The 3D subsurface resistive structure of the Haukadalur hydrothermal field, Iceland
Item Type Article
Authors Lupi, Matteo;Collignon, Marine;Fischanger, Federico;Carrier, Aurore;Trippanera, Daniele;Pioli, Laura
Citation Lupi, M., Collignon, M., Fischanger, F., Carrier, A., Trippanera, D.,
& Pioli, L. (2022). Geysers, boiling groundwater and tectonics: The 3D subsurface resistive structure of the Haukadalur hydrothermal field, Iceland. Journal of Geophysical Research: Solid Earth.
Portico. https://doi.org/10.1029/2022jb024040 Eprint version Post-print
DOI 10.1029/2022jb024040
Publisher American Geophysical Union (AGU)
Journal Journal of Geophysical Research: Solid Earth Download date 2023-12-17 20:40:59
Link to Item http://hdl.handle.net/10754/685044
Supporting Information for:
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Geysers, boiling groundwater and tectonics: the 3D subsurface
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resistive structure of the Haukadalur hydrothermal field, Iceland
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Matteo Lupi1, Marine Collignon1, Federico Fischanger2, Aurore Carrier3, Daniele Trippanera4,
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and Laura Pioli5
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1Department of Earth Sciences, University of Geneva, Switzerland.
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3ADRGT, Grenoble, France
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2Geostudi Astier, S.r.l., Livorno, Italy
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4Department of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Saudi Arabia
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5Department of Chemical and Geological Sciences, University of Cagliari, Italy
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Corresponding author: Matteo Lupi,[email protected]
1 Supplemental online material
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InERTLab Studio an Occam’s regularization inversion algorithm is implemented to minimise the ob-
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jective function (Morelli & LaBrecque, 1996):
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Φ(m) =kWd[d−f(m)k2+αkWm(m−m0)k2 (1) wheremis the model vector,Wd the data weighting matrix,dthe data vector,f the forward model oper-
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ator,αthe regularization parameter,Wm the weight (or roughness) matrix that defines the spatial extent
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and nature of smoothing between each parameter and its neighbors, andm0 the reference parameter vec-
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tor, not necessarily uniform. Assuming uncorrelated data errors, the data weighting matrix may be expressed
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in terms of the data errorsi (i=1, ..., N) as:
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Wd=diag(1/1, ...,1/N) (2) The weight matrixWmmay be constructed to allow anisotropic smoothing, for example, forcing greater hor-
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izontal smoothing than vertical smoothing.
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Using a Gauss-Newton scheme to solve the equation brings to the following iterative scheme:
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GTkWTdWdGk+αWTmWm
∆mk =GTWdTWd[d−f(mk)]−αWTmWm(mk−m0) (3) whereGk is the Jacobian (or sensitivity) matrix evaluated for the current modelmk. The satisfactory so-
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lution of equation above is dependent on appropriate assignment of the data errors inWd. Morelli and LaBrecque
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(1996) proposed a scheme that allows the re-weighting of data during the iterative process. Note that to as-
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sess the resolution of certain experiments, the depth of investigation index (DOI) is often shown. Such a DOI
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(or rather VOI, given that we performed a 3D acquisition) proves to be less effective than global sensitiv-
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ity in representing the low resolution areas for 3D models characterized by a large variability of the resis-
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tivity range (Oldenburg & Li, 1999) (our resistivities span 3 orders of magnitude, i.e. from 1 Ohm m to above
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1000 Ohm m). Indeed, Oldenborger et al. (2007) extended the concept of DOI discussed by Oldenburg and
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Li (1999) suggesting possible bias linked to subjectivity associated with the VOI when choosing reference
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models and/or an appropriate cutoff values. In a context characterized by such a wide range of resistivity
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variations, it is evident that the fit of some resistive areas will be better starting from a resistive model with
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values closer to those areas and heavily penalized for more conductive regions. Vice versa, starting from a
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marked conductive reference model would facilitate the reconstruction of more conductive areas of the sub-
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soil. The result is that, depending on the direction in which the reference model is changed, the DOI val-
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ues are highly inconsistent. Our model is characterised by a range of highly resistive and highly conductive
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values making the sensitivity study shown in Figure S1 more appropriate in our opinion.
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References
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Morelli, G., & LaBrecque, D. J. (1996). Advances in ert inverse modelling. European Journal of Envi-
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ronmental and Engineering Geophysics,1(2), 171–186.
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Oldenborger, G. A., Routh, P. S., & Knoll, M. D. (2007). Model reliability for 3d electrical resistivity
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tomography: Application of the volume of investigation index to a time-lapse monitoring experi-
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ment. Geophysics, 72(4), F167–F175.
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Oldenburg, D. W., & Li, Y. (1999). Estimating depth of investigation in dc resistivity and ip surveys.
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Geophysics,64(2), 403–416.
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Figure S1. Data coverage. The coverage is defined as the sum of absolute sensitivities. Based on data coverage we interpret data up to 200 m depth (see Figures 4 and 5 of the main text).
Figure S2. Histogram of the % standard deviation for inverted resistivity measurements. Values are arithmetically derived from multiple stacks (35-40) implemented for each data point during around 3 minutes of con- tinuous transmission. The orange line is the Pareto cumulative distribution for the sample.
Figure S3. Histogram of the % standard deviation for inverted IP measurements. Values are arithmeti- cally derived from multiple stacks (35-40) implemented for each data point during around 3 minutes of continuous transmission. The orange line is the Pareto cumulative distribution for the sample.
Figure S4. Potential V(mV) and current I(mA) recordings. The potential V(mV) and current I(mA) recordings are shown for two receiving boxes for the same AB transmitter (in yellow on map A). Panels B and C show the 37 recorded stacks for both V and I signal at the two receivers: RX2 (green on map A) is distant around 150 m from the B transmitter; RX12 (orange in map) is around 500 m far from TX B. Panels D and E display the IP decay curves, respectively for RX2 and RX12, derived from stacking averaging.
