Utilizing massively parallel co-processors in the AarhusInv 1D forward and inverse AEM modelling code

As an efficient geophysical exploration method, the time-domain airborne electromagnetic (AEM) data often show sign reversal in late-time channels due to induced polarization (IP) effect. The traditional imaging and inversion methods without considering the IP effect cannot recover the true electrical structure of the earth, so it is necessary to develop 3D EM forward modeling and inversion techniques with IP effect. In this paper, we propose a 3D forward modeling method for time-domain AEM with IP effect based on unstructured finite-element (FE) method. To describe the IP effect of a medium, we introduce the Cole-Cole model and transform it into fractional derivative form using frequency-time conversion. Then, we discretize it using the difference discretization format of Caputo fractional derivative. Finally, we use the vector FE method based on unstructured tetrahedral mesh and unconditionally stable second-order backward Euler’s scheme to discretize Maxwell’s equations in space and time. In this way, we can solve the 3D forward modeling problem for AEM with IP effect in time domain. We verify the accuracy of our algorithm by comparing it with the 1D semi-analytical solution for a half-space model, and then calculate EM responses for typical abnormal models and analyze the characteristics of IP effect.

3D parallel surface-borehole TEM forward modeling with multiple meshes

Multiple paired forward and inverse models for motor control

This project was designed as a broad foundational study of spectral induced polarization (SIP) for characterization of contaminated sites. It encompassed laboratory studies of the effects of chemistry on induced polarization, development of 3D forward modeling and inversion codes, and investigations of inductive and capacitive coupling problems. In the laboratory part of the project a physico-chemical model developed in this project was used to invert laboratory IP spectra for the grain size and the effective grain size distribution of the sedimentary rocks as well as the formation factor, porosity, specific surface area, and the apparent fractal dimension. Furthermore, it was established that the IP response changed with the solution chemistry, the concentration of a given solution chemistry, valence of the constituent ions, and ionic radius. In the field part of the project, a 3D complex forward and inverse model was developed. It was used to process data acquired at two frequencies (1/16 Hz and 1/ 4Hz) in a cross-borehole configuration at the A-14 outfall area of the Savannah River Site (SRS) during March 2003 and June 2004. The chosen SRS site was contaminated with Tetrachloroethylene (TCE) and Trichloroethylene (PCE) that were disposed in this area for several decades till the 1980s. The imaginary conductivity produced from the inverted 2003 data correlated very well with the log10 (PCE) concentration derived from point sampling at 1 ft spacing in five ground-truth boreholes drilled after the data acquisition. The equivalent result for the 2004 data revealed that there were significant contaminant movements during the period March 2003 and June 2004, probably related to ground-truth activities and nearby remediation activities. Therefore SIP was successfully used to develop conceptual models of volume distributions of PCE/TCE contamination. In addition, the project developed non-polarizing electrodes that can be deployed in boreholes for years. A total of 28 of these electrodes were deployed at the SRS site in September of 2002. The project found that (1) currently available field instrumentation need to be faster by an order of magnitude for full SIP to be engaged for broadband characterization in the field, (2) some aspects of the capacitive coupling problem in borehole geometries can be solved by use of a high impedance receiver, (3) a careful investigation of ways to adequately compare inversion results to ground-truth data is warranted, (4) more laboratory studies should be directed to understand the influence of micro-organisms and long residence time of contaminants (aging) on spectral IP properties.

Structural and stratigraphic basin modelling has been used to examine quantitatively the Cretaceous and Tertiary post-rift subsidence history of the northern North Sea Basin following Late Jurassic extension. 2D forward and reverse, syn-rift and post-rift modelling has been used to determine the magnitude and timing of departures from the McKenzie post-rift thermal subsidence trend for regional stratigraphic profiles in the Outer Moray Firth, the South Viking Graben and the North Viking Graben. Observed stratigraphy has been reverse post-rift modelled using flexural backstripping combined with decompaction and reverse thermal subsidence calculations, and forward modelled through the syn-rift and post-rift period using the flexural cantilever model of continental rift basin formation. Long-term global eustasy has been included in the analysis. Only reliable palaeobathymetric markers, such as erosion surfaces and coals, have been used to constrain subsidence history. Both forward and reverse 2D modelling show that a Palaeocene regional uplift followed by a rapid Eocene subsidence must be superimposed on McKenzie post-rift Cretaceous and Tertiary basement subsidence in order to generate the stratigraphy observed. The magnitude of Palaeocene uplift deduced from modelling was of the order of 375 m in the Outer Moray Firth (central North Sea) increasing to 525 m in the North Viking Graben (northern North Sea). Rapid Early Eocene subsidence was of the order of 160–310 m. The most likely mechanism for regional Palaeocene uplift and rapid Eocene subsidence in the northern North Sea was the Palaeocene development of the Iceland plume situated at a distance of 700–900 km from the study area in the Early Tertiary. Forward and reverse modelling predict axial bathymetries in the graben of up to 1300 m for the Early Cretaceous and 900 m for the Upper Cretaceous. The large palaeobathymetries at the end of the Cretaceous provided much of the accommodation space for Tertiary sedimentation.

Inverse and 3D forward gravity modelling for the estimation of the crustal thickness of Egypt

Resistivity methods are commonly used in mineral exploration to map lithology, structure, sulphides and alteration. In the Athabasca Basin, resistivity methods are used to detect alteration associated with uranium. At the Midwest deposit, there is an alteration zone in the Athabasca sandstones that is above a uraniferous conductive graphitic fault in the basement and below a conductive lake at surface. Previous geophysical work in this area has yielded resistivity sections that we feel are ambiguous in the area where the alteration is expected. Resolve® and TEMPEST sections yield an indistinct alteration zone, while two-dimensional (2D) inversions of the ground resistivity data show an equivocal smeared conductive feature in the expected location between the conductive graphite and the conductive lake. Forward modelling alone cannot identify features in the pseudosections that are clearly associated with alteration, as the section is dominated by the feature associated with the near-surface conductive lake; inverse modelling alone produces sections that are smeared and equivocal. We advocate an approach that uses a combination of forward and inverse modelling. We generate a forward model from a synthetic geoelectric section; this forward data is then inverse modelled and compared with the inverse model generated from the field data using the same inversion parameters. The synthetic geoelectric section is then adjusted until the synthetic inverse model closely matches the field inverse model. We found that this modelling process required a conductive alteration zone in the sandstone above the graphite, as removing the alteration zone from the sandstone created an inverse section very dissimilar to the inverse section derived from the field data. We therefore conclude that the resistivity method is able to identify conductive alteration at Midwest even though it is below a conductive lake and above a conductive graphitic fault. We also concluded that resistivity inversions suggest a conductive paleoweathering surface on the top of the basement rocks at the basin/basement unconformity.

Abstract. Volgo–Uralia is a Neoarchaean easternmost part of the East European craton. Recent seismic studies of the Volgo–Uralian region provided new insights into the crustal structure of this area. In this study, we combine satellite gravity and seismic data in a common workflow to perform a complex study of Volgo–Uralian crustal structure, which is useful for further basin analysis of the area. In this light, a new crustal model of the Volgo–Uralian subcraton is presented from a step-wise approach: (1) inverse gravity modelling followed by (2) 3D forward gravity modelling. First, inversion of the satellite gravity gradient data was applied to determine the Moho depth for the area. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region, and the model is constrained by the available active seismic data. The Moho discontinuity obtained from the gravity inversion was consequently modified and complemented in order to define a complete 3D crustal model by adding information on the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modelling, where both seismic and gravity constraints were respected. The obtained model shows crustal thickness variations from 32 to more than 55 km in certain areas. The thinnest crust with a thickness below 40 km is found beneath the Precaspian basin, which is covered by a thick sedimentary layer. The thickest crust is located underneath the Ural Mountains as well as in the centre of the Volgo–Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, initial forward gravity modelling has shown a gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and the forward calculated gravity field in the central area of the Volgo–Uralian subcraton. This misfit was interpreted and modelled as a high-density lower crust, which possibly represents underplated material. Our preferred crustal model of the Volgo–Uralian subcraton respects the gravity and seismic constraints and reflects the main geological features of the region with Moho thickening in the cratons and under the Ural Mountains and thinning along the Palaeoproterozoic rifts, Precaspian sedimentary basin, and Pre-Urals foredeep.

Volgo-Uralia is a Neoarchean easternmost part of the East European craton. Recent seismic studies of the Volgo-Uralian region provided new insights into the crustal structure of this area. In this study, we combine satellite gravity and seismic data in a common workflow to perform a complex study of Volgo-Uralian crustal structure which is useful for further basin analysis of the area. In this light, a new crustal model of the Volgo-Uralian subcraton is presented from a step-wise approach: (1) inverse gravity modeling followed by (2) 3D forward gravity modeling. First, inversion of satellite gravity gradient data was applied to determine the Moho depth for the area. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region, and the model is constrained by the available active seismic data. The Moho discontinuity obtained from the gravity inversion was consequently modified and complemented in order to define a complete 3D crustal model by adding information on the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modeling where both seismic and gravity constraints were respected. The obtained model shows crustal thickness variations from 32 to more than 55 km in certain areas. The thinnest crust with a thickness below 40 km is found beneath the Pericaspian basin, which is covered by a thick sedimentary layer. The thickest crust is located underneath the Ural Mountains as well as in the center of the Volga-Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, initial forward gravity modeling has shown a gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and the forward calculated gravity field in the central area of the Volga-Uralian subcraton. This misfit was interpreted and modeled as a high-density lower crust which possibly represents underplated material. Our preferred crustal model of the Volga-Uralian subcraton respects the gravity and seismic constraints and reflects the main geological features of the region with Moho thickening in the cratons and under the Ural Mountains and thinning along the Paleoproterozoic rifts, Pericaspian sedimentary basin, and Pre-Urals foredeep.

To better understand the Precambrian lithospheric structure beneath the Southwestern Branch (SWB) of the East African Rift System (EARS) and their influence on the development of this rift system, we developed a two-dimensional (2D) forward gravity model across Congo and Zambia that is constrained by the surface geology and results from previous magnetotelluric (MT) lithospheric imaging study. We constructed the 2D forward gravity model from the Bouguer gravity anomalies of the European Improved Gravity Model of the Earth by New Techniques (EIGEN – 6C4), which has spatial resolution of ~15 km X 15 km. Most of the rift basins of the SWB were developed during the Permian – Triassic Karoo rifting event during the early stages of the dispersal of Gondwana, but these were reactivated during the Paleogene – Quaternary rifting event of the EARS. Our results showed that the Archean – Paleoproterozoic Congo craton, the Bangweulu cratonic block and the Niassa craton, and the Mesoproterozoic – Neoproterozoic Southern Irumide orogenic belt surrounding the Niassa craton have thick sub-continental lithospheric mantle (SCLM) with lithospheric thickness reaching ~250 km . This suggests that the Niassa craton underlies the entire surface extent of what has been referred to as the “Southern Irumide orogenic belt”. No rift basins of the SWB have been observed extending within these cratonic blocks with the exception of the Mweru – Wantipa rift found on the northeastern edge of the Bangweulu cratonic block. Our results also found a relatively thinner (~160 km) and uniform lithosphere beneath the Paleoproterozoic – Mesoproterozoic Kibaran orogenic belt and the Neoproterozoic Lufilian foreland basin, which underlie the Upemba, Kundelungu, and Mweru rift basins of the SWB. This suggests that the Lufilian foreland basin was built on a “Kibaran lithosphere” rather than on a “Bangweulu lithosphere”. Further, our results showed that thinner lithosphere (~100 km thick) is present beneath the Mesoproterozoic – Neoproterozoic Irumide metacraton and the Mwembashi shear zone, which represents the suture zone between the metacraton and the Niassa craton. The presence of thinner lithosphere beneath the Irumide metacraton and the Mwembashi shear zone seems to have significantly controlled the development of the Luangwa rift basin of the SWB.

We have developed a technique to calculate lateral density distribution of the sedimentary basin basement by combining linear gravity–density inversion and 2D forward modeling. The procedure requires gravity anomaly data, depth-to-basement data and density data for the sediments (density–depth distribution). Gravity effect of density variations in the basement was extracted from the total gravity anomaly by removing the joint effect of the sediments with vertical density variations and homogeneous basement of average density contrast (calculated by 2D modeling). Gravity effect of the sediments was calculated using depth-to-basement data and density–depth function, based on borehole logging data. Bouguer slab formula was used in order to simplify basement model and calculate the operator for the linear inversion of gravity effect of the basement into lateral density distribution. The results were tested by forward modeling, and differences between observed and modeled gravity data were used for the next iteration of the inversion and correction of density values in each point along the profile. The procedure was tested using synthetic models and field example, and both results were satisfying, especially taking into account the simplicity of the inversion technique. The main problem was the effect of abrupt changes in the basement topography on density distribution, but it was downsized by filtering. Basement density maps were compiled based upon the density distribution along the profiles.

Summary The Semail Ophiolite in Oman represents one of the well-preserved ophiolite complexes globally and provides a unique window into the processes of obduction. The emplacement of Semail ophiolite onto the Arabian lithosphere is a result of intra-oceanic subduction, was strongly influenced by inheritance features preserved from pre-obduction tectonic processes. Therefore, a detailed characterization of the crustal architecture and rheological properties of the lithosphere are essential for improving our understanding of obduction processes. In this study, we investigated the crustal structure and Moho depth beneath the central Oman Mountains through analysis of P-wave receiver functions (PRFs) and Bouguer gravity anomalies. We utilize broadband seismic data recorded at 12 seismic stations spanning the ophiolite belt and surrounding regions (Ghaba basin and Saih Hatat Dome). PRFs analysis reveals noticeable lateral variations in Moho depths ranging from ∼39 km beneath the sedimentary basin to ∼46 km beneath the ophiolite belt, and decreasing to ∼30 km underneath Saih Hatat Dome (SHD). 2D forward modeling of Bouguer gravity anomalies (−36 to 91 mGal) constraints with seismological results shows flexural bending of the Moho topography and thin crust (∼ 30 km) beneath the SHD. The 2D forward flexural modelling analysis suggests that lithospheric flexure is due to the emplacement of the ∼5 km thick Semail Ophiolite. The presence of a thin crust beneath the SHD is caused by Permian rifting and thinning of the continental lithosphere. The observed high value of Vp/Vs (1.75 – 1.87) also provides support for Permian mafic intrusions to the lower crust. The Arabian lithosphere exhibits lower mechanical strength in the southern region (Te = 25 km) relative to the northern area, a characteristic likely inherited from pre-obduction magmatic processes. These results provide new geophysical constraints on the crustal architecture of the southern Oman Mountains and emphasize the role of surface loading in shaping lithospheric structure during ophiolite emplacement.

The results of the 3D finite-difference forward modeling of magnetotelluric data acquired around the Serra da Cangalha impact crater located northeastern Brazil, South America are presented. The 13 km impact structure has been investigated because of its explicit 3D shape. The central part of the model covers an area of approximately 169 Km2. The model of the study area, constructed using a 3D mesh of 22 x 19 x 25 (29325 cells) was based on the a priori information of the geology of the region, and the results of the 2D inversion results. Eleven frequencies were calculated for the 3-D model (0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100, 300, 1000 Hz). The resistivity structure obtained suggests perturbations of the upper crust due meteorite impact; the base of the uplifted structure extending to 3.0 km depth was well delineated. The observed 3D effects are explained as a shallow resistive ring that represents a local 3D body embedded in a regional layered earth. The results confirm the importance of 3D forward modeling in impact crater studies. The three-dimensional model results indicate that a valuable picture of the regional electrical resistivity can be obtained from 3-D interpretation of the determinant impedance tensors using polar diagrams. The study has helped in providing an insight into the post-impact electrical signature of the upper crust.

Identifying the lithospheric structure of a Precambrian orogen using magnetotellurics: The Capricorn Orogen, Western Australia

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for geophysical exploration. The stabilized biconjugate-gradient fast Fourier transform algorithm is used for forward modeling, whereas the distorted Born iterative method is used in the inversion. The conjugate-gradient method is applied at each inversion iteration to minimize the cost function. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, make this method highly efficient, with the requirement of very low time and memory, O (N log N ) and O (N) respectively. Numerical experiments about the 3D forward modeling with application in Borehole to Surface Electromagnetic Method will be presented in this paper; in addition, we will show the examples about 3D inversion applied in geophysical exploration. All these results will demonstrate the high efficiency and accuracy of the proposed method.