On: “A least‐squares approach to depth determination from gravity data” by O.P. Gupta (GEOPHYSICS, 48, 357–360, March 1983)

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 376-377 ◽  
Author(s):  
El‐Sayed M. Abdelrahman
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Residual Gravity ◽  
Depth Determination ◽  
Residual Gravity Anomaly ◽  
Least Squares Approach

In the article by Gupta, the problem of depth determination of a buried structure from the residual gravity anomaly has been transformed into a problem of finding the solution of a nonlinear equation of the form f(z) = 0. Gupta begins his formulation of the problem with equation (1) from Mettleton (1942) Eq. (1) [Formula: see text]

A least‐squares approach to depth determination from gravity data

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 357-360 ◽  
Author(s):  
O. P. Gupta
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Data ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Random Errors ◽  
Depth Determination ◽  
Vertical Fault ◽  
Horizontal Cylinders ◽  
Least Squares Approach

The present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly. The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form [Formula: see text]. Formulas have been derived for a sphere, vertical and horizontal cylinders, and for a vertical fault (thin plate approximation). The procedure is applied to synthetic data with and without random errors. Finally, a field example is presented in which the depth to a fault is estimated at 3.8 km and verified from drilling results.

A least‐squares minimization approach to shape determination from gravity data

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 589-590 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Sharafeldin M. Sharafeldin
Keyword(s):  
Least Squares ◽  
Gravity Anomaly ◽  
Shape Factor ◽  
Gravity Data ◽  
Correlation Factor ◽  
Walsh Transform ◽  
Residual Gravity ◽  
Residual Gravity Anomaly ◽  
Minimization Approach ◽  
Least Squares Minimization

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape (shape‐factor) and depth‐related variables with an amplitude coefficient related to mass (Abdelrahman and El‐Araby, 1993). Few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles. These methods include a Walsh transform approach (Shaw and Agarwal, 1990) and the employment of a correlation factor between successive least‐squares residuals (Abdelrahman and El‐Araby 1993). In the present note, a least‐squares minimization approach to shape‐factor determination from a residual gravity anomaly profile is presented. The problem of the shape‐factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0.

On: “A least‐squares approach to depth determination from gravity data” by G. P. Gupta,(GEOPHYSICS, 48, 357‐360, March 1983).

Geophysics ◽  
1985 ◽  
Vol 50 (2) ◽  
pp. 262-262 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Abdel‐Rhim I. Bayoumi ◽  
Yehia A. Amin
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Data ◽  
Depth Estimation ◽  
Numerical Approach ◽  
Point Of View ◽  
Theory And Practice ◽  
Buried Structures ◽  
Depth Determination ◽  
Least Squares Approach

In his paper, Gupta was able to transform the problem of depth estimation of buried structures into a problem of finding a solution of a nonlinear equation in the form of [Formula: see text]. Gupta also indicated that such a numerical approach is found to be capable of determining optimum depths particularly from residual anomaly profiles even if small segments of the gravity profiles are observed. No doubt this numerical approach has its point of view both in theory and practice over any other depth estimation techniques such as those defined by the [Formula: see text] rule (Nettleton, 1940, 1942; Telford et al., 1976). However, Gupta’s technique would be much more effective if applied not to residuals but to derivative anomalies, particularly when the regional field has few extrema in it; this is obviously due to the following.

scholarly journals Integrated Subsurface Analysis of Thickness and Density for Liquefaction Hazard: Case Study of South Cilacap Region, Indonesia.

2021 ◽  
Vol 6 (1) ◽  
pp. 58-66
Author(s):  
Maulana Rizki Aditama ◽  
Huzaely Latief Sunan ◽  
FX Anjar Tri Laksono ◽  
Gumilar Ramadhan ◽  
Sachrul Iswahyudi ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Near Surface ◽  
Residual Gravity ◽  
Liquefaction Hazard ◽  
Residual Gravity Anomaly ◽  
Resistivity Model ◽  
2D Resistivity

The thickness of the liquefable layer can be the factor inducing liquefaction hazard, apart from seismicity. Several studies have been conducted to predict the possibility of the liquefable layer based on the filed sampling. However, a detailed investigation of the subsurface interpretation has not been defined, in particular the thickness estimation of the liquefable layer. This study is carried out in south Cilacap area where potential liquefaction is exists due to the earthquake history data and near surface condition. The aim of this study is to investigate the physical properties and thickness distribution using GGMplus gravity data and resistivity data. This research is conducted by spectrum analysis of gravity model and 2D resistivity model . This study’s main results is by performing the residual gravity anomaly with the associated SRTM/DEM data to define the subsurface physical distribution and structural orientation of the area. Residual gravity anomaly is also separated through the low pass filter in order to have robust interpretation. The residual anomaly indicates that the area has identical structural pattern with geological and SRTM map. The results show a pattern of high gravity index in the northeast area of ​​the study having range of 70 – 115 MGal gravity index, associated with the volcanic breccia, and a low gravity profile with less than 65 in the southwest, associated with the alluvial and water table dominated distribution. The thickness of Alluvial is determined by resistivity model with H1 at a range of 3 meters and H2 at a range of 4 m. This research is included in the potential liquefaction category with the potential for a large earthquake.

scholarly journals RESIDUAL GRAVITY ANOMALY OF BRAZILIAN MARAJÓ BASIN USING CRUSTAL MODELING: IDENTIFYING STRUCTURAL AND TECTONIC FEATURES

2019 ◽  
Vol 37 (2) ◽  
Author(s):  
Gilberto Carneiro dos Santos Junior ◽  
Cristiano Mendel Martins ◽  
Nelson Ribeiro-Filho
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Sedimentary Basins ◽  
Data Interpretation ◽  
Earth’S Crust ◽  
Residual Gravity ◽  
North Brazil ◽  
Residual Gravity Anomaly ◽  
Earth's Crust ◽  
Tectonic Features

ABSTRACT. Dealing with gravity data at complex geological environments is a hard task because regional and residual anomalies are unknown. Due to the fact former techniques do not apply geologic information for separating gravity data, interpretation could lead to common mistakes. In order to allow a better interpretation at sedimentary basins, we applied a different approach for separating regional and residual anomalies for gravity data: the crustal modeling procedure. This approach consists on discretizing the Earth’s crust in prismatic cells and calculating the predicted signal due to Earth’s crust. We set horizontal dimensions of each prism, while the top and bottom are defined by Earth’s topography and depth of crust-mantle boundary, usually called Moho. Additionally, when the predicted signal is calculated, the residual anomaly is obtained from simple subtraction. We applied our methodology at Marajó basin (North, Brazil), where previous geological studies identified a system of faults and grabens, also known as Marajó graben system. Moreover, our results are well compared with previous interpretation through the seismic method, exemplifying the approach’s quality and efficiency. We believe, therefore, that the crustal modeling approach should be considered for studying any Brazilian sedimentary basin and other interesting areas.Keywords: crustal modeling; residual gravity anomaly; Marajó basin; Marajó graben system. RESUMO. Interpretar dados gravimétricos em ambientes geológicos de grande complexidade é uma tarefa difícil de ser realizada, visto que anomalias regionais e residuais são desconhecidas. Devido ao fato de que conhecidas técnicas de separação regional-residual não consideram informações geológicas, a interpretação final pode fornecer resultados equivocados. A fim de permitir uma melhor interpretação nas bacias sedimentares, aplicamos uma diferente abordagem para separação regional-residual: a modelagem crustal. Esta abordagem consiste em discretizar a crosta terrestre em células prismáticas e calcular o sinal regional predito. Definimos as dimensões horizontais de cada prisma, enquanto o topo e a base são definidos pela topografia e profundidade da interface crosta-manto, respectivamente. Após o cálculo do sinal predito, a anomalia residual é calculada via subtração. Aplicamos nossa metodologia na bacia do Marajó (região Norte, Brasil), onde estudos geológicos identificaram um sistema de falhas e grábens, definido por sistema de gráben do Marajó. Nossos resultados apresentam boa correspondência quando comparados com interpretações realizadas via método sísmico, o que exemplifica a qualidade e eficiência da nossa proposta. Acreditamos, portanto, que esta abordagem de modelagem crustal deve ser considerada para o estudo de qualquer bacia sedimentar brasileira e de outras regiões de interesse.Palavras-chave: modelagem crustal; anomalia gravimétrica residual; bacia do Marajó; sistema de gráben do Marajó.  

Multivariable Modified Teaching Learning Based Optimization (MM-TLBO) Algorithm for Inverse Modeling of Residual Gravity Anomaly Generated by Simple Geometric Shapes

2020 ◽  
Vol 25 (4) ◽  
pp. 463-476
Author(s):  
Ata Eshaghzadeh ◽  
Alireza Hajian
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Optimal Solution ◽  
Model Parameters ◽  
Major Purpose ◽  
Residual Gravity ◽  
Tlbo Algorithm ◽  
Residual Gravity Anomaly ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning

This paper presents an improved nature-based algorithm, namely multivariable modified teaching learning based optimization (MM-TLBO) algorithm, as in an iterative process can estimates the best values for the model parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MM-TLBO algorithm is to improve the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the radius ( R), depth ( h), shape factor ( q), density contrast ( ρ) and axis location ( x0) parameters. We apply MM-TLBO and TLBO methods for the residual gravity anomalies caused by the buried masses with a simple geometry such as spheres, horizontal and vertical cylinders. The efficiency of these methods are also tested by noise corruption synthetic data, as the acceptable results were obtained. The obtained results indicate the better performance the MM-TLBO algorithm than the TLBO algorithm. We have utilized the MM-TLBO for the interpretation of the six residual gravity anomaly profiles from Iran, USA, Sweden and Senegal. The advantage of the MM-TLBO inversion is that it can estimates the best solutions very fast without falling into local minimum and reaches to a premature convergence. The considered primary population for the synthetic and real gravity data are thirty and fifty models. The results show which this method is able to achieve the optimal responses even if a small population of learners had been considered.

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