Linear inversion of gravity data for 3-D density distributions

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1354-1364 ◽  
Author(s):  
Glenn W. Bear ◽  
Haydar J. Al‐Shukri ◽  
Albert J. Rudman
Keyword(s):  
Density Distribution ◽  
Gravity Data ◽  
Linear Equations ◽  
Large Data ◽  
Linear Inversion ◽  
Solution Quality ◽  
Data Set ◽  
User Input ◽  
Statistical Measures ◽  
Unknown Density

We have developed an improved Levenburg‐Marquart technique to rapidly invert Bouguer gravity data for a 3-D density distribution as a source of the observed field. This technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user. Where such information is not available, objective models are generated. The technique estimates the density distribution within the source volume using a least‐squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential Householder transformations. The source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density. This discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution. Convergence of the solution to the system is tightly controlled by a damping parameter which may be varied at each iteration. The associated algorithm generates statistical measures of solution quality not available with most forward methods. Along with the ability to handle large data sets within reasonable time constraints, the advantages of this approach are: (1) the ease with which pre‐existing geological information can be included to constrain the solution, (2) its minimization of subjective user input, (3) the avoidance of difficulties encountered during wavenumber domain transformations, and (4) the objective nature of the solution. Application to a gravity data set from Hamilton County, Indiana, has yielded a geologically reasonable result that agrees with published models derived from interpretation of gravity, magnetic, seismic, and drilling data.

Linear inversion of gravity data using the spectral expansion method

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 820-824 ◽  
Author(s):  
Rene E. Chavez ◽  
George D. Garland
Keyword(s):  
Inverse Problem ◽  
Gravity Data ◽  
Linear Equations ◽  
Thin Sheet ◽  
Gravity Anomalies ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Uniform Density ◽  
Linear Inversion ◽  
Prismatic Structure

Inversion of gravity anomalies in terms of an anomalous mass distribution with irregular outline but uniform density leads to a nonlinear inverse problem. An alternative approach based on the thin‐sheet approximation can, however, be formulated as a linear inverse problem provided the structures are two‐dimensional. The anomalous mass is represented by a thin sheet, which is located at a depth [Formula: see text] and is divided into M strips with N < M data points. Thus, an underdetermined system of linear equations is obtained which is solved by the spectral expansion method for the surface density distribution of each segment. This set of parameters is then transformed into a prismatic structure with variable depth but uniform density. The modeling procedure involves a noniterative method. A gravity problem is investigated, and the solution obtained compares well with previous interpretations.

Convolutional equivalent layer for gravity data processing

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. G129-G141
Author(s):  
Diego Takahashi ◽  
Vanderlei C. Oliveira Jr. ◽  
Valéria C. F. Barbosa
Keyword(s):  
Data Processing ◽  
Gravity Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Large Data ◽  
Sensitivity Matrix ◽  
Data Set ◽  
Layer Technique ◽  
Symmetric Block ◽  
Equivalent Layer

We have developed an efficient and very fast equivalent-layer technique for gravity data processing by modifying an iterative method grounded on an excess mass constraint that does not require the solution of linear systems. Taking advantage of the symmetric block-Toeplitz Toeplitz-block (BTTB) structure of the sensitivity matrix that arises when regular grids of observation points and equivalent sources (point masses) are used to set up a fictitious equivalent layer, we develop an algorithm that greatly reduces the computational complexity and RAM memory necessary to estimate a 2D mass distribution over the equivalent layer. The structure of symmetric BTTB matrix consists of the elements of the first column of the sensitivity matrix, which, in turn, can be embedded into a symmetric block-circulant with circulant-block (BCCB) matrix. Likewise, only the first column of the BCCB matrix is needed to reconstruct the full sensitivity matrix completely. From the first column of the BCCB matrix, its eigenvalues can be calculated using the 2D fast Fourier transform (2D FFT), which can be used to readily compute the matrix-vector product of the forward modeling in the fast equivalent-layer technique. As a result, our method is efficient for processing very large data sets. Tests with synthetic data demonstrate the ability of our method to satisfactorily upward- and downward-continue gravity data. Our results show very small border effects and noise amplification compared to those produced by the classic approach in the Fourier domain. In addition, they show that, whereas the running time of our method is [Formula: see text] s for processing [Formula: see text] observations, the fast equivalent-layer technique used [Formula: see text] s with [Formula: see text]. A test with field data from the Carajás Province, Brazil, illustrates the low computational cost of our method to process a large data set composed of [Formula: see text] observations.

Inferences of the lunar interior from a probabilistic gravity inversion approach

2020 ◽  
Author(s):  
Kristel Izquierdo ◽  
Laurent Montesi ◽  
Vedran Lekic
Keyword(s):  
Gravity Data ◽  
Gravity Inversion ◽  
Positive Density ◽  
The Moon ◽  
Distribution Models ◽  
Linear Inversion ◽  
Spherical Harmonic Degree ◽  
Data Set ◽  
Voronoi Region ◽  
Gravity Acceleration

&lt;p&gt;The shape and location of density anomalies inside the Moon provide insights into processes that produced them and their subsequent evolution. Gravity measurements provide the most complete data set to infer these anomalies on the Moon [1]. However, gravity inversions suffer from inherent non-uniqueness. To circumvent this issue, it is often assumed that the Bouguer gravity anomalies are produced by the relief of the crust-mantle or other internal interface [2]. This approach limits the recovery of 3D density anomalies or any anomaly at different depths. In this work, we develop an algorithm that provides a set of likely three-dimensional models consistent with the observed gravity data with no need to constrain the depth of anomalies a priori.&lt;/p&gt;&lt;p&gt;The volume of a sphere is divided in 6480 tesseroids and n Voronoi regions. The algorithm first assigns a density value to each Voronoi region, which can encompass one or more tesseroids. At each iteration, it can add or delete a region, or change its location [2, 3]. The optimal density of each region is then obtained by linear inversion of the gravity field and the likelihood of the solution is calculated using Bayes&amp;#8217; theorem. After convergence, the algorithm then outputs an ensemble of models with good fit to the observed data and high posterior probability. The ensemble might contain essentially similar interior density distribution models or many different ones, providing a view of the non-uniqueness of the inversion results.&lt;/p&gt;&lt;p&gt;We use the lunar radial gravity acceleration obtained by the GRAIL mission [4] up to spherical harmonic degree 400 as input data in the algorithm. The gravity acceleration data of the resulting models match the input gravity very well, only missing the gravity signature of smaller craters. A group of models show a deep positive density anomaly in the general area of the Clavius basin. The anomaly is centered at approximately 50&amp;#176;S and 10&amp;#176;E, at about 800 km depth. Density anomalies in this group of models remain relatively small and could be explained by mineralogical differences in the mantle. Major variations in crustal structure, such as the near side / far side dichotomy and the South Pole Aitken basin are also apparent, giving geological credence to these models. A different group of models points towards two high density regions with a much higher mass than the one described by the other group of models. It may be regarded as an unrealistic model. Our method embraces the non-uniqueness of gravity inversions and does not impose a single view of the interior although geological knowledge and geodynamic analyses are of course important to evaluate the realism of each solution.&lt;/p&gt;&lt;p&gt;References: [1] Wieczorek, M. A. (2006), Treatise on Geophysics 153-193. doi: 10.1016/B978-0-444-53802-4.00169-X. [2] Izquierdo, K et al. (2019) Geophys. J. Int. 220, 1687-1699, doi: 10.1093/gji/ggz544, [3]&amp;#160; Izquierdo, K. et al., (2019) LPSC 50, abstr. 2157. [4] Lemoine, F. G., et al. ( 2013), J. Geophys. Res. 118, 1676&amp;#8211;1698 doi: 10.1002/jgre.20118.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

Some statistical and CI models to predict chaotic high-frequency financial data

2020 ◽  
Vol 39 (5) ◽  
pp. 6419-6430
Author(s):  
Dusan Marcek
Keyword(s):  
Time Series Data ◽  
Moving Average ◽  
Methodological Approach ◽  
Back Propagation ◽  
Large Data ◽  
Series Data ◽  
Data Set ◽  
Training Time ◽  
Optimal Population ◽  
Forecast Time

To forecast time series data, two methodological frameworks of statistical and computational intelligence modelling are considered. The statistical methodological approach is based on the theory of invertible ARIMA (Auto-Regressive Integrated Moving Average) models with Maximum Likelihood (ML) estimating method. As a competitive tool to statistical forecasting models, we use the popular classic neural network (NN) of perceptron type. To train NN, the Back-Propagation (BP) algorithm and heuristics like genetic and micro-genetic algorithm (GA and MGA) are implemented on the large data set. A comparative analysis of selected learning methods is performed and evaluated. From performed experiments we find that the optimal population size will likely be 20 with the lowest training time from all NN trained by the evolutionary algorithms, while the prediction accuracy level is lesser, but still acceptable by managers.

In silico Prediction of Inhibitory Constant of Thrombin Inhibitors Using Machine Learning

2019 ◽  
Vol 21 (9) ◽  
pp. 662-669 ◽  
Author(s):  
Junnan Zhao ◽  
Lu Zhu ◽  
Weineng Zhou ◽  
Lingfeng Yin ◽  
Yuchen Wang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Prediction Models ◽  
Regression Tree ◽  
Large Data ◽  
Thrombin Inhibitors ◽  
Coagulation Cascade ◽  
Gradient Boosting ◽  
Support Vector ◽  
Data Set ◽  
Descriptor Selection

Background: Thrombin is the central protease of the vertebrate blood coagulation cascade, which is closely related to cardiovascular diseases. The inhibitory constant Ki is the most significant property of thrombin inhibitors. Method: This study was carried out to predict Ki values of thrombin inhibitors based on a large data set by using machine learning methods. Taking advantage of finding non-intuitive regularities on high-dimensional datasets, machine learning can be used to build effective predictive models. A total of 6554 descriptors for each compound were collected and an efficient descriptor selection method was chosen to find the appropriate descriptors. Four different methods including multiple linear regression (MLR), K Nearest Neighbors (KNN), Gradient Boosting Regression Tree (GBRT) and Support Vector Machine (SVM) were implemented to build prediction models with these selected descriptors. Results: The SVM model was the best one among these methods with R2=0.84, MSE=0.55 for the training set and R2=0.83, MSE=0.56 for the test set. Several validation methods such as yrandomization test and applicability domain evaluation, were adopted to assess the robustness and generalization ability of the model. The final model shows excellent stability and predictive ability and can be employed for rapid estimation of the inhibitory constant, which is full of help for designing novel thrombin inhibitors.

scholarly journals Correlation between the structure and skin permeability of compounds

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ruolan Zeng ◽  
Jiyong Deng ◽  
Limin Dang ◽  
Xinliang Yu
Keyword(s):  
Large Data ◽  
Qsar Model ◽  
Coefficient Of Determination ◽  
Support Vector ◽  
Skin Permeability ◽  
Data Set ◽  
Test Set ◽  
Svm Algorithm ◽  
Svm Model ◽  
Toxicity Relationship

AbstractA three-descriptor quantitative structure–activity/toxicity relationship (QSAR/QSTR) model was developed for the skin permeability of a sufficiently large data set consisting of 274 compounds, by applying support vector machine (SVM) together with genetic algorithm. The optimal SVM model possesses the coefficient of determination R2 of 0.946 and root mean square (rms) error of 0.253 for the training set of 139 compounds; and a R2 of 0.872 and rms of 0.302 for the test set of 135 compounds. Compared with other models reported in the literature, our SVM model shows better statistical performance in a model that deals with more samples in the test set. Therefore, applying a SVM algorithm to develop a nonlinear QSAR model for skin permeability was achieved.

scholarly journals Galaxy spin direction distribution in HST and SDSS show similar large-scale asymmetry

2020 ◽  
Vol 37 ◽  
Author(s):  
Lior Shamir
Keyword(s):  
Large Scale ◽  
Spiral Galaxies ◽  
Hubble Space Telescope ◽  
Gravitational Interaction ◽  
Large Data ◽  
Sloan Digital Sky Survey ◽  
Data Sets ◽  
Dipole Axis ◽  
Data Set ◽  
The Asymmetry

Abstract Several recent observations using large data sets of galaxies showed non-random distribution of the spin directions of spiral galaxies, even when the galaxies are too far from each other to have gravitational interaction. Here, a data set of $\sim8.7\cdot10^3$ spiral galaxies imaged by Hubble Space Telescope (HST) is used to test and profile a possible asymmetry between galaxy spin directions. The asymmetry between galaxies with opposite spin directions is compared to the asymmetry of galaxies from the Sloan Digital Sky Survey. The two data sets contain different galaxies at different redshift ranges, and each data set was annotated using a different annotation method. The results show that both data sets show a similar asymmetry in the COSMOS field, which is covered by both telescopes. Fitting the asymmetry of the galaxies to cosine dependence shows a dipole axis with probabilities of $\sim2.8\sigma$ and $\sim7.38\sigma$ in HST and SDSS, respectively. The most likely dipole axis identified in the HST galaxies is at $(\alpha=78^{\rm o},\delta=47^{\rm o})$ and is well within the $1\sigma$ error range compared to the location of the most likely dipole axis in the SDSS galaxies with $z>0.15$ , identified at $(\alpha=71^{\rm o},\delta=61^{\rm o})$ .

scholarly journals The Complete DNA Sequence of the Mitochondrial Genome of a “Living Fossil,” the Coelacanth (Latimeria chalumnae)

Genetics ◽  
1997 ◽  
Vol 146 (3) ◽  
pp. 995-1010 ◽  
Author(s):  
Rafael Zardoya ◽  
Axel Meyer
Keyword(s):  
Mitochondrial Genome ◽  
Tandem Repeats ◽  
Phylogenetic Analyses ◽  
Large Data ◽  
Molecular Data ◽  
Phylogenetic Position ◽  
Data Set ◽  
Living Fossil ◽  
Latimeria Chalumnae ◽  
Relationship Of

The complete nucleotide sequence of the 16,407-bp mitochondrial genome of the coelacanth (Latimeria chalumnae) was determined. The coelacanth mitochondrial genome order is identical to the consensus vertebrate gene order which is also found in all ray-finned fishes, the lungfish, and most tetrapods. Base composition and codon usage also conform to typical vertebrate patterns. The entire mitochondrial genome was PCR-amplified with 24 sets of primers that are expected to amplify homologous regions in other related vertebrate species. Analyses of the control region of the coelacanth mitochondrial genome revealed the existence of four 22-bp tandem repeats close to its 3′ end. The phylogenetic analyses of a large data set combining genes coding for rRNAs, tRNA, and proteins (16,140 characters) confirmed the phylogenetic position of the coelacanth as a lobe-finned fish; it is more closely related to tetrapods than to ray-finned fishes. However, different phylogenetic methods applied to this largest available molecular data set were unable to resolve unambiguously the relationship of the coelacanth to the two other groups of extant lobe-finned fishes, the lungfishes and the tetrapods. Maximum parsimony favored a lungfish/coelacanth or a lungfish/tetrapod sistergroup relationship depending on which transversion:transition weighting is assumed. Neighbor-joining and maximum likelihood supported a lungfish/tetrapod sistergroup relationship.

Climatology of nutrient distributions in the South China Sea based on a large data set derived from a new algorithm

2021 ◽  
pp. 102586
Author(s):  
Chuanjun Du ◽  
Ruoying He ◽  
Zhiyu Liu ◽  
Tao Huang ◽  
Lifang Wang ◽  
...  
Keyword(s):  
South China Sea ◽  
South China ◽  
Large Data ◽  
The South China Sea ◽  
The South ◽  
Data Set ◽  
China Sea ◽  
Large Data Set

scholarly journals Spike detection: Inter-reader agreement and a statistical Turing test on a large data set

2017 ◽  
Vol 128 (1) ◽  
pp. 243-250 ◽  
Author(s):  
Mark L. Scheuer ◽  
Anto Bagic ◽  
Scott B. Wilson
Keyword(s):  
Large Data ◽  
Turing Test ◽  
Spike Detection ◽  
Data Set ◽  
Large Data Set
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