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Wang, S., Bastani, M., Constable, S., Kalscheuer, T. & Malehmir, A. (2019). Boat-towed radio-magnetotelluric and controlled source audio-magnetotelluric study to resolve fracture zones at Äspö Hard Rock Laboratory site, Sweden. Geophysical Journal International, 218(2), 1008-1031
Open this publication in new window or tab >>Boat-towed radio-magnetotelluric and controlled source audio-magnetotelluric study to resolve fracture zones at Äspö Hard Rock Laboratory site, Sweden
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2019 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 218, no 2, p. 1008-1031Article in journal (Refereed) Published
Abstract [en]

Boat-towed radio-magnetotelluric (RMT) measurements using signals between 14 and 250 kHz have attracted increasing attention in the near-surface applications for shallow water and archipelago areas. A few large-scale underground infrastructure projects, such as the Stockholm bypass in Sweden, are planned to pass underneath such water zones. However, in cases with high water salinity, RMT signals have a penetration depth of a few metres and do not reach the geological structures of interest in the underlying sediments and bedrock. To overcome this problem, controlled source signals at lower frequencies of 1.25 to 12.5 kHz can be utilized to improve the penetration depth and to enhance the resolution for modelling deeper underwater structures. Joint utilization of boat-towed RMT and controlled source audio-magnetotellurics (CSAMT) was tested for the first time at the Aspo Hard Rock Laboratory (HRL) site in south-eastern Sweden to demonstrate acquisition efficiency and improved resolution to model fracture zones along a 600-m long profile. Pronounced galvanic distortion effects observed in 1-D inversion models of the CSAMT data as well as the predominantly 2-D geological structures at this site motivated usage of 2-D inversion. Two standard academic inversion codes, EMILIA and MARE2DEM, were used to invert the RMT and CSAMT data. EMILIA, an object-oriented Gauss-Newton inversion code with modules for 2-D finite difference and 1-D semi-analytical solutions, was used to invert the RMT and CSAMT data separately and jointly under the plane-wave approximation for 2-D models. MARE2DEM, a Gauss-Newton inversion code for controlled source electromagnetic 2.5-D finite element solution, was modified to allow for inversions of RMT and CSAMT data accounting for source effects. Results of EMILIA and MARE2DEM reveal the previously known fracture zones in the models. The 2-D joint inversions of RMT and CSAMT data carried out with EMILIA and MARE2DEM show clear improvement compared with 2-D single inversions, especially in imaging uncertain fracture zones analysed in a previous study. Our results show that boat-towed RMT and CSAMT data acquisition systems can be utilized for detailed 2-D or 3-D surveys to characterize near-surface structures underneath shallow water areas. Potential future applications may include geo-engineering, geohazard investigations and mineral exploration.

Place, publisher, year, edition, pages
OXFORD UNIV PRESS, 2019
Keywords
Marine electromagnetics, Joint inversion, Fractures, faults and high strain deformation zones, Magnetotellurics, Electrical properties
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-390504 (URN)10.1093/gji/ggz162 (DOI)000474771100020 ()
Funder
Swedish Research Council Formas, 25220121907
Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved
Abtahi, S. M., Pedersen, L. B., Kamm, J. & Kalscheuer, T. (2018). A new reference model for 3D inversion of airborne magnetic data in hilly terrain: A case study from northern Sweden. Geophysics, 83(1), B1-B12
Open this publication in new window or tab >>A new reference model for 3D inversion of airborne magnetic data in hilly terrain: A case study from northern Sweden
2018 (English)In: Geophysics, ISSN 0016-8033, E-ISSN 1942-2156, Vol. 83, no 1, p. B1-B12Article in journal (Refereed) Published
Abstract [en]

The inherent nonuniqueness in modeling magnetic data can be partly reduced by adding prior information, either as mathematical constructs or simply as bounds on magnetization obtained from laboratory measurements. If a good prior model can be used as a reference model, then the quality of estimated models through an inverse approach can be greatly improved. But even though data on magnetic properties of rocks might exist, their distribution may often be quite irregular on local and regional scales, so that it is difficult to define representative classes of rock types suitable for constraining geophysical models of magnetization. We have developed a new way of constructing a reference model that varies only laterally and is confined to the part of the terrain that lies above the lowest topography in the area. To obtain this model, several estimated 2D magnetization distributions were constructed by data inversion as a function of the iteration number. Then, a suitable 2D model of the magnetization in the topography was chosen as a starting point for constructing a 3D reference model by modifying it with a vertical decay such that its average source depth was the same for all horizontal positions. The average source depth of the reference model was chosen to satisfy the average source depth obtained from analyzing the radial power spectrum of the area studied. Finally, the measured magnetic data were inverted in three dimensions using the given reference model. For a selected reference model, shallow structures indicated a better overall correlation with large remanent magnetizations measured on rock samples from the area. Throughout the entire model, the direction of magnetization was allowed to vary freely. We found that the Euclidean norm of the estimated model was reduced compared with the case where the magnetization direction was fixed.

Place, publisher, year, edition, pages
SOC EXPLORATION GEOPHYSICISTS, 2018
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-353001 (URN)10.1190/GEO2016-0331.1 (DOI)000429311000001 ()
Available from: 2018-07-13 Created: 2018-07-13 Last updated: 2018-07-13Bibliographically approved
Chen, C., Ren, Z., Pan, K., Tang, J., Kalscheuer, T., Maurer, H., . . . Li, Y. (2018). Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders. Geophysical Journal International, 214(3), 2115-2132
Open this publication in new window or tab >>Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders
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2018 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 214, no 3, p. 2115-2132Article in journal (Refereed) Published
Abstract [en]

We present general closed-form solutions for the vertical gravitational anomaly caused by a polyhedral prism with mass density contrast varying with depth. Our equations are the first ones to implement a polynomial vertical mass density contrast of arbitrary order. Singularities in the gravity field which arise when the observation site is close to or in the anomalous polyhedral prism are removed in our analytic expressions. Therefore, the observation site can be located outside, on the faces of or inside the anomalous mass bodies. A simple prismatic body of anomalous density is adopted to test the accuracy of our newly developed closed-form solution. Cases of constant, linear, quadratic, cubic and quartic polynomial orders of mass density contrast are tested. For cases of constant, linear, quadratic and cubic polynomial orders, the relative errors between our results and other published exact solutions are less than 10(-11)%. For the case of quartic polynomial order, relative errors less than 10(-10)% are obtained between our solutions and those computed by a high-order Gaussian quadrature rule (512 x 512 x 512 = 134 217 728 quadrature points), where our new analytic solution needs significantly less computational time (0.0009 versus 31.106 s). These numerical experiments not only verified the accuracy of our new formula but also demonstrated their potential in computing exact gravity anomalies for complicated mass density distributions in the Earth.

Place, publisher, year, edition, pages
Oxford University Press, 2018
Keywords
Geopotential theory, Gravity anomalies and Earth structure, Numerical approximations and analysis, Numerical modelling, Numerical solutions
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-362027 (URN)10.1093/gji/ggy250 (DOI)000439648000038 ()
Available from: 2018-10-16 Created: 2018-10-16 Last updated: 2018-10-16Bibliographically approved
Ren, Z., Zhong, Y., Chen, C., Tang, J., Kalscheuer, T., Maurer, H. & Li, Y. (2018). Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts. Surveys in geophysics, 39(5), 901-935
Open this publication in new window or tab >>Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts
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2018 (English)In: Surveys in geophysics, ISSN 0169-3298, E-ISSN 1573-0956, Vol. 39, no 5, p. 901-935Article, review/survey (Refereed) Published
Abstract [en]

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Gravity gradient tensor, Polyhedral bodies, Polynomial mass contrast, Shallow target detection, Gravity explorations
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-365674 (URN)10.1007/s10712-018-9467-1 (DOI)000440819200003 ()
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved
Wang, S., Kalscheuer, T., Bastani, M., Malehmir, A., Pedersen, L. B., Dahlin, T. & Naser, M. (2018). Joint inversion of lake-floor electrical resistivity tomography and boat-towed radio-magnetotelluric data illustrated on synthetic data and an application from the Äspö Hard Rock Laboratory site, Sweden. Geophysical Journal International, 213(1), 511-533
Open this publication in new window or tab >>Joint inversion of lake-floor electrical resistivity tomography and boat-towed radio-magnetotelluric data illustrated on synthetic data and an application from the Äspö Hard Rock Laboratory site, Sweden
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2018 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 213, no 1, p. 511-533Article in journal (Refereed) Published
Abstract [en]

The electrical resistivity tomography (ERT) method provides moderately good constraints for both conductive and resistive structures, while the radio-magnetotelluric (RMT) method is well suited to constrain conductive structures. Additionally, RMT and ERT data may have different target coverage and are differently affected by various types of noise. Hence, joint inversion of RMT and ERT data sets may provide a better constrained model as compared to individual inversions. In this study, joint inversion of boat-towed RMT and lake-floor ERT data has for the first time been formulated and implemented. The implementation was tested on both synthetic and field data sets incorporating RMT transverse electrical mode and ERT data. Results from synthetic data demonstrate that the joint inversion yields models with better resolution compared with individual inversions. A case study from an area adjacent to the Aspo Hard Rock Laboratory (HRL) in southeastern Sweden was used to demonstrate the implementation of the method. A 790-m-long profile comprising lake-floor ERT and boat-towed RMT data combined with partial land data was used for this purpose. Joint inversions with and without weighting (applied to different data sets, vertical and horizontal model smoothness) as well as constrained joint inversions incorporating bathymetry data and water resistivity measurements were performed. The resulting models delineate subsurface structures such as a major northeasterly directed fracture system, which is observed in the HRL facility underground and confirmed by boreholes. A previously uncertain weakness zone, likely a fracture system in the northern part of the profile, is inferred in this study. The fractures are highly saturated with saline water, which make them good targets of resistivity-based geophysical methods. Nevertheless, conductive sediments overlain by the lake water add further difficulty to resolve these deep fracture zones. Therefore, the joint inversion of RMT and ERT data particularly helps to improve the resolution of the resistivity models in areas where the profile traverses shallow water and land sections. Our modification of the joint inversion of RMT and ERT data improves the study of geological units underneath shallow water bodies where underground infrastructures are planned. Thus, it allows better planning and mitigating the risks and costs associated with conductive weakness zones.

National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-327094 (URN)10.1093/gji/ggx414 (DOI)000448715000035 ()
Funder
Swedish Research Council Formas, 25220121907
Available from: 2017-08-02 Created: 2017-08-02 Last updated: 2019-01-18Bibliographically approved
Kalscheuer, T., Juhojuntti, N. & Vaittinen, K. (2018). Two-dimensional audiomagnetotelluric and magnetotelluric modelling of ore deposits: Improvements in model constraints by inclusion of borehole measurements. Surveys in geophysics, 39(3), 467-507
Open this publication in new window or tab >>Two-dimensional audiomagnetotelluric and magnetotelluric modelling of ore deposits: Improvements in model constraints by inclusion of borehole measurements
2018 (English)In: Surveys in geophysics, ISSN 0169-3298, E-ISSN 1573-0956, Vol. 39, no 3, p. 467-507Article in journal (Refereed) Published
Abstract [en]

A combination of magnetotelluric (MT) measurements on the surface and in boreholes (without metal casing) can be expected to enhance resolution and reduce the ambiguity in models of electrical resistivity derived from MT surface measurements alone. In order to quantify potential improvement in inversion models and to aid design of electromagnetic (EM) borehole sensors, we considered two synthetic 2D models containing ore bodies down to 3000 m depth (the first with two dipping conductors in resistive crystalline host rock and the second with three mineralisation zones in a sedimentary succession exhibiting only moderate resistivity contrasts). We computed 2D inversion models from the forward responses based on combinations of surface impedance measurements and borehole measurements such as (1) skin-effect transfer functions relating horizontal magnetic fields at depth to those on the surface, (2) vertical magnetic transfer functions relating vertical magnetic fields at depth to horizontal magnetic fields on the surface and (3) vertical electric transfer functions relating vertical electric fields at depth to horizontal magnetic fields on the surface. Whereas skin-effect transfer functions are sensitive to the resistivity of the background medium and 2D anomalies, the vertical magnetic and electric field transfer functions have the disadvantage that they are comparatively insensitive to the resistivity of the layered background medium. This insensitivity introduces convergence problems in the inversion of data from structures with strong 2D resistivity contrasts. Hence, we adjusted the inversion approach to a three-step procedure, where (1) an initial inversion model is computed from surface impedance measurements, (2) this inversion model from surface impedances is used as the initial model for a joint inversion of surface impedances and skin-effect transfer functions and (3) the joint inversion model derived from the surface impedances and skin-effect transfer functions is used as the initial model for the inversion of the surface impedances, skin-effect transfer functions and vertical magnetic and electric transfer functions. For both synthetic examples, the inversion models resulting from surface and borehole measurements have higher similarity to the true models than models computed exclusively from surface measurements. However, the most prominent improvements were obtained for the first example, in which a deep small-sized ore body is more easily distinguished from a shallow main ore body penetrated by a borehole and the extent of the shadow zone (a conductive artefact) underneath the main conductor is strongly reduced. Formal model error and resolution analysis demonstrated that predominantly the skin-effect transfer functions improve model resolution at depth below the sensors and at distance of similar to 300-1000 m laterally off a borehole, whereas the vertical electric and magnetic transfer functions improve resolution along the borehole and in its immediate vicinity. Furthermore, we studied the signal levels at depth and provided specifications of borehole magnetic and electric field sensors to be developed in a future project. Our results suggest that three-component SQUID and fluxgate magnetometers should be developed to facilitate borehole MT measurements at signal frequencies above and below 1 Hz, respectively.

National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-353476 (URN)10.1007/s10712-017-9454-y (DOI)000429112400006 ()
Projects
Innovative Deep Exploration (INDEX)
Funder
VINNOVA, 2015-01301Swedish Research Council FormasSwedish Energy Agency
Available from: 2018-06-13 Created: 2018-06-13 Last updated: 2018-08-10Bibliographically approved
Yan, P., Garcı́a Juanatey, M. A., Kalscheuer, T., Juhlin, C., Hedin, P., Savvaidis, A., . . . Kück, J. (2017). A magnetotelluric investigation of the Scandinavian Caledonides in western Jämtland, Sweden, using the COSC borehole logs as prior information. Geophysical Journal International, 208(3), 1465-1489
Open this publication in new window or tab >>A magnetotelluric investigation of the Scandinavian Caledonides in western Jämtland, Sweden, using the COSC borehole logs as prior information
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2017 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 208, no 3, p. 1465-1489Article in journal (Refereed) Published
Abstract [en]

In connection with the Collisional Orogeny in the Scandinavian Caledonides (COSC) project, broad-band magnetotelluric (MT) data were acquired at 78 stations along a recent ca. 55km- long NW-SE directed reflection seismic profile (referred to as the COSC Seismic Profile; CSP), with the eastern end located similar to 30 km to the west of the orogenic Caledonian front. The MT component of the project aims at (i) delineating the highly conductive (similar to 0.1 Omega . m) alum shales that are associated with an underlying main decollement and (ii) calibrating the MT model to borehole logs. Strike and distortion analyses of the MT data show a 3-D structure in the western 10 km of the profile around the 2.5 km deep COSC-1 borehole (IGSN: ICDP5054EHW1001) and a preferred strike angle of N34 degrees E in the central and eastern parts of the profile. 2-D modelling of MT impedances was tested using different inversion schemes and parameters. To adjust the resistivity structure locally around the borehole, resistivity logging data from COSC-1 were successfully employed as prior constraints in the 2-D MT inversions. Compared with the CSP, the model inverted from the determinant impedances shows the highest level of structural similarity. A shallow resistor (> 1000 Omega . m) in the top 2-3 km depth underneath the western most 10 km of the profile around COSC-1 corresponds to a zone of high seismic reflectivity, and a boundary at less than 1 km depth where the resistivity decreases rapidly from > 100 to < 1 Omega . m in the central and eastern parts of the profile coincides with the first seismic reflections. The depth to this boundary is well constrained as shown by 1-D inversions of the MT data from five selected sites and it decreases towards the Caledonian front in the east. Underneath the easternmost part of the profile, the MT data show evidence of a second deeper conductor (resistivity < 1 Omega . m) at > 3 km depth. Based upon the COSC-1 borehole logs, the CSP reflection seismic image, and the surface geologic map, the MT resistivity models were interpreted geologically. In the vicinity of COSC-1, the resistor down to 2-3 km depth pertains to the metamorphic Middle Allochthon. The up to 1000-m-thick shallow resistor in the central and eastern parts of the profile is interpreted to overly an imbricated unit at the bottom of the Lower Allochthon that includes the alum shales. In the MT resistivity model, the 300-500 m thick imbricated unit masks the main Caledonian decollement at its bottom. A second possible interpretation, though not favoured here, is that the decollement occurs along a much deeper seismic reflection shallowing from 4.5 km depth in the west to similar to 600 m depth in the east. An additional borehole (COSC-2) is planned to penetrate the Lower Allochthon and the main decollement surface in the central part of the profile and can provide information to overcome this interpretational ambiguity. Using a synthetic study, we evaluate how resistivity logs from COSC-2 can improve the 2-D inversion model.

Keywords
Inverse theory, Downhole methods, Magnetotellurics, Continental tectonics: compressional, Europe
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-303495 (URN)10.1093/gji/ggw457 (DOI)000396818900016 ()
Funder
Swedish Research Council, 2013-5780The Geological Survey of Sweden (SGU)
Available from: 2016-09-20 Created: 2016-09-20 Last updated: 2017-04-27Bibliographically approved
Wang, S., Bastani, M., Kalscheuer, T., Malehmir, A. & Dynesius, L. (2017). Controlled Source Boat-towed Radio-magnetotellurics for Site Investigation at Äspö Hard Rock Laboratory, Southeastern Sweden. In: : . Paper presented at 79th EAGE Conference and Exhibition, 12–15 June 2017, Paris, France (pp. 1-5).
Open this publication in new window or tab >>Controlled Source Boat-towed Radio-magnetotellurics for Site Investigation at Äspö Hard Rock Laboratory, Southeastern Sweden
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2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The radio-magnetotelluric (RMT) method has traditionally been used for land investigations. However, with the development of the boat-towed RMT system, this method is used on shallow water. The lowest frequency of the RMT method is about 14 kHz and in addition water resistivity is quite low in some cases, therefore controlled source measurements is naturally considered for data acquisition. In order to resolve a fracture zone under a brackish water body, the controlled source boat-towed RMT (CSRMT) approach was tested. CSRMT and RMT one-dimensional inversions were carried out separately to analyze galvanic distortions and source effects in our dataset. Serious distortions observed in both inversions as well as the two-dimensional (2D) structure observed in our previous study made us consider 2D inversion for modeling the data. Due to the sufficiently large distance between transmitter and receivers, the CSRMT data were inverted using a 2D inversion code originally designed for plane-wave RMT data. Occam and damped Occam schemes were used in our 2D inversions for CSRMT and RMT data. The results show that CSRMT can better resolve the fracture zone than RMT. This study further illustrates the use of the boat-towed RMT system and particularly when combined with controlled source.

National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-325421 (URN)10.3997/2214-4609.201700565 (DOI)
Conference
79th EAGE Conference and Exhibition, 12–15 June 2017, Paris, France
Available from: 2017-06-23 Created: 2017-06-23 Last updated: 2018-06-04Bibliographically approved
Ren, Z., Tang, J., Kalscheuer, T. & Maurer, H. (2017). Fast 3-D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method. Journal of Geophysical Research - Solid Earth, 122(1), 79-109
Open this publication in new window or tab >>Fast 3-D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method
2017 (English)In: Journal of Geophysical Research - Solid Earth, ISSN 2169-9313, E-ISSN 2169-9356, Vol. 122, no 1, p. 79-109Article in journal (Refereed) Published
Abstract [en]

A novel fast and accurate algorithm is developed for large-scale 3-D gravity and magnetic modeling problems. An unstructured grid discretization is used to approximate sources with arbitrary mass and magnetization distributions. A novel adaptive multilevel fast multipole (AMFM) method is developed to reduce the modeling time. An observation octree is constructed on a set of arbitrarily distributed observation sites, while a source octree is constructed on a source tetrahedral grid. A novel characteristic is the independence between the observation octree and the source octree, which simplifies the implementation of different survey configurations such as airborne and ground surveys. Two synthetic models, a cubic model and a half-space model with mountain-valley topography, are tested. As compared to analytical solutions of gravity and magnetic signals, excellent agreements of the solutions verify the accuracy of our AMFM algorithm. Finally, our AMFM method is used to calculate the terrain effect on an airborne gravity data set for a realistic topography model represented by a triangular surface retrieved from a digital elevation model. Using 16 threads, more than 5800 billion interactions between 1,002,001 observation points and 5,839,830 tetrahedral elements are computed in 453.6s. A traditional first-order Gaussian quadrature approach requires 3.77days. Hence, our new AMFM algorithm not only can quickly compute the gravity and magnetic signals for complicated problems but also can substantially accelerate the solution of 3-D inversion problems.

Place, publisher, year, edition, pages
American Geophysical Union (AGU), 2017
National Category
Geochemistry Geophysics
Identifiers
urn:nbn:se:uu:diva-319326 (URN)10.1002/2016JB012987 (DOI)000395658900005 ()
Available from: 2017-04-03 Created: 2017-04-03 Last updated: 2017-11-29Bibliographically approved
Ren, Z., Chen, C., Pan, K., Kalscheuer, T., Maurer, H. & Tang, J. (2017). Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts. Surveys in geophysics, 38(2), 479-502
Open this publication in new window or tab >>Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts
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2017 (English)In: Surveys in geophysics, ISSN 0169-3298, E-ISSN 1573-0956, Vol. 38, no 2, p. 479-502Article, review/survey (Refereed) Published
Abstract [en]

During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of , where m, n, t are nonnegative integers and a, b, c are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of , , , and an analytic formula of the gravity potential in the case of . For a rectangular prism, we derive an analytic formula of the gravity potential for , and and closed forms of the gravity field are presented for , and . Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.

Place, publisher, year, edition, pages
SPRINGER, 2017
Keywords
Gravity, Singularity-free, Polyhedral body, Prism, Horizontal and vertical mass contrasts
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-320971 (URN)10.1007/s10712-016-9395-x (DOI)000395073900003 ()
Available from: 2017-04-27 Created: 2017-04-27 Last updated: 2017-04-27Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-3819-8182

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