Implementation of Two-point Quadrature Gauss-Legendre Method on 2D Gravity Anomaly Modeling in Basins with Density Distribution Varied Polynomially as a Function of Depth

Study of basin geometry basin is important in geosciences and geophysical exploration. Gravity method can be used to address this issue by measuring gravity anomalies on the surface caused by density contrast between the bedrock and the sediment that fills the basin, geometry of the basin and surface topography. Numerically, gravity anomaly modeling can be conducted using two-point rule Gauss-Legendre Quadrature method, for a case where density contrast varies with depth exponentially. Within the scope of this study, gravity anomalies on the surface are significantly affected by the geometry of the curvature of the bedrock as well as the topographic elevation of the surface and the selected density contrast, and are not significantly affected by the undulation of the bedrock curvature.

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Stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations

Geophysics ◽

10.1190/1.1444585 ◽

1999 ◽

Vol 64 (3) ◽

pp. 754-764 ◽

Cited By ~ 40

Author(s):

Valéria C. F. Barbosa ◽

João B. C. Silva ◽

Walter E. Medeiros

Keyword(s):

Gravity Anomaly ◽

Gravity Data ◽

A Priori ◽

Bouguer Anomaly ◽

Gravity Anomalies ◽

Sedimentary Basins ◽

Upper And Lower Bounds ◽

Density Contrast ◽

Good Precision ◽

Rift Basins

We present a new, stable method for interpreting the basement relief of a sedimentary basin which delineates sharp discontinuities in the basement relief and incorporates any law known a priori for the spatial variation of the density contrast. The subsurface region containing the basin is discretized into a grid of juxtaposed elementary prisms whose density contrasts are the parameters to be estimated. Any vertical line must intersect the basement relief only once, and the mass deficiency must be concentrated near the earth’s surface, subject to the observed gravity anomaly being fitted within the experimental errors. In addition, upper and lower bounds on the density contrast of each prism are introduced a priori (one of the bounds being zero), and the method assigns to each elementary prism a density contrast which is close to either bound. The basement relief is therefore delineated by the contact between the prisms with null and nonnull estimated density contrasts, the latter occupying the upper part of the discretized region. The method is stabilized by introducing constraints favoring solutions having the attributes (shared by most sedimentary basins) of being an isolated compact source with lateral borders dipping either vertically or toward the basin center and having horizontal dimensions much greater than its largest vertical dimension. Arbitrary laws of spatial variations of the density contrast, if known a priori, may be incorporated into the problem by assigning suitable values to the nonnull bound of each prism. The proposed method differs from previous stable methods by using no smoothness constraint on the interface to be estimated. As a result, it may be applied not only to intracratonic sag basins where the basement relief is essentially smooth but also to rift basins whose basements present discontinuities caused by faults. The method’s utility in mapping such basements was demonstrated in tests using synthetic data produced by simulated rift basins. The method mapped with good precision a sequence of step faults which are close to each other and present small vertical slips, a feature particularly difficult to detect from gravity data only. The method was also able to map isolated discontinuities with large vertical throw. The method was applied to the gravity data from Reco⁁ncavo basin, Brazil. The results showed close agreement with known geological structures of the basin. It also demonstrated the method’s ability to map a sequence of alternating terraces and structural lows that could not be detected just by inspecting the gravity anomaly. To demostrate the method’s flexibility in incorporating any a priori knowledge about the density contrast variation, it was applied to the Bouguer anomaly over the San Jacinto Graben, California. Two different exponential laws for the decrease of density contrast with depth were used, leading to estimated maximum depths between 2.2 and 2.4 km.

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General line integrals for gravity anomalies of irregular 2D masses with horizontally and vertically dependent density contrast

Geophysics ◽

10.1190/1.3073761 ◽

2009 ◽

Vol 74 (2) ◽

pp. I1-I7 ◽

Cited By ~ 18

Author(s):

Xiaobing Zhou

Keyword(s):

Gravity Anomaly ◽

Gravity Anomalies ◽

Density Contrast ◽

Vertical Position ◽

Horizontal Position ◽

Surface Integral ◽

Cross Sectional ◽

Contrast Model ◽

Contrast Function ◽

Dependent Density

Line integrals (LIs) are an efficient tool in calculating the gravity anomaly caused by an irregular 2D mass body because the 2D surface integral is reduced to a 1D LI. Historically, LIs have been derived for 2D mass bodies of depth-dependent density contrast. I derive LIs for 2D mass bodies with density contrast dependent on (1) horizontal and (2) horizontal and vertical directions. Assuming the density contrast depends only on horizontal position, two types of representative LIs are derived: LIs with logarithmic kernel and density-integrated LIs for any integrable density-contrast function. A general density-contrast model that depends on horizontal and vertical directions is developed to include three components: a function of horizontal position, a function of vertical position, and a sum of crossterms of horizontal and vertical positions. Based on the general density-contrast model defined and proper selection of 2D vector gravity potentials, general LIs are derived to calculate the gravity anomaly. The newly developed LI method is then compared with two cases from the literature in calculating gravity anomaly, and agreement is obtained. However, the new LI method allows for more general 2D density-contrast variations and can be used to calculate the gravity anomaly of a 2D mass body. Such a mass body can have any cross-sectional profile that can be approximated by a polygonal cross section with any density-contrast function that can be approximated by a rich set of basis functions.

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GRAVSYS Software Based on Scratch Programming for 2D Gravity Anomalies Source Responses and Its Implementation in Trangkil Gunungpati

KnE Social Sciences ◽

10.18502/kss.v3i18.4755 ◽

2019 ◽

Author(s):

Supriyadi . ◽

Jefta Heparona ◽

Sugiyanto . ◽

Mahardika . ◽

Rini Kusumawardhani ◽

...

Keyword(s):

Water Pollution ◽

Iron Ore ◽

2D Gravity ◽

Gravity Anomalies ◽

Data Input ◽

Resource Potential ◽

Gravity Method ◽

Software Products ◽

2D Simulation ◽

Implementation Stage

Gravsyssoftwarewascreatedwiththeaimtoovercomestudent’sproblemswhichhave difﬁculty in understanding the concept of gravity. This software was developed using Scratch programming which has features to make a simple appearance in the form of images, animations and simulations. Therefore, an innovation of software products can be established as a learning media for students who take gravity method courses. Broadly speaking, Gravsys has several main features, namely data input of parameter model, creating 2D simulation of uniform object, and displays the response of the gravitationalﬁeldanomalyingraphicalform,sothatitcanhelpstudentstounderstand the concept of anomalous source objects and response to gravity anomalies caused by source objects for various subsurface cases, seawater intrusion, water pollution, natural resource potential (coal, iron ore), prediction of bunker existence, decrease and increase of ground water level. In the implementation stage of Ayodya, Trangkil, Gunungpati, the subproject layer showed that 3 layers were sandy clay with density 1,4 gr/cm3, sand with density of 2.3 gr/cm3, bedrock with density 2.6 gr/cm3, each at a depth of 0-30 meters, 30-60 meters, and over 60 meters.

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Gravity inversion of basement relief and estimation of density contrast variation with depth

Geophysics ◽

10.1190/1.2236383 ◽

2006 ◽

Vol 71 (5) ◽

pp. J51-J58 ◽

Cited By ~ 48

Author(s):

João B. Silva ◽

Denis C. Costa ◽

Valéria C. Barbosa

Keyword(s):

Gravity Anomaly ◽

Surface Density ◽

Prior Information ◽

Bouguer Anomaly ◽

Gravity Anomalies ◽

Sedimentary Basins ◽

Density Contrast ◽

Gravity Inversion ◽

Contrast Variation ◽

Interpretation Model

We present a method to estimate the basement relief as well as the density contrast at the surface and the hyperbolic decaying factor of the density contrast with depth, assuming that the gravity anomaly and the depth to the basement at a few points are known. In both cases, the interpretation model is a set of vertical rectangular 2D prisms whose thicknesses are parameters to be estimated and that represent the depth to the interface separating sediments and basement. The solutions to both problems are stable because of the incorporation of additional prior information about the smoothness of the estimated relief and the depth to the basement at a few locations, presumably provided by boreholes. The method was tested with synthetic gravity anomalies produced by simulated sedimentary basins with smooth relief, providing not only well-resolved estimated relief, but also good estimates for the density contrasts at the surface and for the decaying factors of the density contrast with depth. The method was applied to the Bouguer anomaly from Recôncavo Basin, estimating the surface density contrast and the decaying factor of the density contrast with depth as [Formula: see text] and [Formula: see text], respectively.

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Gravity anomalies of two‐dimensional bodies of irregular cross‐section with density contrast varying with depth

Geophysics ◽

10.1190/1.1441023 ◽

1979 ◽

Vol 44 (9) ◽

pp. 1525-1530 ◽

Cited By ~ 58

Author(s):

I. V. Radhakrishna Murthy ◽

D. Bhaskara Rao

Keyword(s):

Gravity Anomaly ◽

Cross Section ◽

Cross Sections ◽

Integral Method ◽

Gravity Anomalies ◽

Density Contrast ◽

Two Dimensional ◽

Gravity Effect ◽

Line Integral ◽

Exponential Increase

The line‐integral method of Hubbert (1948) is extended to obtain the gravity anomalies of two‐dimensional bodies of arbitrary cross‐sections with density contrast varying linearly with depth. The cross‐section is replaced by an N‐sided polygon. The coordinates of two vertices of any given side are used to determine the associated contribution to the gravity anomaly. The gravity contribution of each side is then summed to yield the total gravity effect. The case where density contrast varies exponentially with depth is also considered. This technique is used to obtain the structure of the San Jacinto Graben, California, where sediments filling the graben have an exponential increase in density with depth.

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Gravity anomaly modelling of multiple geological sources having differing strike lengths and arbitrary density contrast variations

Near Surface Geophysics ◽

10.3997/1873-0604.2013001 ◽

2012 ◽

Vol 11 (4) ◽

pp. 363-370 ◽

Cited By ~ 1

Author(s):

V. Chakravarthi ◽

B. Ramamma

Keyword(s):

Gravity Anomaly ◽

Density Contrast

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Basin Depth Mapping Beneath Wellington City Based on Residual Gravity Anomalies

10.26686/wgtn.15176061 ◽

2021 ◽

Author(s):

◽

Alistair Stronach

Keyword(s):

Gravity Anomaly ◽

Sedimentary Basin ◽

Gravity Data ◽

Three Dimensional ◽

Maximum Amplitude ◽

Central Business District ◽

Gravity Anomalies ◽

Depth Map ◽

Capital City ◽

Detailed Knowledge

New Zealand’s capital city of Wellington lies in an area of high seismic risk, which is further increased by the sedimentary basin beneath the Central Business District (CBD). Ground motion data and damage patterns from the 2013 Cook Strait and 2016 Kaikōura earthquakes indicate that two- and three-dimensional amplification effects due to the Wellington sedimentary basin may be significant. These effects are not currently accounted for in the New Zealand Building Code. In order for this to be done, three-dimensional simulations of earthquake shaking need to be undertaken, which requires detailed knowledge of basin geometry. This is currently lacking, primarily because of a dearth of deep boreholes in the CBD area, particularly in Thorndon and Pipitea where sediment depths are estimated to be greatest. A new basin depth map for the Wellington CBD has been created by conducting a gravity survey using a modern Scintrex CG-6 gravity meter. Across the study area, 519 new high precision gravity measurements were made and a residual anomaly map created, showing a maximum amplitude anomaly of -6.2 mGal with uncertainties better than ±0.1 mGal. Thirteen two-dimensional geological profiles were modelled to fit the anomalies, then combined with existing borehole constraints to construct the basin depth map. Results indicate on average greater depths than in existing models, particularly in Pipitea where depths are interpreted to be as great as 450 m, a difference of 250 m. Within 1 km of shore depths are interpreted to increase further, to 600 m. The recently discovered basin bounding Aotea Fault is resolved in the gravity data, where the basement is offset by up to 13 m, gravity anomaly gradients up to 8 mGal/km are observed, and possible multiple fault strands identified. A secondary strand of the Wellington Fault is also identified in the north of Pipitea, where gravity anomaly gradients up to 18 mGal/km are observed.

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Evaluation of Marine Gravity Anomaly Calculation Accuracy by Multi-Source Satellite Altimetry Data

Frontiers in Earth Science ◽

10.3389/feart.2021.730777 ◽

2021 ◽

Vol 9 ◽

Author(s):

Shanwei Liu ◽

Yinlong Li ◽

Qinting Sun ◽

Jianhua Wan ◽

Yue Jiao ◽

...

Keyword(s):

Root Mean Square Error ◽

Gravity Anomaly ◽

Mean Square Error ◽

Spatial Resolution ◽

Satellite Altimetry ◽

Gravity Anomalies ◽

Mean Square ◽

Altimetry Data ◽

Marine Gravity ◽

Satellite Altimetry Data

The purpose of this paper is to analyze the influence of satellite altimetry data accuracy on the marine gravity anomaly accuracy. The data of 12 altimetry satellites in the research area (5°N–23°N, 105°E–118°E) were selected. These data were classified into three groups: A, B, and C, according to the track density, the accuracy of the altimetry satellites, and the differences of self-crossover. Group A contains CryoSat-2, group B includes Geosat, ERS-1, ERS-2, and Envisat, and group C comprises T/P, Jason-1/2/3, HY-2A, SARAL, and Sentinel-3A. In Experiment I, the 5′×5′ marine gravity anomalies were obtained based on the data of groups A, B, and C, respectively. Compared with the shipborne gravity data, the root mean square error (RMSE) of groups A, B, and C was 4.59 mGal, 4.61 mGal, and 4.51 mGal, respectively. The results show that high-precision satellite altimetry data can improve the calculation accuracy of gravity anomaly, and the single satellite CryoSat-2 enables achieving the same effect of multi-satellite joint processing. In Experiment II, the 2′×2′ marine gravity anomalies were acquired based on the data of groups A, A + B, and A + C, respectively. The root mean square error of the above three groups was, respectively, 4.29 mGal, 4.30 mGal, and 4.21 mGal, and the outcomes show that when the spatial resolution is satisfied, adding redundant low-precision altimetry data will add pressure to the calculation of marine gravity anomalies and will not improve the accuracy. An effective combination of multi-satellite data can improve the accuracy and spatial resolution of the marine gravity anomaly inversion.

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Towards an updated, enhanced regional gravity field solution for Antarctica

10.5194/egusphere-egu21-9873 ◽

2021 ◽

Author(s):

Mirko Scheinert ◽

Philipp Zingerle ◽

Theresa Schaller ◽

Roland Pail ◽

Martin Willberg

Keyword(s):

Gravity Anomaly ◽

Gravity Field ◽

Gravity Data ◽

Gravity Anomalies ◽

Data Set ◽

Gravity Field Model ◽

Terrestrial Gravity ◽

Field Solution ◽

Gravity Disturbances ◽

Regional Gravity

In the frame of the IAG Subcommission 2.4f &#8220;Gravity and Geoid in Antarctica&#8221; (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth&#8217;s interior (cf. the contribution of Schaller et al. in session G4.3).

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Empirical Determination of the Gravity Anomaly Covariance Function in Mountainous Areas

The Canadian Surveyor ◽

10.1139/tcs-1980-0035 ◽

1980 ◽

Vol 34 (3) ◽

pp. 251-264 ◽

Cited By ~ 3

Author(s):

Gerard Lachapelle ◽

K. P. Schwarz

Keyword(s):

Gravity Anomaly ◽

Covariance Function ◽

Physical Geodesy ◽

Gravity Anomalies ◽

Mountainous Areas ◽

The North ◽

Regression Parameters ◽

Free Air ◽

Vening Meinesz ◽

Free Air Gravity

An evaluation of the empirical gravity anomaly covariance function using over 95 000 surface gravity anomalies in the North American Western Cordillera was carried out. A regression analysis of the data exhibits a strong and quasi-linear correlation of free air gravity anomalies with heights. This height correlation is removed from the free air anomalies prior to the numerical evaluation of the gravity anomaly covariance function. This covariance function agrees well with that evaluated previously by the authors for the remainder of Canada. A possible use for such a covariance function of ‘height independent’ gravity anomalies in mountainous areas is described. First, the height independent gravity anomaly at a point of known height is evaluated by least squares prediction using neighboring measured height independent gravity anomalies. Secondly, the part caused by the height correlation is calculated using linear regression parameters estimated previously and added to the predicted height independent gravity anomaly to obtain a predicted standard free air anomaly. This technique can be used to densify the coverage of free air anomalies for subsequent use in integral formulas of physical geodesy, e.g., those of Stokes and Vening Meinesz. This method requires that point topographic heights be given on a grid.

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