Inversion of gravity‐field inclination to map the basement relief of sedimentary basins

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1240-1251 ◽  
Author(s):  
Carlos Alberto Mendonça
Keyword(s):  
Inverse Problem ◽  
Gravity Anomaly ◽  
Gravity Field ◽  
Random Search ◽  
Vertical Component ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Constant Density ◽  
Source Geometry ◽  
Field Inclination

This paper presents a method to map the basement relief of homogeneous sedimentary basins that does not require the knowledge of the basin density contrast. To reach this task, the proposed method relies on the invariance of the inclination of the anomalous gravity field with the density contrast caused by models constituted by two homogeneous media. This invariance occurs because the density contrast appears as a constant factor in both vertical and horizontal gravity components, therefore being canceled out when these components are divided during the evaluation of the field inclination. For such media, the field inclination is independent of the density contrast, thus allowing the source geometry reconstruction even when the density contrast is unknown. As the inclination is rarely measured, the gravity anomaly (i.e., the field vertical component) is initially used to compute the horizontal component of the gravity field by applying a suitable linear transform. The field inclination is estimated from both components and then used to invert the source geometry by fitting the inclination values under the geologic constraints attributed to the causative sources. In this process, the density contrast is not required nor introduced as an unknown parameter in the formulated inverse problem. Moreover, it can be estimated later by solving a new inverse problem where the source geometry determined from the inverted inclination is fixed and the constant density contrast is determined by fitting the gravity anomaly. This paper applies such ideas to map the basement relief of a sedimentary basin and to estimate its density contrast. The inversion is implemented by a random search procedure that excludes extreme models, and imposes constraints that the unknown interface is smooth everywhere and assumes known depth values at isolated points investigated by wells. The proposed technique is tested with synthetic noisy data from homogeneous and heterogeneous basin models and is applied to invert a gravity profile from the Recôncavo Basin, Brazil. The results from the real data application are compared with well data and previously published results.

Efficient gravity inversion of basement relief using a versatile modeling algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. G23-G34 ◽  
Author(s):  
João B. C. Silva ◽  
Darcicléa F. Santos
Keyword(s):  
Gravity Anomaly ◽  
Region Of Interest ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Gravity Inversion ◽  
Deep Basin ◽  
Novel Approach ◽  
Green’S Operator ◽  
Translation Symmetry ◽  
Observation Position

We have developed a novel approach to compute, in an efficient and versatile way, the gravity anomaly produced by an arbitrary, discrete 3D distribution of density contrast. The method allows adjustable precision and is particularly suited for the interpretation of sedimentary basins. Because the gravity field decays with the square of the distance, we use a discrete Green’s operator that may be made much smaller than the whole study area. For irregularly positioned observations, this discrete Green’s operator must be computed just at the first iteration, and because each of its horizontal layers presents a center of symmetry, only one-eighth of its total elements need to be calculated. Furthermore, for gridded data on a plane, this operator develops translation symmetry for the whole region of interest and has to be computed just once for a single arbitrary observation position. The gravity anomaly is obtained as the product of this small operator by any arbitrary density contrast distribution in a convolution-like operation. We use the proposed modeling to estimate the basement relief of a [Formula: see text] basin with density contrast varying along [Formula: see text] only using a smaller Green’s operator at all iterations. The median of the absolute differences between relief estimates, using the small and a large operator (the latter covering the whole basin) has been approximately 9 m for a 3.6 km deep basin. We also successfully inverted the anomaly of a simulated basin with density contrast varying laterally and vertically, and a real anomaly produced by a steeply dipping basement. The proposed modeling is very fast. For 10,000 observations gridded on a plane, the inversion using the proposed approach for irregularly spaced data is two orders of magnitude faster than using an analytically derived fitting, and this ratio increases enormously with the number of observations.

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

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 754-764 ◽  
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.

3D vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3D variable density contrast

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. I43-I53 ◽  
Author(s):  
Xiaobing Zhou
Keyword(s):  
Gravity Anomaly ◽  
Integral Method ◽  
Numerical Solutions ◽  
Vertical Component ◽  
Building Blocks ◽  
Variable Density ◽  
Rectangular Prism ◽  
Density Contrast ◽  
Gravity Potential ◽  
Line Integral

Three-dimensional rectangular prisms are building blocks for calculating gravity anomalies from irregular 3D mass bodies with spatially variable density contrasts. A 3D vector gravity potential is defined for a 3D rectangular prism with density contrast varying in depth and horizontally. The vertical component of the gravity anomaly equals the flux of the 3D vector gravity potential through the enclosed surface of the prism. Thus, the 3D integral for the gravity anomaly is reduced to a 2D surface integral. In turn, a 2D vector gravity potential is defined. The vertical component of the gravity anomaly equals the net circulation of the 2D vector gravity potential along the enclosed contour bounding the surfaces of the prism. The 3D integral for the gravity anomaly is reduced to 1D line integrals. Further analytical or numerical solutions can then be obtained from the line integrals, depending on the forms of the density contrast functions. If an analytical solution cannot be obtained, the line-integral method is semianalytical, requiring numerical quadratures to be carried out at the final stages. Singularity and discontinuity exist in the algorithm and the method of exclusive infinitesimal sphere or circle is effective to remove them. Then the vector-potential line-integral method can calculate the gravity anomaly resulting from a rectangular prism with density contrast, varying simply in one direction and sophisticatedly in three directions. The advantage of the method is that the constraint to the form of the density contrast is greatly reduced and the numerical calculation for the gravity anomaly is fast.

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

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. J51-J58 ◽  
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.

Harmonic Correction for Residual Terrain Modelling (RTM) Technique in Physical Geodesy Applications

2021 ◽  
Author(s):  
Meng Yang ◽  
Xiao-Le Deng ◽  
Min Zhong
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Physical Geodesy ◽  
Geoid Height ◽  
Gravity Field Modelling ◽  
Field Modelling ◽  
Condensation Method ◽  
Residual Terrain Modelling ◽  
Harmonic Correction ◽  
Terrain Modelling

<p>       In physical geodesy, the harmonic correction (HC), as one of the main problems when using residual terrain modelling (RTM), has become a research focus of high-frequency gravity field modelling. Over past decades, though various methods have been proposed to handle the HC issues for RTM technique, most of them focused on the HC for RTM gravity anomaly rather than other gravity functionals, such as RTM geoid height and gravity gradient. In practice, the HC for RTM geoid height was generally assumed to be negligible, but a quantification is yet studied. In this study, besides the highlighted HC for gravity anomaly in previous studies, the expressions of HC terms for RTM geoid height are provided in the framework of the classical condensation method under infinite Bouguer plate approximation. The errors involved by various assumption of the classical condensation method, e.g., mass inconsistency between infinite masses in the HC and limited masses in the RTM, and planar assumption of the Earth’s surface, are further studied. Based on the derived formulas, the quantification of HC for RTM geoid height when reference surface is expanded to degree and order of 2,159 is given. Our results showed the significance of HC for RTM geoid height, with values up to ~10 cm, in cm-level and mm-level geoid determination. With integration masses extending up to a sufficient distance, such as 1° from calculation point for the determination of RTM geoid height, the errors due to an infinite Bouguer plate approximation are neglectable small. The validation through comparison with terrestrial measurements proved that the HC terms provided in this study can improve the accuracy of RTM derived geoid height and are expected to be useful for applications of RTM technique in regional and global gravity field modelling.</p>

Towards an updated, enhanced regional gravity field solution for Antarctica

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

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (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).</p><p>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).</p><p>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’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

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