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Ruan, J. (author), Ghose, R. (author), Mulder, W.A. (author)Induced seismicity from a gas-producing region such as Groningen is believed to be caused by reservoir depletion due to long-term 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)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 finite-difference 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)3-D controlled-source 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 open-source finite-element code featuring quasi-static loading, co-seismic 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 finite-element 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 finite-element basis functions are continuous across...journal article 2020
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J (author)We present a new accuracy condition for constructing mass-lumped elements. This condition is less restrictive than the one previously used and enabled us to construct new mass-lumped tetrahedral elements for 3D wave propagation modelling. The new degree-2 and degree-3 elements require significantly fewer nodes than previous versions and mass...abstract 2019
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Werthmüller, D. (author), Mulder, W.A. (author), Slob, E.C. (author)Controlled-source electromagnetic (CSEM) surveys are a common geophysical investigationtool in the search for, amongst other, groundwater, hydrocarbons, and minerals. The nu-merical 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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Cupillard, Paul (author), Mulder, W.A. (author), Irakarama, Modeste (author), Mazuyer, Antoine (author), Anquez, Pierre (author)Within the last decade, non-periodic 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 small-scale structures and it eases the numerical simulation of wave propagation in complex geological settings by...abstract 2019
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J.J.W. (author)We present new and efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for wave propagation modeling. These quadrature rules allow for a more efficient implementation of the mass-lumped finite element method and can handle materials that are heterogeneous within the element without loss of the...journal article 2019
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Mulder, W.A. (author), Geevers, S. (author), van der Vegt, J. (author)Mass-lumped finite elements on tetrahedra offer more flexibility than their counterpart on hexahedra for the simulation of seismic wave propagation, but there is no general recipe for their construction, unlike as with hexahedra. Earlier, we found new elements up to degree 4 that have significantly less nodes than previously known elements by...conference paper 2019
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J. J.W. (author)We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The...journal article 2018
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Mulder, W.A. (author)One way to deal with the storage problem for the forward source wavefield in reverse time migration and full-waveform inversion is the reconstruction of that wavefield during reverse time stepping along with the receiver wavefield. Apart from the final states of the source wavefield, this requires a strip of boundary values for the whole time...journal article 2018
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Shamasundar, R. (author), Mulder, W.A. (author)Finite elements can, in some cases, outperform finite-difference methods for modelling wave propagation in complex geological models with topography. In the weak form of the finiteelement method, the delta function is a natural way to represent a point source. If, instead of the usual second-order form, the first-order form of the wave equation...journal article 2018
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J. J.W. (author)We present a new accuracy condition for the construction of continuous mass-lumped elements. This condition is less restrictive than the one currently used and enabled us to construct new mass-lumped tetrahedral elements of degrees 2 to 4. The new degree-2 and degree-3 tetrahedral elements require 15 and 32 nodes per element, respectively, while...journal article 2018
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J.J.W. (author)Spectral elements with mass lumping allow for explicit time stepping and are therefore attractive for modelling seismic wave propagation. Their formulation on rectangular elements is straighforward, but for tetrahedra only elements up to degree 3 are known. To preserve accuracy after mass lumping, these elements require additional nodes that...conference paper 2018
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Ponomarenko, A. V. (author), Kashtan, B. M. (author), Troyan, V. N. (author), Mulder, W.A. (author)Surface waves are often used to estimate a near-surface shear-velocity profile. The inverse problem is solved for the locally one-dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P-wave velocity profile, the P-guided waves should be included in the...journal article 2017
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Mulder, W.A. (author)The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free surface can decrease that error. An existing...journal article 2017
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Kadu, Ajinkya (author), van Leeuwen, Tristan (author), Mulder, W.A. (author)Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a...journal article 2017
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Huiskes, M.J. (author), Plessix, RE (author), Mulder, W.A. (author)In land applications, topography variation may impact the imaging if not taken into account. With low-frequency and wide-aperture data, the long-to-intermediate wavelength components of the velocity model can be recovered by full-waveform inversion. Standard static corrections to handle the topography do not work satisfactorily on long-offset...conference paper 2017