3D Resistivity Inversion Research Articles

2D resistivity inversion of 1D electrical-sounding measurements in deltaic complex geology: application to the delta Wadi El-Arish, Northern Sinai, Egypt

This study is an application of the 2D resistivity inversion of Schlumberger electrical sounding. The 2D resistivity inversion was performed using a code based on the finite-element technique and regularization method. Twenty-nine electrical soundings collected in the delta of Wadi El-Arish, Northern Sinai, were used as a case study. The main objective is to compare the 1D and 2D inversion results of the subsurface resistivity distribution in areas where the lateral resistivity variation cannot be neglected. The examination of the resulting 2D, 1D resistivity models and geological cross-section built from borehole information approximately at the same location showed a significant reliability of 2D models. Some subsurface geological and hydrogeological features could be interpreted such as the identification of clay lenses, potentiometric surface of the quaternary aquifer, potentiometric depression due to over-pumping, the high resistivity contrast due to lateral facies change, and basin-like structural features.

An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.

VLF‐EM study for archaeological investigation of the labyrinth mortuary temple complex at Hawara area, Egypt

ABSTRACTThe present study is a test of the applicability of the VLF‐EM method in archaeological prospecting. The Hawara area is about 90 km south of Cairo and is the location of an important archaeological site known as the labyrinth mortuary temple complex, situated south of the Hawara pyramid. No official excavations have been carried out in the labyrinth complex since 1911. VLF‐EM was employed in this study using a small grid, 2 m between profiles and stations. The measured data were interpreted using Fraser and Karous‐Hjelt filters. Two‐dimensional (2D) resistivity cross‐sections have been calculated inverting VLF‐EM data in a quantitative manner. A three‐dimensional (3D) resistivity inversion scheme has been applied to a grid of nine Schlumberger vertical electrical soundings to provide information on the resistivity of the shallow and deep structures in the study area. Results show a large group of elongated and square subsurface anomalies at shallow depths, connected in some parts and separated in others. The spatial distribution of the anomalies significantly matches a historical description by Herodotus.

Integrated geophysical interpretation for the area located at the eastern part of Ismailia Canal, Greater Cairo, Egypt

The integrated geophysical interpretation for the different geophysical tools such as resistivity and gravity is usually used to define the structural elements, stratigraphic units, groundwater potentiality, and depth to the basement rocks. In the present work, gravity and resistivity data were utilized for detecting the groundwater aquifer and structural elements, as well as the upper and lower surfaces of the subsurface basaltic sheet in an area located at the eastern side of Ismailia Canal, northeastern Greater Cairo, Egypt. Two hundred and ten gravity stations were measured using an Autograv instrument through a grid pattern of 50 × 50 m. The different required corrections were carried out, such as drift, elevation, tide, and latitude corrections. The final corrected data represented by the Bouguer anomaly map were filtered using high- and low-pass filters into regional and residual gravity anomaly maps. The resulting residual gravity anomaly map was used for gravity modeling to calculate the depths to the upper and lower surfaces of the basaltic sheet. The resulting gravity models indicated that the depths to the upper surface of the basaltic sheet are ranged between 26 and 314 m, where the shallower depths were found around the southern and eastern parts. The depths to the lower surface of the basaltic sheet are varied from 86 to 338 m, and the thickness of the basaltic sheet is ranged from 24 to 127 m, where the biggest thicknesses were found around the southern and northern parts of the study area. Forty-two vertical electrical soundings (VES) were carried out using Schlumberger configuration with AB/2 spacings ranged from 1.5 to 500 m. 1D quantitative interpretation was carried out through manual and analytical interpretations. The VES data were also inverted assuming a 3D resistivity distribution. The results from the 3D resistivity inversion indicated that the subsurface section consists of sand, sandstone, and sandy–clays of Miocene deposits overlying the basalts. Such basaltic features (of Oligocene age) are underlain by Gabal Ahmar Formation of Oligocene deposits, which are composed of sand and sandstone. Therefore, two aquifers were deduced in the area. The first is the Miocene aquifer (shallower) and the other is the Oligocene aquifer (deeper).

Explicit expressions for the Fréchet derivatives in 3D anisotropic resistivity inversion

We have developed explicit expressions for the Fréchet derivatives or sensitivity functions in resistivity imaging of a heterogeneous and fully anisotropic earth. The formulation involves the Green’s functions and their gradients, and it is developed from a formal perturbation analysis and by means of a numerical (finite-element) method. A critical factor in the equations is the derivative of the electrical conductivity tensor with respect to the principal conductivity values and the angles defining the axes of symmetry. The Fréchet derivative expressions were derived for the 2.5D and 3D problems using constant-point and constant-block model parameterizations. Special cases such as an isotropic earth and tilted transversely isotropic (TTI) media emerge from the general solutions. Numerical examples were investigated for various sensitivities as functions of dip angle and strike of the plane of stratification in uniform TTI media.

Integrated geophysical mapping of the Ifewara transcurrent fault system, Nigeria

Integrated geophysical methods involving magnetic and dipole–dipole resistivity (DDR) were conducted across a prominent zone of weakness clearly observable in Landsat MSS and SLAR images in the Precambrian basement complex of southwestern Nigeria. Up till now, the location and existence of this megascopic structure have not been confirmed using geophysical methods. With the objective of delineating this weak zone and its structural attributes, three traverses were established at 500 m intervals across it, and geophysical measurements were made at 10 m intervals along these traverses. Qualitative interpretation of the magnetic data obtained shows a diagnostic signature of a near-vertical fault, trending along a NNE–SSW direction. Also, the quantitative interpretation of the data using the non-linear least-squares regression technique indicates that the width of the magnetic anomaly ranges from 90 to 150 m, its dip angle varies between 75° and 85°; the anomaly is concealed by a regolith of approximately 15 m thickness. Furthermore, a 2D resistivity inversion of the field resistivity data reveals a three-layer model, representing thin resistive topsoil underlain by weathered bedrock, resistive bedrock with a distinct low resistivity zone located within the bedrock. The most plausible explanation for this low resistivity zone is that it was formed by shearing activities during Late Precambrian times. Conclusively, the integrated approach employed in this research confirms the existence of the supposed Ifewara shear zone (ISZ).

Magnetotelluric soundings and crustal architecture at Century mine, northern Australia

Magnetotelluric soundings were obtained along two traverse lines to the north and west of the Century mine in northwest Queensland. The survey was designed to cross the Termite Range Fault, a major structure on the Lawn Hill Platform, and to provide insights into the crustal-scale architecture that may have controlled the location of this world-class zinc deposit. The projected surface trace of the Termite Range Fault is coincident with a major change in resistivity character that extends to a significant depth. A relatively flat-lying, stacked series of resistive/conductive layers occurs on the northeastern side of the fault , while on the southwestern side the resistive/conductive layers are much less evident. The major contrast in resistivity is interpreted as due to a steep northeast-dipping Termite Range Fault that may extend to 20 km depth. To the southwest of the Termite Range Fault, a second major fault, the Riversleigh Lineament, is inferred from geology and gravity data, although there is no corresponding resistivity contrast seen across this fault in the magnetotelluric-derived model. This fault is interpreted as a buried structure, as distinct from the reactivated Termite Range Fault, and the two faults together may have created a wide damage zone (with an associated strike change) in the crust. A regional-scale 3D geological model of the Lawn Hill Platform provides a basis for correlating the resistive/conductive layers with major lithological units in the area. The stacked layers in the 2D resistivity inversion model of the Termite Range Fault hangingwall are reasonably well correlated with lithological units, particularly in the near-surface. A key point is that although similar geological units occur on either side of the Termite Range Fault, the contrasting electrical properties of these units are pronounced and their source is not well constrained; increased carbonaceous material in the Termite Range Fault hangingwall units is implied. In addition, there is a strong gradient in the Bouguer gravity field in the region of the Termite Range Fault and Riversleigh Lineament structures. This gradient provides supporting evidence for a northeast-facing fault structure in the basement and cover architecture. Newly acquired seismic data in the area has yet to be evaluated and compared with the magnetotelluric model. These results demonstrate an important role for magnetotelluric soundings in determining resistivity contrasts relating to the configuration of geological units and the architecture of deep-seated mineralising faults.

Application of 3D Resistivity Tomography to Delineate Subsurface Structures

We have developed a three-dimensional (3D) resistivity inversion code for resistivity tomography, where resistivity data are measured using electrodes installed in several boreholes as well as at the Earth surface. The algorithm is based on finite element approximations for forward modelling, and the ACB (Active Constraint Balancing) algorithm is adopted to enhance the resolving power of the smoothness-constrained least-squares inversion. Resolution analysis with numerical examples shows that 3D resistivity tomography is a promising tool to construct high-resolution 3D images of subsurface structures. We have also shown thai topography effects should be incorporated in the inversion to gel accurate 3D images -without artefacts, in the application of the method to a field data set acquired ai a granite quarry, we could successfully delineate the 3D attitude of faults or fractures in the site.

Integrated geophysical studies in the upper part of Sardis archaeological site, Turkey

Sardis is one of the most important archaeological sites of western Turkey, and the city covered with very thick soil layer. Thus, it is very difficult to predict the ruins from the surface. To determine the buried archaeological structures under the very thick soil, the integrated geophysical methods might effectively be useful. Thus, an integrated geophysical investigation, including magnetic, 2D resistivity, VLF-R and seismic methods, were carried out in the area. Magnetic data were collected using gradient measuring technique in the area that is about 2 ha. The data were processed with different signal and image processing techniques. Resistivity surveys have been applied using Wenner (only over the test profile) and pole–pole arrays in three investigation levels. Afterwards, the resistivity data were processed with 2D resistivity inversion, which includes two different solution techniques such as smoothness constrained and robust inversion. The VLF-R method has also been applied in limited area in which a very large anomaly zone was determined by magnetic and resistivity methods to test the responses of electromagnetic VLF-R data in archaeological sites. In addition, seismic tomography method was tested to observe the response of method for archaeological problems over the test profiles. Integrated geophysical methods indicated that the usage of many geophysical techniques linked with each other is very useful and efficient to determine the buried archaeological structures.

An integrated magnetotelluric and aeromagnetic investigation of the Serra da Cangalha impact crater, Brazil

The research is aimed at delineating the post-impact structural characteristics across the Serra da Cangalha impact crater in Brazil using a combination of magnetotelluric (MT) and aeromagnetic data. The MT survey was carried out along three radial MT profiles trending NW–SE, ENE–WSW and NNE–SSW across the crater. For MT sites located further away from the centre of the crater, isotropic MT responses were observed, suggesting a 1D conductivity distribution in the subsurface in the frequency range of 100–10 Hz. For sites located in the vicinity of the inner ring of the crater, anisotropic responses were observed for the same frequency range. We believe that this zone probably represents the areas of structural disturbance. A 2D resistivity inversion of these data reveals a four-layer model, representing a thin resistive layer underlain by a conductive layer, a weathered basement and a resistive crystalline basement. The depth to the top of the basement is estimated to be about 1.2 km. This is in good agreement with the estimation of depth to the basement of about 1.1 km, calculated using the aeromagnetic data. However, in view of the circular geometry of the crater, we have carried out a 3D forward modeling computation to supplement the derived 2D model. The 3D resistivity forward model, fitting the MT responses by trial-by-error revealed a five-layer model, showing a significant reduction in the basement resistivity. This, perhaps, could be due to the structural disturbances that have been caused by the impact on the crater, resulting in brecciation, fracturing, alteration and shocked zone filled with weak-magnetic materials and fluids. We have calculated the effect of the impact on the overall structural deformation beneath the Serra da Cangalha crater, following the classical crater scaling relation of Holsapple and Schmidt [Holsapple, K.A., Schmidt, R.M., 1982. On the scaling of crater dimensions. II. Impact processes. J. Geophys. Res. 87, 1849–1870] and found to be about 2 km.

Computations of secondary potential for 3D DC resistivity modelling using an incomplete Choleski conjugate‐gradient method

ABSTRACTAn accurate and efficient 3D finite‐difference (FD) forward algorithm for DC resistivity modelling is developed. In general, the most time‐consuming part of FD calculation is to solve large sets of linear equations: Ax=b, where A is a large sparse band symmetric matrix. The direct method using complete Choleski decomposition is quite slow and requires much more computer storage. We have introduced a row‐indexed sparse storage mode to store the coefficient matrix A and an incomplete Choleski conjugate‐gradient (ICCG) method to solve the large linear systems. By taking advantage of the matrix symmetry and sparsity, the ICCG method converges much more quickly and requires much less computer storage. It takes approximately 15 s on a 533 MHz Pentium computer for a grid with 46 020 nodes, which is approximately 700 times faster than the direct method and 2.5 times faster than the symmetric successive over‐relaxation (SSOR) conjugate‐gradient method. Compared with 3D finite‐element resistivity modelling with the improved ICCG solver, our algorithm is more efficient in terms of number of iterations and computer time. In addition, we solve for the secondary potential in 3D DC resistivity modelling by a simple manipulation of the FD equations. Two numerical examples of a two‐layered model and a vertical contact show that the method can achieve much higher accuracy than solving for the total potential directly with the same grid nodes. In addition, a 3D cubic body is simulated, for which the dipole–dipole apparent resistivities agree well with the results obtained with the finite‐element and integral‐equation methods. In conclusion, the combination of several techniques provides a rapid and accurate 3D FD forward modelling method which is fundamental to 3D resistivity inversion.

3D resistivity inversion using 2D measurements of the electric field

Field and ‘noisy’ synthetic measurements of electric‐field components have been inverted into 3D resistivities by smoothness‐constrained inversion. Values of electrical field can incorporate changes in polarity of the measured potential differences seen when 2D electrode arrays are used with heterogeneous ‘geology’, without utilizing negative apparent resistivities or singular geometrical factors. Using both the X‐ and Y‐components of the electric field as measurements resulted in faster convergence of the smoothness‐constrained inversion compared with using one component alone. Geological structure and resistivity were reconstructed as well as, or better than, comparable published examples based on traditional measurement types. A 2D electrode grid (20 × 10), incorporating 12 current‐source electrodes, was used for both the practical and numerical experiments; this resulted in 366 measurements being made for each current‐electrode configuration. Consequently, when using this array for practical field surveys, 366 measurements could be acquired simultaneously, making the upper limit on the speed of acquisition an order of magnitude faster than a comparable conventional pole–dipole survey. Other practical advantages accrue from the closely spaced potential dipoles being insensitive to common‐mode noise (e.g. telluric) and only 7% of the electrodes (i.e. those used as current sources) being susceptible to recently reported electrode charge‐up effects.

Fault Detection by 2D Resistivity Inversion on a Topographic Area

Direct current (DC) resistivity data acquired on rough terrain can be interpreted by using an appropriate two-dimensional (2-D) finite element inversion with the topography-incorporated technique developed by Tong and Yang (1990). This technique is computation ally efficient and provides a geological interpretation that is an improvement on the standard 2-D inversion. The main feature of this scheme is that sounding data incorporated the topography into the inversion without any previous topographic correction of field data. Thus errors inherited by the inversion data from an imperfect topographic correction can be avoided, especially in an area that has complex subsurface structures. In addition, the penetration depth of a Schlumberger four symmetric collinear electrode (4-electrode survey) array is often limited by obstacles at ground-level; especially in mountainous areas. This drawback may be overcome by using a Schlumberger three asymmetric collinear electrode (3-electrode survey) array. In order to demonstrate the advantage of using the 3-electrode survey, model studies were performed, and the results show that the DC resistivity responses obtained from the 4-electrode and 3-electrode surveys have similar features for a given spread length. However, under the same topographic constraints, the 3-electrode configuration has a more extension of a spread length, and therefore, a greater penetration depth. To seek verification of our strategy, DC resistivity sounding was applied to the Kanchiao fault area of northern Taiwan. The results stressed fault detection in this area. A Schlumberger 3-electrode survey was carried out in the field, and the data collected were inverted to the geoelectric models by using Tong and Yang's scheme (1990). In addition, synthetic apparent resistivity pseudosections were also computed from the final inversion models. Comparison of the synthetic with the observed apparent resistivity profiles is sufficient to reveal the Kanchiao fault position. The implications of the results obtained by combining the special electrode layout of the DC resistivity soundings with the previously mentioned finite element inversion technique are highlighted. The techniques used here does provide users with a guide of what to do in a topographic area. The techniques are superior to conventional techniques as applied to a complex subsurface structure.