Three-dimensional modelling of gravity data using finite differences

Farquharson, Colin G.; Mosher, Craig R. W.

doi:10.1016/j.jappgeo.2009.03.007

Cited by 52 publications

(24 citation statements)

References 22 publications

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“…The minimum-structure borehole inversion procedure investigated here implements a forward-modelling procedure that evaluates the finite-difference solution to Poisson 's equation (Farquharson and Mosher, 2009) seen in equation (18) and is discussed in greater detail in Chapter 2.…”

Section: Forward Modelingmentioning

confidence: 99%

“…The success of the forward modelling for 2-D and 3-D magnetotelluric inversions presented by Mackie and Madden (1993) and Rodi and Mackie (2001 ) provided the inspiration to create a similar method to forward model gravity data (Farquharson and Mosher , 2009). This method uses a conjugate-gradient procedure that implicitly performs matrix-vector products of the J acobian.…”

Section: Computationmentioning

confidence: 99%

“…The forward modeller program described above was created by Farquharson (Farquharson and Mosher, 2009). Testing of the code was performed by Mosher and is presented in Section 2.4.…”

Section: Computationmentioning

confidence: 99%

“…The steps taken in this method are analogous to the process described by Farquharson and Mosher (2009).…”

Section: Theorymentioning

confidence: 99%

“…To usc t he finite-difference approximation to Poisson's equation to create synthetic gravity dat a for a specific model, the matrices in equation (38) (Farquharson and Mosher, 2009) .…”

Section: Forward Modellingmentioning

confidence: 99%

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Minimum‐structure borehole gravity inversion

Mosher

Farquharson

Hurich

2008

SEG Technical Program Expanded Abstracts 2008

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Section: Forward Modelingmentioning

confidence: 99%

Section: Computationmentioning

confidence: 99%

“…The forward modeller program described above was created by Farquharson (Farquharson and Mosher, 2009). Testing of the code was performed by Mosher and is presented in Section 2.4.…”

Section: Computationmentioning

confidence: 99%

“…The steps taken in this method are analogous to the process described by Farquharson and Mosher (2009).…”

Section: Theorymentioning

confidence: 99%

“…To usc t he finite-difference approximation to Poisson's equation to create synthetic gravity dat a for a specific model, the matrices in equation (38) (Farquharson and Mosher, 2009) .…”

Section: Forward Modellingmentioning

confidence: 99%

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Minimum‐structure borehole gravity inversion

Mosher

Farquharson

Hurich

2008

SEG Technical Program Expanded Abstracts 2008

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Fast 3‐D large‐scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method

et al. 2017

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A novel fast and accurate algorithm is developed for large‐scale 3‐D gravity and magnetic modeling problems. An unstructured grid discretization is used to approximate sources with arbitrary mass and magnetization distributions. A novel adaptive multilevel fast multipole (AMFM) method is developed to reduce the modeling time. An observation octree is constructed on a set of arbitrarily distributed observation sites, while a source octree is constructed on a source tetrahedral grid. A novel characteristic is the independence between the observation octree and the source octree, which simplifies the implementation of different survey configurations such as airborne and ground surveys. Two synthetic models, a cubic model and a half‐space model with mountain‐valley topography, are tested. As compared to analytical solutions of gravity and magnetic signals, excellent agreements of the solutions verify the accuracy of our AMFM algorithm. Finally, our AMFM method is used to calculate the terrain effect on an airborne gravity data set for a realistic topography model represented by a triangular surface retrieved from a digital elevation model. Using 16 threads, more than 5800 billion interactions between 1,002,001 observation points and 5,839,830 tetrahedral elements are computed in 453.6 s. A traditional first‐order Gaussian quadrature approach requires 3.77 days. Hence, our new AMFM algorithm not only can quickly compute the gravity and magnetic signals for complicated problems but also can substantially accelerate the solution of 3‐D inversion problems.

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Development of an infinite element boundary to model gravity for subsurface civil engineering applications

Haji

Faramarzi

Metje

et al. 2019

Num Anal Meth Geomechanics

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The accurate modelling of gravity is of crucial importance for a variety of issues including, but not restricted to, the identification of buried objects. Gravity is an unbounded problem, which causes challenges when applying numerical models, i..e.., it results in computational difficulties when specifying the relevant boundary conditions. In order to address this, previous research has tended to generate artificial boundary conditions, e.g., truncating the simulated domain and adding many unrealistic zero-density layers, which introduces more unknown parameters and unnecessarily excessive computational time. In order to overcome such inaccuracies, this paper proposes an innovative development of the finite element modelling technique, which represents a step change in the field of gravity forward modelling. A comprehensive formulation of an infinite element to reproduce the far-field boundary effect using only one layer of infinite elements is presented. The developed model considerably reduces the computational time while obtaining high degrees of accuracy. The model is validated against the exact solution of the problem, and its results show an excellent performance. The proposed method can significantly improve the postprocessing and interpretation stages of data analysis relevant to micro-gravity sensors. The new method is applied to subsurface civil engineering although its applicability is manifold.

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Three-dimensional modelling of gravity data using finite differences

Cited by 52 publications

References 22 publications

Minimum‐structure borehole gravity inversion

Minimum‐structure borehole gravity inversion

Fast 3‐D large‐scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method

Development of an infinite element boundary to model gravity for subsurface civil engineering applications

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