The Role of Model Weighting Functions in the Gravity and DC Resistivity Inversion

Varfinezhad, Ramin; Fedi, Maurizio; Milano, Maurizio

doi:10.1109/tgrs.2022.3149139

Cited by 15 publications

(3 citation statements)

References 30 publications

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“…Menke, 2012):

\begin{equation}{\bf{m}}\; = {{\bf{m}}_{\rm{r}}}{\rm{\;}} + \left( {{\bf{W}}_{\rm{m}}^{ - 1}{{\bf{A}}^{\rm{T}}}} \right){\left( {{\bf{AW}}_{\rm{m}}^{ - 1}{{\bf{A}}^{\rm{T}}} + \alpha {{\bf{W}}_{\rm{d}}}} \right)^{ - 1}}\left( {{\bf{d}} - {\bf{A}}{{\bf{m}}_{\rm{r}}}} \right),\end{equation}

where W m is a model‐weighting matrix produced by the multiplication of compactness and depth‐weighting functions and

{{\bf{W}}_{\rm{d}}} = \;I

. This algorithm has been successfully manipulated for the inversion of DC resistivity (Varfinezhad et al., 2022), gravity (Varfinezhad & Ardestani, 2021), magnetic (Milano et al., 2021; Varfinezhad et al., 2020), and EM‐LIN (Parnow et al., 2021; Varfinezhad & Parnow, 2022) data.…”

Section: Methodsmentioning

confidence: 99%

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

Ghari

Varfinezhad

Parnow

2023

Near Surface Geophysics

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As geophysical parameters are not always functionally related, treating multiple geophysical data sets to have a realistic geological model is not straightforward. An effective strategy to derive a geological interpretation is a combination of several geophysical methods with geological and well observations, each with its advantages and limitations. Gravity and magnetic methods are encouraging tools to investigate salt domes due to enough density and susceptibility contrasts between salt minerals and the background sedimentary rocks. In this paper, the dome-shaped salt unit in the Qarah-Aghaje area in Zanjan, located in the northwestern part of Iran, is investigated through the integration of 3D inversion models obtained from gravity and magnetic data and geological and well information. The 3D inversion of both data sets is made using a weighted damped minimum length solution for which model weighting is constructed from multiplying depth weighting and compactness constraints. At first, a synthetic case with a high degree of similarity to the real case is considered to evaluate the efficiency of the adopted inverse algorithm. Then, the inversion algorithm is implemented on the collected gravity and magnetic methods, and interpretation is made utilizing 3D obtained inverse models and geologic and well data. The result shows a dome-shaped potash-bearing salt unit that starts from a depth of 12 m and continues to the depth of 200 m. The drilled well in the centre of the main source of the salt (Well 3) demonstrates a depth range of 11-115 m.

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“…Menke, 2012):

\begin{equation}{\bf{m}}\; = {{\bf{m}}_{\rm{r}}}{\rm{\;}} + \left( {{\bf{W}}_{\rm{m}}^{ - 1}{{\bf{A}}^{\rm{T}}}} \right){\left( {{\bf{AW}}_{\rm{m}}^{ - 1}{{\bf{A}}^{\rm{T}}} + \alpha {{\bf{W}}_{\rm{d}}}} \right)^{ - 1}}\left( {{\bf{d}} - {\bf{A}}{{\bf{m}}_{\rm{r}}}} \right),\end{equation}

where W m is a model‐weighting matrix produced by the multiplication of compactness and depth‐weighting functions and

{{\bf{W}}_{\rm{d}}} = \;I

Section: Methodsmentioning

confidence: 99%

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

Ghari

Varfinezhad

Parnow

2023

Near Surface Geophysics

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“…In this sense, note that previous formulation [34,35] becomes a particular case of this more general relationship, since β =N=3 holds only for homogeneous, spherical-like, source distributions. The good behaviour of this approach in compact inversions has been discussed and the role of an appropriate model weighting function has been proved to be even more important in joint inversions [47,48].…”

Section: B Separate Inversionsmentioning

confidence: 99%

Multiorder Sequential Joint Inversion of Gravity Data With Inhomogeneous Depth Weighting: From Near Surface to Basin Modeling Applications

Bianco,

Tavakoli,

Vitale

et al. 2024

IEEE Trans. Geosci. Remote Sensing

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We have established a workflow for a multi-order sequential joint inversion (MOSJI) of gravity and gravity gradients, that aims at modelling of vertically-stacked sources in various geological scenarios. We consider the joint inversion of the gravity data and one of the h th order derivative of the gravity data. The first step involves separate inversions, which are fundamental to fully exploit the different wavelength-content of the two quantities to invert. The joint inversion is warranted by using the scheme of a sequential joint inversion with a cross-gradient constraint. The algorithm is able to exploit different types of a priori information, such as compactness and inhomogeneous model-weighting function. Firstly, we test this approach on a realistic synthetic model from the SEg Advanced Modelling (SEAM) Phase I model, involving salt and mother salt structures. Then, we consider a synthetic model containing either shallower or deeper karst cavities. These tests produced a better modelling of both shallower and deeper sources, when compared to the separate unconstrained inversions. Thanks to these good results, we apply our method to a real case for cavity detection in Southern Spain. The method shows an accurate modelling of the expected sources. In all the aforementioned tests, we obtain a strong decrease of the cross-gradient values and a meaningful linearization in the scatter plots of physical parameters, both indicating the good performance of the joint inversion.

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“…The compactness stabilizer (Last & Kubik, 1983) also known as the minimum support stabilizer (Port-niaguine & Zhdanov, 1999) has been borrowed and implemented by other researchers in various geophysical inversion methods (Ajo-Franklin et al, 2007;Stocco et al, 2009;Fei et al, 2018;Feng et al, 2020;Varfinezhad et al, 2020). As it was demonstrated by a number of researchers (Zhdanov & Tolstaya, 2004;Feng et al, 2020;Varfinezhad et al, 2022), this stabilizer is known to yield a compact or focused geophysical model with sharp boundaries. Apart from the inversion methods which produce focused images mentioned above, sparse geophysical inversion approaches derived from L p -norm (0 ≤ p ≤ 1) stabilization have been developed by many researchers.…”

Section: Introductionmentioning

confidence: 99%

Gravity Inversion Method to Produce Compact and Sharp Images Using L₀-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria

Gebre

Lewi

2022

Preprint

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Abstract. We present a gravity inversion method that can produce compact and sharp images, to assist the modeling of non-smooth geologic features. The proposed iterative inversion approach makes use of L0-norm stabilizing functional, hard, and physical parameter inequality constraints, and depth weighting function. The method incorporates an auto-adaptive regularization technique, which automatically determines a suitable regularization parameter and error weighting function that helps to improve both the stability and convergence of the method. The auto-adaptive regularization and error weighting matrix are not dependent on the known noise level. Because of that, the method yields reasonable results even the noise level of the data is not known properly. The utilization of an effectively combined stopping rule to terminate the inversion process is another improvement that is introduced in this work. The capacity and the efficiency of the new inversion method were tested by inverting randomly chosen synthetic and measured data. The synthetic test models consist of multiple causative blocky bodies, with different geometries and density distributions that are vertically and horizontally distributed adjacent to each other. Inversion results of the synthetic data show that the developed method can recover models that adequately match the real geometry, location, and densities of the synthetic causative bodies. Furthermore, the testing of the improved approach using published real gravity data confirmed the potential, and practicality of the method in producing compact and sharp inverse images of the subsurface.

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The Role of Model Weighting Functions in the Gravity and DC Resistivity Inversion

Cited by 15 publications

References 30 publications

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

Multiorder Sequential Joint Inversion of Gravity Data With Inhomogeneous Depth Weighting: From Near Surface to Basin Modeling Applications

Gravity Inversion Method to Produce Compact and Sharp Images Using L₀-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria

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The Role of Model Weighting Functions in the Gravity and DC Resistivity Inversion

Cited by 15 publications

References 30 publications

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

Multiorder Sequential Joint Inversion of Gravity Data With Inhomogeneous Depth Weighting: From Near Surface to Basin Modeling Applications

Gravity Inversion Method to Produce Compact and Sharp Images Using L0-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria

Contact Info

Product

Resources

About

Gravity Inversion Method to Produce Compact and Sharp Images Using L₀-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria