Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation

The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia.

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Gravity Data Inversion with Method of Local Corrections for Finite Elements Models

Geosciences ◽

10.3390/geosciences8100373 ◽

2018 ◽

Vol 8 (10) ◽

pp. 373 ◽

Cited By ~ 2

Author(s):

Petr Martyshko ◽

Igor Ladovskii ◽

Denis Byzov ◽

Alexander Tsidaev

Keyword(s):

Finite Element ◽

Finite Elements ◽

Gravity Field ◽

Gravity Data ◽

Gradient Methods ◽

Iteration Algorithm ◽

Constant Density ◽

Field Calculation ◽

Data Set ◽

Data Inversion

We present a new method for gravity data inversion for the linear problem (reconstruction of density distribution by given gravity field). This is an iteration algorithm based on the ideas of local minimization (also known as local corrections method). Unlike the gradient methods, it does not require a nonlinear minimization, is easier to implement and has better stability. The algorithm is based on the finite element method. The finite element approach in our study means that the medium (part of a lithosphere) is represented as a set of equal rectangular prisms, each with constant density. We also suggest a time-efficient optimization, which speeds up the inversion process. This optimization is applied on the gravity field calculation stage, which is a part of every inversion iteration. Its idea is to replace multiple calculations of the gravity field for all finite elements in all observation points with a pre-calculated set of uniform fields for all distances between finite element and observation point, which is possible for the current data set. Method is demonstrated on synthetic data and real-world cases. The case study area is located on the Timan-Pechora plate. This region is one of the promising oil- and gas-producing areas in Russia. Note that in this case we create a 3D density model using joint interpretation of seismic and gravity data.

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The stability criterion for downward continuation of surface gravity data with various spatial resolutions over Ireland

Studia Geophysica et Geodaetica ◽

10.1007/s11200-020-0769-7 ◽

2021 ◽

Author(s):

Sajjad Sajjadi ◽

Zdeněk Martinec ◽

Patrick Prendergast ◽

Jan Hagedoorn ◽

Libor Šachl

Keyword(s):

Stability Criterion ◽

Gravity Data ◽

Downward Continuation ◽

Surface Gravity ◽

The Stability ◽

Surface Gravity Data

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Gravity data inversion based genetic algorithm and generalized least squares

2009 IEEE International Conference on Intelligent Computing and Intelligent Systems ◽

10.1109/icicisys.2009.5358049 ◽

2009 ◽

Author(s):

Ning Qiu ◽

Qingsheng Liu ◽

Quanye Gao

Keyword(s):

Genetic Algorithm ◽

Least Squares ◽

Gravity Data ◽

Generalized Least Squares ◽

Data Inversion

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Disjoint interval bound constraints using the alternating direction method of multipliers (ADMM) for geologically constrained inversion: Application to gravity data

Geophysics ◽

10.1190/geo2019-0633.1 ◽

2020 ◽

pp. 1-45

Author(s):

Vitaliy Ogarko ◽

Jérémie Giraud ◽

Roland Martin ◽

Mark Jessell

Keyword(s):

Gravity Data ◽

Alternating Direction Method ◽

Rock Properties ◽

Model Parameters ◽

Method Of Multipliers ◽

Geological Modeling ◽

Bound Constraints ◽

Data Inversion ◽

Alternating Direction ◽

Geological Information

To reduce uncertainties in reconstructed images, geological information must be introduced in a numerically robust and stable way during the geophysical data inversion procedure. In the context of potential (gravity) data inversion, it is important to bound the physical properties by providing probabilistic information on the number of lithologies and ranges of values of possibly existing related rock properties (densities). For this purpose, we introduce a generalization of bounding constraints for geophysical inversion based on the alternating direction method of multipliers (ADMM). The flexibility of the proposed technique enables us to take into account petrophysical information as well as probabilistic geological modeling, when it is available. The algorithm introduces a priori knowledge in terms of physically acceptable bounds of model parameters based on the nature of the modeled lithofacies in the region under study. Instead of introducing only one interval of geologically acceptable values for each parameter representing a set of rock properties, we define sets of disjoint intervals using the available geological information. Different sets of intervals are tested, such as quasi-discrete (or narrow) intervals as well as wider intervals provided by geological information obtained from probabilistic geological modeling. Narrower intervals can be used as soft constraints encouraging quasi-discrete inversions. The algorithm is first applied to a synthetic 2D case for proof-of-concept validation and then to the 3D inversion of gravity data collected in the Yerrida basin (Western Australia). Numerical convergence tests show the robustness and stability of the bound constraints we apply, which is not always trivial for constrained inversions. This technique can be a more reliable uncertainty reduction method as well as an alternative to other petrophysically or geologically constrained inversions based on more classical “clustering” or Gaussian-mixture approaches.

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