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Mulder, W.A. (author)To estimate the depth errors in a subsurface model obtained from the inversion of seismic data, the stationary-phase approximation in a two-dimensional constant-velocity model with a dipped reflector is applied to migration with a time-shift extension. This produces two asymptotic solutions: one is a straight line, and the other is a curve....journal article 2024
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Mulder, W.A. (author), Shamasundar, R. (author)Dispersion error analysis can help to assess the performance of finite-element discretizations of the wave equation. Although less general than the convergence estimates offered by standard finite-element error analysis, it can provide more detailed insight as well as practical guidelines in terms of the number of elements per wavelength needed...journal article 2024
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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), Kuvshinov, B. (author)The uncertainty of model parameters obtained by full-waveform inversion can be determined from the hessian of the least-squares 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 stationary-phase method applied to migration with a time-shift extension in a 2-D constant-velocity 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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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)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)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)Temporal dispersion correction of second-order finite-difference 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)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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Mulder, W.A. (author)When solving the wave equation with finite elements, mass lumping allows for explicit time stepping, avoiding the cost of a lower-upper 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 fault-rupture 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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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 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...conference paper 2021
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Mulder, W.A. (author)Multi-parameter inversion of linear systems appears in many problems. The focus here is on isotropic elastic iterative reverse-time migration for three position-dependent 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 non-reflecting 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 higher-order 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)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