensitive to L2. 1057

1058

Figure 4: Results of the sensitivity test for the H1 anomaly. Values obtained by 1059


containing H1 anomaly and the forward responses of the background 1-D layered model 1061



periods that are non-sensitive to H1 (differences smaller than the assumed error). Red 1064

and blue areas are periods that are sensitive to H1. 1065

1066

Figure 5: Results of the sensitivity test for the combined L1+L2+H1 anomalies. Values 1067

obtained by calculating the differences between the forward responses of the 1-D 1068

layered model containing L1+L2+H1 anomalies and the forward responses of the 1069

background 1-D layered model without anomalies. The differences are divided by the 1070

assumed error, thus showing how sensitive the responses are to the anomalies with 1071

respect to the errors. White areas are periods that are non-sensitive to L1+L2+H1 1072


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

anomalies (differences smaller than the assumed error). Red and blue areas are periods 1073

that are sensitive to L1+L2+H1. 1074

1075

Figure 6: Results from the sensitivity test to quantify the effect of each anomaly on the 1076

Z, Zo, H and T responses. White areas are periods that are not sensitive to the anomalies. 1077

Note that all plots have different colour scales. Grey thick lines at the top of each 1078

pseudo-section show the location of the studied anomalies along the profile. 1079

1080

Figure 7: a) Phase tensor dimensionality analysis using Z responses. White-grey colours 1081

are periods affected by signal associated with 1-D or 2-D structures. Rainbow colours 1082

are periods affected by signal associated with 3-D anomalies. b) Results from the 1083

dimensionality analysis using variations of the H responses (H-I), where I is the 1084

identity. Dots are related to periods affected by signal associated with 1-D structures. 1085

Lines are related to periods affected by signal associated with 2-D structures. Ellipses 1086

are related to periods affected by signal associated with 3-D anomalies. White-grey 1087

colours are periods that, because of the assumed errors, do not require the presence of 3-1088

D anomalies. Rainbow colours are periods affected by signal that, even with the 1089

assumed errors, requires the presence of 3-D anomalies. c) Induction arrows from T 1090

responses, following the Parkinson criteria, used to characterize the dimensionality of 1091

the area. White-grey colours are periods that, because of the assumed errors, do not 1092

require the presence of 3-D anomalies. Rainbow colours are periods affected by signal 1093

that, even with the assumed errors, requires the presence of 3-D anomalies. 1094

1095

Figure 8: a) Results of the different inversion process below the MT profile using 1096

neighbouring reference sites located at different places along the MT profile. White 1097


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dashed lines are plotted to better compare the results with the original synthetic model. 1098

b) nRMS of each inversion processes for each site and for each type of data. Circles are 1099

the nRMS of the corresponding site. 1100

1101

1102

Figure 9: a) Results of the different inversion process below the MT profile. b) 1103

Horizontal slices showing the results of the inversion processes at 650 m depth. c) 1104

Horizontal slices showing the results of the inversion processes at 1550 m depth. a5), 1105

b5) and c5) are the original synthetic model. White dashed lines are plotted to better 1106

compare the results with the original synthetic model. 1107

1108

Figure 10: a) Results of the different inversion processes beneath the MT profile. b) 1109

Horizontal slices showing the results of the inversion processes at 650 m depth. c) 1110

Horizontal slices showing the results of the inversion processes at 1550 m depth. White 1111

dashed lines are plotted to better compare the results with the original synthetic model. 1112

1113

Figure 11: nRMS of each inversion processes for each site and for each type of data. 1114

Circles are the nRMS of the corresponding site. Excellent nRMS misfits of between 1.0 1115

and 1.05 were achieved for all inversions using different types of responses. 1116

1117

Figure 12: Differences, using decadic logarithm electrical resistivity values, between 1118

models obtained from the inversion process and the synthetic model. 1119


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

NS

De

pth

(m

)

1000

2000

3000

0

0

4000

-4000

0-6000 6000

No

rth

ing

(m

)

Easting (m)

0

4000

-4000

0-6000 6000

No

rth

ing

(m

)

Easting (m)

8000

-8000 -8000

8000

b) Horizontal slice (700 m depth) c) Horizontal slice (1500 m depth)

0 8000-8000 -4000 4000

Distance Profile (m)

Figure 1 (Campanyà et al. 2016)

400 ohm·m

200 ohm·m

(L3) 10 ohm·m

3 ohm·m

400 ohm·m

(L1)3 ohm·m

(L2)3 ohm·m

(H1)400 ohm·m

(L3)10 ohm·m

(H1)

(L1)

1 14 217 28

a) MT profile

Electrical resistivity [log10(ohm·m)]

0 0.5 1.5 2.51 2

Synthetic model


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L1 anomaly

Difference / Errorfloor

a)

Hxx real Hxy real Hyx real Hyy real

Hxx imag Hxy imag Hyx imag Hyy imag

Zxx real Zxy real Zyx real Zyy real

Zxx imag Zxy imag Zyx imag Zyy imag

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Sites1 26Sites1 26 Sites1 26 Sites1 26

b)

c) Tx real Tx imag Ty real Ty imag

3-3-4 -2 0 2 41-1


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a) Zxx real Zxy real Zyx real Zyy real


Pe

rio

ds

(lo

g1

0(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g1

0(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g1

0(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g1

0(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g1

0(s

))

-4-3

-2-10123


b)

c)


L2 anomaly

3-3-4 -2 0 2 41-1



Tx real Tx imag Ty real Ty imag


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Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123

Pe

rio

ds

(lo

g10(s

))

-4-3

-2-10123


b)

c)

H1 anomaly

3-3-4 -2 0 2 41-1





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3-3






Periods

(log

10(s

))

-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123


b)

c)

-4 -2 0 2 41-1

L1, L2 and H1 anomalies


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42.51 63.51

71 4

Periods

(log

10(s

))

-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123

HT

Periods

(log

10(s

))-4-3

-2-10123

Periods

(log

10(s

))

-4-3

-2-10123

Z_all

Zo


L1 L2 H1 L1, L2, H1




1891 1261

96481 1681 126 10011 50

126.51

1051 51 101 5.53

a)

b)

c)

d)


1001 50 1001 50

1161


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Periods

(log

10(s

))-4

-3

-2

-1

0

1

2

3

a)


41 6 11 16 21 26

Phase Tensor (Z)

abs(Skew angle beta /error Skew angle beta)sites

Pe

rio

ds

(lo

g10(s

))

-4

-3

-2

-1

0

1

2

3

c)

41 6 11 16 21 26

Induction Arrows (T)

sites

Pe

rio

ds

(lo

g10(s

))

-4

-3

-2

-1

0

1

2

3

b)

41 6 11 16 21 26

variation of H

0 1 2 3

abs(Phi_min /error Phi_min)sites

0 1 2 3

0 1 2 3

abs( angle difference / error angle difference)

L2 L1 H1

L2 L1 H1

L2 L1 H1

real imag0.3 0.3


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0 0.5 1.5 2.51 2


RMS:1.09

RMS:1.98RMS:1.25

Depth

(km

)

1

2

3

0

0-4 4Distance Profile (km)

8-8

2 431

b1 b2 b3 b4

De

pth

(km

)

1

2

3

0

a1) Z+H, close L2 a2) Z+H, top L1S N S N

0-4 4Distance Profile (m)

RMS:1.35De

pth

(km

)

1

2

3

0



a3) Z+H, top H1 a4) Z+H

1.5

1

0.5

RM

S

2

2.5

1.5

1

0.5

2

2.5

Z H

Sites1 28 Sites1 28Sites1 28 Sites1 28

b)

a)


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Depth

(km

)

1

2

3

0

0-4 4Distance Profile (km)

0 0.5 1.5 2.51 2


b)

c)

0

4

-4Nort

hin

g (

km)

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

c1) Zo c3) Zo+H+T c2) Z c4) Z+H+T c5) S. Model

0

4

-4Nort

hin

g (

km)

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

0Easting (km)

-4 4

b1) Zo b3) Zo+H+T b2) Z b4) Z+H+T b5) S. Model

a)

Depth

(km

)

1

2

3

0

Depth

(km

)

1

2

3

0

0-4 4

Distance Profile (km)

a1) Zo a2) Z

a3) Zo+H+T a4) Z+H+T

a5) Synthetic Model

8-8

-8 8

S N S N



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

b)

c)

a)

0 0.5 1.5 2.51 2


De

pth

(km

)

1

2

3

0

a1) Zo+T a2) Zo+H S N S N


0

4

-4

0-4 4

No

rth

ing

(km

)

Easting (km)0-4 4

Easting (km)

b1) Zo+T b2) Zo+H

0-4 4Easting (km)

0-4 4Easting (km)

c1) Zo+T c2) Zo+H

De

pth

(km

)

1

2

3

0

De

pth

(km

)

1

2

3

0



a3) Z+T a4) Z+H

a5) T+H

0-4 4Easting (km)

0-4 4Easting (km)

0-4 4Easting (km)

b3) Z+T b5) H+T b4) Z+H

0

4

-4

0-4 4

No

rth

ing

(km

)

Easting (km)0-4 4

Easting (km)0-4 4

Easting (km)

c3) Z+T c5) H+T c4) Z+H


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1.5

1

0.5

RM

S

1.5

1

0.5

RM

S

1.5

1

0.5

RM

S

Sites1 28 Sites1 28 Sites1 28

Zo inversion Zo+T inversion Zo+H inversion

Z inversion Z+T inversion Z+H inversion

Zo+T+H inversion Z+T+H inversion T+H inversion

Zo Z T H

1.5

1

0.5

1.5

1

0.5

1.5

1

0.5


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De

pth

(km

)

1

2

3

0

e) Zo+H f) Z+H


De

pth

(km

)

1

2

3

0

De

pth

(km

)

1

2

3

0


g) Zo+T+H h) Z+T+H

i) T+H

b) Z S N

De

pth

(km

)

1

2

3

0

c) Zo+T d) Z+T

a) Zo S N

De

pth

(km

)

1

2

3

0

0 0.5-0.5-0.75 0.75-0.25 0.25

Difference electrical resistivity [ohm·m]log10(Synth. mod) - log10(Inv. mod)


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

Supplementary material S1 Campanyà et al., 2016 GJI Supplementary 1: Implementation of the H responses

Following the mathematical recipes (Egbert and Kelbert, 2012) and the practical

implementation of ModEM (Kelbert et al., 2014) we modified the code accordingly to allow

inverting for horizontal magnetic inter-station transfer functions. The modifications are

implemented mainly in the data functional module within the interface layer (Kelbert et al.,

2014, Fig. 1). In the data functional module (data responses routine), all kinds of transfer

functions are computed from the electric field solution (primary field) obtained from solving

the induction problem in 3-D. For the horizontal inter-station transfer functions we use the

magnetic field (dual field) derived from the electric field using Faraday's law. To simulate the

process of measuring EM components (e.g., inter-station horizontal magnetic transfers

functions) the magnetic field is interpolated at specific locations (local and neighbouring

reference sites). Using the interpolated horizontal magnetic field components (ℎ! and ℎ!) at

the local (𝒉!) and neighbouring reference site (𝒉!), we construct the inter-station horizontal

magnetic transfer functions (𝑯) equation S1.

𝒉! = 𝐇 !"𝒉! (𝑆1)

For the inversion process in ModEM we use the None Linear Conjugate Gradients algorithm

(NLCG), which is based on a direct minimization of the penalty functional (Egbert and

Kelbert, 2012). All gradient-based optimization algorithm (including NLCG) require the

sensitivity of the data at each iteration. The sensitivity matrix in ModEM is computed by

multiplying several sub matrices (Egbert and Kelbert, 2012; Eqs. 14 and 15). The matrix that

depends on the inverted data type (e.g., H) is the so-called L matrix that represents the

linearized data functional. Mimicking the computation of the L matrix for the impedances

transfer functions (Z; Egbert and Kelbert, 2012; Eqs. 42 and 43) we computed the sensitivity

matrix for the inter-station horizontal magnetic transfer functions (𝑯). Hence, most of the

modifications required to compute the sensitivity matrix in case of inverting for H are

implemented in the none linearized data functional routine within the data functional module.


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

a) Zo inversionlo

g10 f

req. (H

z)Zxy real Zxy imag Zyx real Zyx imag

Sites1 28

Sites1 28

Sites1 28

Sites1 28

b) Z inversion

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28

Figure S2a,b (Campanyà et al. 2016)

(data - model_response) / error


123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

c) Zo+T inversionlo

g10 f

req. (H

z)Zxy real Zxy imag Zyx real Zyx imag

d) Z+T inversion

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Figure S2c,d (Campanyà et al. 2016)

log1

0 fr

eq. (H

z)


Sites1 28

Sites1 28

Sites1 28

Sites1 28

log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

e) Zo+H inversionlo

g10 f

req. (H

z)

Zxy real Zxy imag Zyx real Zyx imag

log1

0 fr

eq. (

Hz)


Figure S2e (Campanyà et al. 2016)

log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

f) Z+H inversionlo

g10 f

req. (H

z)


log1

0 fr

eq. (

Hz)


Figure S2f (Campanyà et al. 2016)

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

g) Zo+T+H inversionlo

g10 f

req. (H

z)

Zxy real Zxy imag Zyx real Zyx imag

log1

0 fr

eq. (

Hz)


Figure S2g (Campanyà et al. 2016)

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28



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h) Z+T+H inversionlo

g10 f

req. (H

z)


log1

0 fr

eq. (

Hz)


Figure S2h (Campanyà et al. 2016)

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28

log1

0 fr

eq. (

Hz)




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i) T+H inversionlo

g10 f

req. (H

z)


Figure S2i (Campanyà et al. 2016)

log1

0 fr

eq. (

Hz)


log1

0 fr

eq. (

Hz)


Sites1 28

Sites1 28

Sites1 28

Sites1 28



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