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Ruan, J. (author), Masfara, L.O.M. (author), Ghose, R. (author), Mulder, W.A. (author)Geomechanical modelling is generally used to simulate the nucleation of induce d earthquakes in, for instance the Groningen gas field. We apply quasi static simulation to investigate the stress changes from gas production. When a fault reaches a critical state, dynamic simulation provides information on the dynamic rupture during ea rthqu ake...poster 2022
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 Cupillard, Paul (author), Mulder, W.A. (author) abstract 2022
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 Ruan, J. (author), Masfara, L.O.M. (author), Ghose, R. (author), Mulder, W.A. (author) abstract 2022
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Ruan, J. (author), Masfara, La ODE Marzujriban (author), Ghose, R. (author), Mulder, W.A. (author)Dynamic geomechanical modeling can generate the seismic wavefield caused by a fault rupture. In dynamic faultrupture modeling, the source is considered to be finite, with a limited extent both in space and in time. This contrasts with the definition of a point source, which is generally assumed to explain the seismic wavefield caused by an...book chapter 2022
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Mulder, W.A. (author)When solving the wave equation with finite elements, mass lumping allows for explicit time stepping, avoiding the cost of a lowerupper decomposition of the large sparse mass matrix. Mass lumping on the reference element amounts to numerical quadrature. The weights should be positive for stable time stepping and preserve numerical accuracy....journal article 2022
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Mulder, W.A. (author)Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In 2D on quadrilaterals, spectral elements are the obvious choice. Triangles are more flexible for meshing, but the construction of polynomial elements is less...conference paper 2022
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Cupillard, Paul (author), Mulder, W.A. (author), Anquez, Pierre (author), Mazuyer, Antoine (author), Barthélémy, J. (author)The Earth interior contains heterogeneities at all scales, ranging from pores and mineral grains to major global units. On the contrary, seismic recordings only contain variations larger than the minimum wavelength λmin. The heterogeneities smaller than λmin are naturally smoothed by the wavefield, leading to effective media when inverting...conference paper 2021
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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)Induced seismicity from a gasproducing region such as Groningen is believed to be caused by reservoir depletion due to longterm gas production. However, because of the complexity and uncertainty regarding the underground structure and composition, it is difficult to quantify the effect on induced seismicity due to gas production. Here we use...poster 2021
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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)Induced seismicity from a gasproducing region such as Groningen is believed to be caused by reservoir depletion due to longterm gas production. However, because of the complexity and uncertainty regarding the underground structure and composition, it is difficult to quantify the effect on induced seismicity due to gas production. Here we use...abstract 2021
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Mulder, W.A. (author)The representation of a force or of a moment point source in a spectral finiteelement code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finiteelement basis functions are continuous across...conference paper 2021
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Mulder, W.A. (author)Multiparameter inversion of linear systems appears in many problems. The focus here is on isotropic elastic iterative reversetime migration for three positiondependent subsurface model parameters, which amounts to data fitting of processed seismic data with synthetics from the Born approximation of the elastic wave equation. In that case, the...conference paper 2021
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Mulder, W.A. (author)Recently introduced nonreflecting boundary conditions are numerically exact: the solution on a given domain is the same as a subset of one on an enlarged domain where boundary reflections do not have time to reach the original domain. In 1D with second or higherorder finite differences, a recurrence relation based on translation invariance...conference paper 2021
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Mulder, W.A. (author)ABSTRACTWhen modeling wave propagation, truncation of the computational domain to a manageable size requires nonreflecting boundaries. To construct such a boundary condition on one side of a rectangular domain for a finitedifference discretization of the acoustic wave equation in the frequency domain, the domain is extended on that one side to...journal article 2021
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Werthmüller, D. (author), Mulder, W.A. (author), Slob, E.C. (author)3D controlledsource electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if...journal article 2021
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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)Modelling dynamic rupture is essential to correctly describe the process of induced seismicity. Defmod, an opensource finiteelement code featuring quasistatic loading, coseismic volumetric strain, and dynamic rupture, is used to simulate the entire chain of induced seismicity, from pressure evolution due to fluid injection and extraction,...abstract 2020
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Mulder, W.A. (author)Simulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice...journal article 2020
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Mulder, W.A. (author)The representation of a force or moment point source in a spectral finiteelement code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finiteelement basis functions are continuous across...journal article 2020
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Cupillard, Paul (author), Mulder, W.A. (author), Irakarama, Modeste (author), Mazuyer, Antoine (author), Anquez, Pierre (author)Within the last decade, nonperiodic homogenization proved to be an accurate upscaling method for computing smooth equivalent media of elastic models of the earth interior. Doing so, it reveals the seismic anisotropy induced by smallscale structures and it eases the numerical simulation of wave propagation in complex geological settings by...abstract 2019
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Werthmüller, D. (author), Mulder, W.A. (author), Slob, E.C. (author)Controlledsource electromagnetic (CSEM) surveys are a common geophysical investigationtool in the search for, amongst other, groundwater, hydrocarbons, and minerals. The numerical modelling of CSEM data requires the solution of the Maxwell equations. These canbe simplified in the particular case of CSEM, as the frequencies used in surveys are...journal article 2019
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J (author)We present a new accuracy condition for constructing masslumped elements. This condition is less restrictive than the one previously used and enabled us to construct new masslumped tetrahedral elements for 3D wave propagation modelling. The new degree2 and degree3 elements require significantly fewer nodes than previous versions and mass...abstract 2019