| 1. |
- Chen, Chaojian, et al.
(författare)
-
Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders
- 2018
-
Ingår i: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 214:3, s. 2115-2132
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 2. |
- Farinotti, Daniel, et al.
(författare)
-
Results from the Ice Thickness Models Intercomparison eXperiment Phase 2 (ITMIX2)
- 2021
-
Ingår i: Frontiers in Earth Science. - : Frontiers Media S.A.. - 2296-6463. ; 8
-
Tidskriftsartikel (refereegranskat)abstract
- Knowing the ice thickness distribution of a glacier is of fundamental importance for a number of applications, ranging from the planning of glaciological fieldwork to the assessments of future sea-level change. Across spatial scales, however, this knowledge is limited by the paucity and discrete character of available thickness observations. To obtain a spatially coherent distribution of the glacier ice thickness, interpolation or numerical models have to be used. Whilst the first phase of the Ice Thickness Models Intercomparison eXperiment (ITMIX) focused on approaches that estimate such spatial information from characteristics of the glacier surface alone, ITMIX2 sought insights for the capability of the models to extract information from a limited number of thickness observations. The analyses were designed around 23 test cases comprising both real-world and synthetic glaciers, with each test case comprising a set of 16 different experiments mimicking possible scenarios of data availability. A total of 13 models participated in the experiments. The results show that the inter-model variability in the calculated local thickness is high, and that for unmeasured locations, deviations of 16% of the mean glacier thickness are typical (median estimate, three-quarters of the deviations within 37% of the mean glacier thickness). This notwithstanding, limited sets of ice thickness observations are shown to be effective in constraining the mean glacier thickness, demonstrating the value of even partial surveys. Whilst the results are only weakly affected by the spatial distribution of the observations, surveys that preferentially sample the lowest glacier elevations are found to cause a systematic underestimation of the thickness in several models. Conversely, a preferential sampling of the thickest glacier parts proves effective in reducing the deviations. The response to the availability of ice thickness observations is characteristic to each approach and varies across models. On average across models, the deviation between modeled and observed thickness increase by 8.5% of the mean ice thickness every time the distance to the closest observation increases by a factor of 10. No single best model emerges from the analyses, confirming the added value of using model ensembles.
|
|
| 3. |
|
|
| 4. |
- Kalscheuer, Thomas, et al.
(författare)
-
Joint inversions of three types of electromagnetic data explicitly constrained by seismic observations : results from the central Okavango Delta, Botswana
- 2015
-
Ingår i: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 202:3, s. 1429-1452
-
Tidskriftsartikel (refereegranskat)abstract
- The Okavango Delta of northern Botswana is one of the world’s largest inland deltas or megafans. To obtain information on the character of sediments and basement depths, audio-magnetotelluric (AMT), controlled-source audiomagnetotelluric (CSAMT) and central-loop transient electromagnetic (TEM) data were collected on the largest island within the delta. The data were inverted individually and jointly for 1-D models of electric resistivity. Distortion effects in the AMT and CSAMT data were accounted for by including galvanic distortion tensors as free parameters in the inversions. By employing Marquardt–Levenberg inversion, we found that a 3-layer model comprising a resistive layer overlying sequentially a conductive layer and a deeper resistive layer was sufficient to explain all of the electromagnetic data. However, the top of the basal resistive layer from electromagnetic-only inversions was much shallower than the well-determined basement depth observed in high-quality seismic reflection images and seismic refraction velocity tomograms. To resolve this discrepancy, we jointly inverted the electromagnetic data for 4-layer models by including seismic depths to an interface between sedimentary units and to basement as explicit a priori constraints. We have also estimated the interconnected porosities, clay contents and pore-fluid resistivities of the sedimentary units from their electrical resistivities and seismic P-wave velocities using appropriate petrophysical models. In the interpretation of our preferred model, a shallow ∼40 m thick freshwater sandy aquifer with 85–100 Ohmm resistivity, 10–32 per cent interconnected porosity and <13 per cent clay content overlies a 105–115 m thick conductive sequence of clay and intercalated salt-water-saturated sands with 15–20 Ohmm total resistivity, 1−27 per cent interconnected porosity and 15–60 per cent clay content. A third ∼60 m thick sandy layer with 40–50 Ohmm resistivity, 10–33 per cent interconnected porosity and <15 per cent clay content is underlain by the basement with 3200–4000 Ohmm total resistivity. According to an interpretation of helicopter TEM data that cover the entire Okavango Delta and borehole logs, the second and third layers may represent lacustrine sediments from Paleo Lake Makgadikgadi and a moderately resistive freshwater aquifer comprising sediments of the recently proposed Paleo Okavango Megafan, respectively.
|
|
| 5. |
- Podgorski, Joel E., et al.
(författare)
-
Integrated interpretation of helicopter and ground-based geophysical data recorded within the Okavango Delta, Botswana
- 2015
-
Ingår i: Journal of Applied Geophysics. - : Elsevier BV. - 0926-9851 .- 1879-1859. ; 114, s. 52-67
-
Tidskriftsartikel (refereegranskat)abstract
- Integration of information from the following sources has been used to produce a much better constrained and more complete four-unit geological/hydrological model of the Okavango Delta than previously available: (i) a 3D resistivity model determined from helicopter time-domain electromagnetic (HTEM) data recorded across most of the delta, (ii) 2D models and images derived from ground-based electrical resistance tomographic, transient electromagnetic, and high resolution seismic reflection/refraction tomographic data acquired at four selected sites in western and north-central regions of the delta, and (iii) geological details extracted from boreholes in northeastern and southeastern parts of the delta. The upper heterogeneous unit is the modern delta, which comprises extensive dry and freshwater-saturated sand and lesser amounts of clay and salt. It is characterized by moderate to high electrical resistivities and very low to low P-wave velocities. Except for images of several buried abandoned river channels, it is non-reflective. The laterally extensive underlying unit of low resistivities, low P-wave velocity, and subhorizontal reflectors very likely contains saline-water-saturated sands and clays deposited in the huge Paleo Lake Makgadikgadi (PLM), which once covered a 90,000 km(2) area that encompassed the delta, Lake Ngami, the Mababe Depression, and the Makgadikgadi Basin. Examples of PLM sediments are intersected in many boreholes. Low permeability clay within the PLM unit seems to be a barrier to the downward flow of the saline water. Below the PLM unit, freshwater-saturated sand of the Paleo Okavango Megafan (POM) unit is distinguished by moderate to high resistivities, low P-wave velocity, and numerous subhorizontal reflectors. The POM unit is interpreted to be the remnants of a megafan based on the arcuate nature of its front and the semi-conical shape of its upper surface in the HTEM resistivity model. Moderate to high resistivity subhorizontal layers are consistent with this interpretation. The deepest unit is the basement with very high resistivity, high P-wave velocity, and low or complex reflectivity. The interface between the POM unit and basement is a prominent seismic reflector. (C) 2015 Elsevier B.V. All rights reserved.
|
|
| 6. |
- Reiser, Fabienne, et al.
(författare)
-
Constraining helicopter electromagnetic models of the Okavango Delta with seismic-refraction and seismic-reflection data
- 2014
-
Ingår i: Geophysics. - 0016-8033 .- 1942-2156. ; 79:3, s. B123-B134
-
Tidskriftsartikel (refereegranskat)abstract
- Electrical resistivity models derived from exceptionally high-quality helicopter transient electromagnetic data recorded across the Okavango Delta in Botswana, one of the world's great inland deltas or megafans, include three principal layers: (1) an upper heterogeneous layer of dry and water-saturated sand, (2) an intermediate electrically conductive layer that likely comprises saline-water-saturated sand and clay, and (3) a lower fan-shaped electrically resistive layer of freshwater-saturated sand/gravel and/or crystalline basement. If part of the lower layer comprises a freshwater aquifer, it would be evidence for a recently proposed Paleo Okavango Megafan and a major new source of freshwater. In an attempt to constrain the interpretation of the lower layer, we acquired two high-resolution seismic refraction and reflection data sets at each of two investigation sites: one near the center of the delta and one along its western edge. The interface between unconsolidated sediments and basement near the center of the delta is well defined by an similar to 1800 to similar to 4500 m/s increase in P-wave velocities, a change in seismic reflection facies, and a strong continuous reflection. This interface is about 45 m deeper than the top of the lower resistive layer, thus providing support for the Paleo Okavango Megafan hypothesis. Subhorizontal seismic reflectors are additional evidence for a sedimentary origin of the upper part of the lower resistive layer. In contrast to the observations at the delta's center, the interface between unconsolidated sediments and basement along its western edge, which is also defined by a similar to 1800 to similar to 4500 m/s increase in P-wave velocities and a continuous reflection, coincides with the top of the resistive layer.
|
|
| 7. |
- Ren, Zhengyong, et al.
(författare)
-
A finite-element-based domain-decomposition approach for plane wave 3D electromagnetic modeling
- 2014
-
Ingår i: Geophysics. - : Society of Exploration Geophysicists. - 0016-8033 .- 1942-2156. ; 79:6, s. E255-E268
-
Tidskriftsartikel (refereegranskat)abstract
- We developed a novel parallel domain-decomposition approach for 3D large-scale electromagnetic induction modeling in the earth. We used the edge-based finite-element method and unstructured meshes. Unstructured meshes were divided into sets of nonoverlapping subdomains. We used the curl-curl electric field equation to carry out the analysis. In each subdomain, the electric field was discretized by first-order vector shape functions along the edges of tetrahedral elements. The tangential components of the magnetic field on the interfaces of the subdomains were defined as a set of Lagrange multipliers. The unknown Lagrange multipliers were solved from an interface problem defined on the interfaces of the subdomains. With the availability of the Lagrange multipliers, the electric field values in each subdomain were solved independently. Three synthetic examples were evaluated to verify our code. Excellent agreement with previously published solutions was obtained. Synthetic examples revealed that our domain decomposition technique is scalable with respect to the number of subdomains and robust with regard to frequency and the heterogeneous distribution of material parameters, i.e., electric conductivity, electric permittivity, and magnetic permeability.
|
|
| 8. |
|
|
| 9. |
|
|
| 10. |
|
|
| 11. |
|
|
| 12. |
- Ren, Zhengyong, et al.
(författare)
-
Fast 3-D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method
- 2017
-
Ingår i: Journal of Geophysical Research - Solid Earth. - : American Geophysical Union (AGU). - 2169-9313 .- 2169-9356. ; 122:1, s. 79-109
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 13. |
- Ren, Zhengyong, et al.
(författare)
-
Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts
- 2017
-
Ingår i: Surveys in geophysics. - : SPRINGER. - 0169-3298 .- 1573-0956. ; 38:2, s. 479-502
-
Forskningsöversikt (refereegranskat)abstract
- 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.
|
|
| 14. |
- Ren, Zhengyong, et al.
(författare)
-
Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts
- 2018
-
Ingår i: Surveys in geophysics. - : Springer. - 0169-3298 .- 1573-0956. ; 39:5, s. 901-935
-
Forskningsöversikt (refereegranskat)abstract
- 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.
|
|
| 15. |
- Ren, Zhengyong, et al.
(författare)
-
Recursive Analytical Formulae of Gravitational Fields and Gradient Tensors for Polyhedral Bodies with Polynomial Density Contrasts of Arbitrary Non-negative Integer Orders
- 2020
-
Ingår i: Surveys in geophysics. - : SPRINGER. - 0169-3298 .- 1573-0956. ; 41:4, s. 695-722
-
Tidskriftsartikel (refereegranskat)abstract
- Exact computation of the gravitational field and gravitational gradient tensor for a general mass body is a core routine to model the density structure of the Earth. In this study, we report on the existence of closed-form solutions of the gravitational potential, gravitational field and gravitational gradient tensor for a general polyhedral mass body with a polynomial density function of arbitrary non-negative integer orders that can simultaneously vary in both horizontal and vertical directions. Our closed-form solutions of the gravitational potential and the gravitational field are singularity-free, which implies that the observation sites can have arbitrary geometric relationships with polyhedral mass source bodies. However, weak logarithmic singularities exist on the edges of polyhedra for the gravitational gradient tensor. A simple prismatic mass body with polynomial density contrast varying in the vertical direction and a complicated dodecahedral mass body with quartic-order density contrasts were tested to verify the accuracy of the newly derived closed-form solutions. For the gravitational potential, gravitational fields and gradient tensors, our closed-form solutions are in excellent agreement with previously published analytical solutions and Gaussian numerical quadrature solutions.
|
|
