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Mulder, W.A. (author)Finite elements with polynomial basis functions on the simplex with a symmetric distribution of nodes should have a unique polynomial representation. Unisolvence not only requires that the number of nodes equals the number of independent polynomials spanning a polynomial space of a given degree, but also that the Vandermonde matrix...journal article 2023
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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)To investigate the physical processes behind induced seismicities due to, for example, production of hydrocarbons from a reservoir, most of the earlier studies performed geomechanical simulations on a simple reservoir geometry. The effect of fluid depletion is, in general, simulated for such a simple geometry. Neglecting the contribution of...conference paper 2023
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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 two dimensions on quadrilaterals, spectral elements are the obvious choice. Triangles offer more flexibility for meshing, but the construction of polynomial...journal article 2023
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Mulder, W.A. (author), Kuvshinov, B. (author)The uncertainty of model parameters obtained by fullwaveform inversion can be determined from the hessian of the leastsquares error functional. Because the hessian is generally too costly to compute and too large to be stored, a segmented representation of perturbations of the reconstructed subsurface model in the form of geological units is...conference paper 2023
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Mulder, W.A. (author)The stationaryphase method applied to migration with a timeshift extension in a 2D constantvelocity model with a dipped reflector produces two solutions in the domain of the extended image: one a straight line and the other a curve. If the velocity differs from the true one, the depth error follows from the depth and apparent dip of the...conference paper 2023
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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)Intersecting faults are often ignored in the geomechanical simulation of induced seismicity. To investigate the effects of fault intersection and the resulting reservoir geometry on induced seismicity, caused, for instance, by gas extraction, we have developed 3D geomechanical models considering two intersecting normal faults and the...conference paper 2023
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Mulder, W.A. (author)Temporal dispersion correction of secondorder finitedifference time stepping for numerical wave propagation modelling exploits the fact that the discrete operator is exact but for the wrong frequencies. Mapping recorded traces to the correct frequencies removes the numerical error. Most of the implementations employ forward and inverse...journal article 2023
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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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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)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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 Ruan, J. (author), Masfara, La ODE Marzujriban (author), Ghose, R. (author), Mulder, W.A. (author) abstract 2022
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 Cupillard, Paul (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)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), 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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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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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)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