Robust polynomial fitting method for regional gravity estimation

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 80-89 ◽  
Author(s):  
J. F. Beltrão ◽  
J. B. C. Silva ◽  
J. C. Costa
Keyword(s):  
Gravity Data ◽  
Crustal Thickening ◽  
Polynomial Fitting ◽  
Shallow Subsurface ◽  
Residual Field ◽  
Fitting Method ◽  
Definition Of ◽  
Regional Gravity ◽  
Lower Crustal ◽  
Polynomial Surface

Standard polynomial fitting methods are inconsistent in their formulation. The regional field is approximated by a polynomial fitted to the observed field. As a result, in addition to the nonuniqueness in the definition of the regional field, the fitted polynomial is strongly influenced by the residual field (observed field minus regional field). We present a regional‐residual separation method for gravity data which uses a robust procedure to determine the coefficients of a polynomial fitted to the observations. Under the hypothesis that the regional can be modeled correctly by the polynomial surface, the proposed method minimizes the influence of the residual field in the fitted surface. The proposed method was applied to real gravity data from Ceará state, Brazil, and produced information on zones of possible crustal thickening and the occurrence of lower‐crustal granulitic rocks thrust into the shallow subsurface.

Antarctica crustal model by means of the Bayesian gravity inversion

2020 ◽  
Author(s):  
Martina Capponi ◽  
Daniele Sampietro
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Mass Density ◽  
Geophysical Methods ◽  
Gravity Inversion ◽  
Inversion Algorithm ◽  
Global Gravity ◽  
Uniqueness Of The Solution ◽  
Definition Of ◽  
Regional Gravity

<p>The Antarctica crustal structure is still not completely unveiled due to the presence of thick ice shields all over the continent which prevent direct in situ measurements. In the last decades, various geophysical methods have been used to retrieve information of the upper crust and sediments distribution however there are still regions, especially in central Antarctica, where our knowledge is limited. For these kind of situations, in which the indirect investigation of the subsurface is the only valuable solution, the gravity data are an important source of information. After the recent dedicated satellite missions, like GRACE and GOCE, it has been possible to obtain global gravity field data with spatial resolution and accuracy almost comparable to those of local/regional gravity acquisitions, paving the way to new geophysical applications. The new challenge today is the capability to invert such gravity data on large areas with the aim to obtain a 3D density model of the Earth crust. This is in fact a problem characterized by intrinsic instability and non-uniqueness of the solution that to be solved requires the definition of strong constrains and numerical regularization.</p><p>In this work the authors propose the application of a Bayesian inversion algorithm to the Antarctica continent to infer a model of mass density distribution. The first operation is the definition of an initial geological model in terms of geological horizons and density. These two variables are considered as random variables and, within the iterative procedure based on Markov Chain Monte Carlo methods, they are adjusted in such a way to fit the gravity field on the surface. The test performed show that the method is capable of retrieving an estimated model consistent with the prior information and fitting the gravity observations according to their accuracy.</p>

scholarly journals High-Order Polynomial Fitting Assistance for Fast Double-Peak Finding in Brillouin-Distributed Sensing

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 187
Author(s):  
Marcelo A. Soto ◽  
Alin Jderu ◽  
Dorel Dorobantu ◽  
Marius Enachescu ◽  
Dominik Ziegler
Keyword(s):  
Optical Fibers ◽  
High Order ◽  
Polynomial Fitting ◽  
Gaussian Fitting ◽  
Peak Finding ◽  
Fitting Method ◽  
Fold Reduction ◽  
Order Polynomial ◽  
Fitting In ◽  
Distributed Brillouin Sensor

A high-order polynomial fitting method is proposed to accelerate the computation of double-Gaussian fitting in the retrieval of the Brillouin frequency shifts (BFS) in optical fibers showing two local Brillouin peaks. The method is experimentally validated in a distributed Brillouin sensor under different signal-to noise ratios and realistic spectral scenarios. Results verify that a sixth-order polynomial fitting can provide a reliable initial estimation of the dual local BFS values, which can be subsequently used as initial parameters of a nonlinear double-Gaussian fitting. The method demonstrates a 4.9-fold reduction in the number of iterations required by double-Gaussian fitting and a 3.4-fold improvement in processing time.

Polynomial Moving Fitting Method for Edge Identification

2011 ◽  
Vol 308-310 ◽  
pp. 2560-2564 ◽  
Author(s):  
Xiang Rong Yuan
Keyword(s):  
Edge Detection ◽  
Curve Fitting ◽  
Polynomial Function ◽  
High Order ◽  
Polynomial Fitting ◽  
Fitting Method ◽  
Order Polynomial ◽  
Better Than ◽  
Low Order

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

Highly efficient density inversion of gravity data using nonlinear density polynomial fitting

Geophysics ◽  
2021 ◽  
pp. 1-34
Author(s):  
Guoqing Ma ◽  
Zongrui Li ◽  
Lili Li ◽  
Taihan Wang
Keyword(s):  
Weighting Function ◽  
Gravity Data ◽  
Real Life ◽  
Density Variation ◽  
Density Change ◽  
Inversion Method ◽  
Density Inversion ◽  
Perspective View ◽  
Polynomial Fitting ◽  
Polynomial Coefficients

The density inversion of gravity data is commonly achieved by discretizing the subsurface into prismatic cells and calculating the density of each cell. During this process, a weighting function is introduced to the iterative computation to reduce the skin effect during the inversion. Thus, the computation process requires a significant number of matrix operations, which results in low computational efficiency. We have adopted a density inversion method with nonlinear polynomial fitting (NPF) that uses a polynomial to represent the density variation of prismatic cells in a certain space. The computation of each cell is substituted by the computation of the nonlinear polynomial coefficients. Consequently, the efficiency of the inversion is significantly improved because the number of nonlinear polynomial coefficients is less than the number of cells used. Moreover, because representing the density change of all of the cells poses a significant challenge when the cell number is large, we adopt the use of a polynomial to represent the density change of a subregion with fewer cells and multiple nonlinear polynomials to represent the density changes of all prism cells. Using theoretical model tests, we determine that the NPF method more efficiently recovers the density distribution of gravity data compared with conventional density inversion methods. In addition, the density variation of a subregion with 8 × 8 × 8 prismatic cells can be accurately and efficiently obtained using our cubic NPF method, which can also be used for noisy data. Finally, the NPF method was applied to real gravity data in an iron mining area in Shandong Province, China. Convergent results of a 3D perspective view and the distribution of the iron ore bodies were acquired using this method, demonstrating the real-life applicability of this method.

scholarly journals DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

2021 ◽  
Vol 6 (24) ◽  
pp. 213-225
Author(s):  
Shazad Jamal Jalal ◽  
Tajul Ariffin Musa ◽  
Ami Hassan Md Din ◽  
Wan Anom Wan Aris
Keyword(s):  
Gravity Data ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Gravity Survey ◽  
Mountainous Areas ◽  
Entire Study ◽  
Terrestrial Gravity ◽  
The Past ◽  
Regional Gravity ◽  
Entire Study Area

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

Crustal velocity structure from SAREX, the Southern Alberta Refraction Experiment

2002 ◽  
Vol 39 (3) ◽  
pp. 351-373 ◽  
Author(s):  
Ron M Clowes ◽  
Michael JA Burianyk ◽  
Andrew R Gorman ◽  
Ernest R Kanasewich
Keyword(s):  
Velocity Structure ◽  
Data Interpretation ◽  
Crustal Thickening ◽  
Tectonic Zone ◽  
Crustal Layer ◽  
Crustal Velocity ◽  
Crustal Velocity Structure ◽  
Southern Alberta ◽  
Magmatic Underplating ◽  
Lower Crustal

Lithoprobe's Southern Alberta Refraction Experiment, SAREX, extends 800 km from east-central Alberta to central Montana. It was designed to investigate crustal velocity structure of the Archean domains underlying the Western Canada Sedimentary Basin. From north to south, SAREX crosses the Loverna domain of the Hearne Province, the Vulcan structure, the Medicine Hat block (previously considered part of the Hearne Province), the Great Falls tectonic zone, and the northern Wyoming Province. Ten shot points along the profile in Canada were recorded on 521 seismographs deployed at 1 km intervals. To extend the line, an additional 140 seismographs were deployed at intervals of 1.25–2.50 km in Montana. Data interpretation used an iterative application of damped least-squares inversion of traveltime picks and forward modeling. Results show different velocity structures for the major blocks (Loverna, Medicine Hat, and Wyoming), indicating that each is distinct. Wavy undulations in the velocity structure of the Loverna block may be associated with internal crustal deformation. The most prominent feature of the model is a thick (10–25 km) lower crustal layer with high velocities (7.5–7.9 km/s) underlying the Medicine Hat and Wyoming blocks. Based on data from lower crustal xenoliths in the region, this layer is interpreted to be the result of Paleoproterozoic magmatic underplating. Crustal thickness varies from 40 km in the north to almost 60 km in the south, where the high-velocity layer is thickest. Uppermost mantle velocities range from 8.05 to 8.2 km/s, with the higher values below the thicker crust. Results from SAREX and other recent studies are synthesized to develop a schematic representation of Archean to Paleoproterozoic tectonic development for the region encompassing the profile. Tectonic processes associated with this development include collisions of continental blocks, subduction, crustal thickening, and magmatic underplating.

The gravity field over the Ungava Bay region from satellite altimetry and new land-based data: implications for the geology of the area

1999 ◽  
Vol 36 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Hamid Telmat ◽  
Jean-Claude Mareschal ◽  
Clément Gariépy
Keyword(s):  
Satellite Altimetry ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Gravity Models ◽  
Crustal Thickening ◽  
Seismic Line ◽  
Crustal Thinning ◽  
Gravity Measurements ◽  
George River ◽  
Superior Craton

Gravity data were obtained along two transects on the southern coast of Ungava Bay, which provide continuous gravity coverage between Leaf Bay and George River. The transects and the derived gravity profiles extend from the Superior craton to the Rae Province across the New Quebec Orogen (NQO). Interpretation of the transect along the southwestern coast of Ungava Bay suggests crustal thickening beneath the NQO and crustal thinning beneath the Kuujjuaq Terrane, east of the NQO. Two alternative interpretations are proposed for the transect along the southeastern coast of the bay. The first model shows crustal thickening beneath the George River Shear Zone (GRSZ) and two shallow bodies correlated with the northern extensions of the GRSZ and the De Pas batholith. The second model shows constant crustal thickness and bodies more deeply rooted than in the first model. The gravity models are consistent with the easterly dipping reflections imaged along a Lithoprobe seismic line crossing Ungava Bay and suggest westward thrusting of the Rae Province over the NQO. Because no gravity data have been collected in Ungava Bay, satellite altimetry data have been used as a means to fill the gap in data collected at sea. The satellite-derived gravity data and standard Bouguer gravity data were combined in a composite map for the Ungava Bay region. The new land-based gravity measurements were used to verify and calibrate the satellite data and to ensure that offshore gravity anomalies merge with those determined by the land surveys in a reasonable fashion. Three parallel east-west gravity profiles were extracted: across Ungava Bay (59.9°N), on the southern shore of the bay (58.5°N), and onshore ~200 km south of Ungava Bay (57.1°N). The gravity signature of some major structures, such as the GRSZ, can be identified on each profile.

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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