SP2DINV: A 2D forward and inverse code for streaming potential problems

Ahmed, A. Soueid; Jardani, Abderrahim; Revil, A.; Dupont, Jean-Paul

doi:10.1016/j.cageo.2013.05.008

Cited by 44 publications

(21 citation statements)

References 33 publications

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“…Recent advances to solve the inverse problem of SP data are based on the use of deterministic approaches that utilize the regularized least squares techniques and the differentiability of the objective function subject to minimization (e.g., Mehanee 2014a; Soueid Ahmeda et al 2013). This paper builds on the existing literature and describes a new and very fast method capable of interpreting the observed SP anomalies (caused primarily by graphite precipitation formed on a shear plane(s) within the continental crust) by a single 2D conductive thin sheet to trace paleo-shear zones.…”

Section: Introductionmentioning

confidence: 99%

Tracing of paleo-shear zones by self-potential data inversion: case studies from the KTB, Rittsteig, and Grossensees graphite-bearing fault planes

Mehanee

2015

Earth Planets Space

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This paper describes a new method for tracing paleo-shear zones of the continental crust by self-potential (SP) data inversion. The method falls within the deterministic inversion framework, and it is exclusively applicable for the interpretation of the SP anomalies measured along a profile over sheet-type structures such as conductive thin films of interconnected graphite precipitations formed on shear planes. The inverse method fits a residual SP anomaly by a single thin sheet and recovers the characteristic parameters (depth to the top h, extension in depth a, amplitude coefficient k, and amount and direction of dip θ) of the sheet. This method minimizes an objective functional in the space of the logarithmed and non-logarithmed model parameters (log(h), log(a), log(k), and θ) successively by the steepest descent (SD) and Gauss-Newton (GN) techniques in order to essentially maintain the stability and convergence of this inverse method. Prior to applying the method to real data, its accuracy, convergence, and stability are successfully verified on numerical examples with and without noise. The method is then applied to SP profiles from the German Continental Deep Drilling Program (Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschla -KTB), Rittsteig, and Grossensees sites in Germany for tracing paleo-shear planes coated with graphitic deposits. The comparisons of geologic sections constructed in this paper (based on the proposed deterministic approach) against the existing published interpretations (obtained based on trial-and-error modeling) for the SP data of the KTB and Rittsteig sites have revealed that the deterministic approach suggests some new details that are of some geological significance. The findings of the proposed inverse scheme are supported by available drilling and other geophysical data. Furthermore, the real SP data of the Grossensees site have been interpreted (apparently for the first time ever) by the deterministic inverse scheme from which interpretive geologic cross sections are suggested. The computational efficiency, analysis of the numerical examples investigated, and comparisons of the real data inverted here have demonstrated that the developed deterministic approach is advantageous to the existing interpretation methods, and it is suitable for meaningful interpretation of SP data acquired elsewhere over graphitic occurrences on fault planes.

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Section: Introductionmentioning

confidence: 99%

Tracing of paleo-shear zones by self-potential data inversion: case studies from the KTB, Rittsteig, and Grossensees graphite-bearing fault planes

Mehanee

2015

Earth Planets Space

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“…With the finite‐element method, Equation can be written in matrix form as (Soueid Ahmed et al )

{boldd}_{normalp} = Km

where d p represents the predicted SP data at a set of stations, m represents the vector of current density (for each cell and in 2D, the current density has two components), and K is called the kernel and corresponds to the Green's functions of the problem, which accounts for the resistivity distribution. An extensive discussion about the computation of the kernel for the source current density is given by Jardani et al (), and more recently, a free software has been developed by Soueid Ahmed et al (). An important point is that the kernel cannot be computed correctly without the knowledge of the resistivity distribution.…”

Section: Description Of the Geophysical Methodsmentioning

confidence: 99%

“…The minimization of the objective function ∂ P λ ( m )/∂ m = 0 is conducted with the Gauss‐Newton algorithm implemented in Matlab (see Richards et al and Soueid Ahmed et al ). The program was initiated with a prior model and λ = 1, which reduces at each iteration to half of the value at the previous iteration.…”

Section: Description Of the Geophysical Methodsmentioning

confidence: 99%

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Characterization of Focused Seepage Through an Earthfill Dam Using Geoelectrical Methods

et al. 2013

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Resistivity and self-potential tomography can be used to investigate anomalous seepage inside heterogeneous earthen dams. The self-potential (SP) signals provide a unique signature to groundwater flow because the source current density responsible for the SP signals is proportional to the Darcy velocity. The distribution of the SP signals is also influenced by the distribution of the resistivity; therefore, resistivity and SP need to be used in concert to elucidate groundwater flow pathways. In this study, a survey is conducted at a small earthen dam in Colorado where anomalous seepage is observed on the downstream face at the dam toe. The data reveal SP and direct current resistivity anomalies that are used to delineate three anomalous seepage zones within the dam and to estimate the source of the localized seepage discharge. The SP data are inverted in two dimensions using the resistivity distribution to determine the distribution of the Darcy velocity responsible for the observed seepage. The inverted Darcy velocity agrees with an estimation of the Darcy velocity from the hydraulic conductivity obtained from a slug test and the observed head gradient.

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“…The self‐potential signals that were recorded in the field were modeled and inverted to recover the 2D distribution of the causative electrical current sources within the dam and subsurface. The inverted electrical current sources were used to quantify the Darcy velocity, as described below (see Soueid Ahmed et al , for additional tests of this methodology).…”

Section: Forward and Inverse Modeling Of The Self‐potential Fieldmentioning

confidence: 99%

Geophysical Investigation of Seepage Beneath an Earthen Dam

et al. 2014

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A hydrogeophysical survey is performed at small earthen dam that overlies a confined aquifer. The structure of the dam has not shown evidence of anomalous seepage internally or through the foundation prior to the survey. However, the surface topography is mounded in a localized zone 150 m downstream, and groundwater discharges from this zone periodically when the reservoir storage is maximum. We use self-potential and electrical resistivity tomography surveys with seismic refraction tomography to (1) determine what underlying hydrogeologic factors, if any, have contributed to the successful long-term operation of the dam without apparent indicators of anomalous seepage through its core and foundation; and (2) investigate the hydraulic connection between the reservoir and the seepage zone to determine whether there exists a potential for this success to be undermined. Geophysical data are informed by hydraulic and geotechnical borehole data. Seismic refraction tomography is performed to determine the geometry of the phreatic surface. The hydro-stratigraphy is mapped with the resistivity data and groundwater flow patterns are determined with self-potential data. A self-potential model is constructed to represent a perpendicular profile extending out from the maximum cross-section of the dam, and self-potential data are inverted to recover the groundwater velocity field. The groundwater flow pattern through the aquifer is controlled by the bedrock topography and a preferential flow pathway exists beneath the dam. It corresponds to a sandy-gravel layer connecting the reservoir to the downstream seepage zone.

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SP2DINV: A 2D forward and inverse code for streaming potential problems

Cited by 44 publications

References 33 publications

Tracing of paleo-shear zones by self-potential data inversion: case studies from the KTB, Rittsteig, and Grossensees graphite-bearing fault planes

Tracing of paleo-shear zones by self-potential data inversion: case studies from the KTB, Rittsteig, and Grossensees graphite-bearing fault planes

Characterization of Focused Seepage Through an Earthfill Dam Using Geoelectrical Methods

Geophysical Investigation of Seepage Beneath an Earthen Dam

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