- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
Kadu, Ajinkya (author), Mulder, W.A. (author), van Leeuwen, Tristan (author)Full-waveform inversion attempts to estimate a high-resolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains high-contrast bodies such as salt and if su ciently low frequencies are absent from the data. Salt bodies are important for hydrocarbon exploration because oil or gas reservoirs are...conference paper 2017
- document
-
Shamasundar, R. (author), Mulder, W.A. (author)For seismic modelling, imaging and inversion, finite-difference methods are still the workhorse of the industry despite their inability to meet the increasing demand for improved accuracy in subsurface imaging. Finiteelement methods offer better accuracy but at a higher computational cost. A stress-velocity formulation with linear elements and...conference paper 2017
- document
-
Mulder, W.A. (author)Storage of the source wavefield during reverse-time migration and full-waveform inversion can be avoided by reconstructing that wavefield during reverse-time stepping along with the receiver wavefield. With absorbing boundary conditions, this requires the final states of the source wavefield and a strip of boundary values at all times. The width...conference paper 2017
- document
-
Huiskes, M.J. (author), Plessix, RE (author), Mulder, W.A. (author)We propose a finite-difference scheme for the simulation of seismic waves interacting with 3-D freesurface topography. The intended application is velocity model building by acoustic full-waveform inversion (FWI). The scheme follows an immersed boundary approach for wave equations in the firstorder stress-velocity formulation, discretized on a...conference paper 2016
- document
-
Kadu, Ajinkya (author), van Leeuwen, Tristan (author), Mulder, W.A. (author)<br/>In seismic exploration, the delineation of large bodies with hard exterior contrasts but nearly constant interior properties is a challenge. Examples include salt diapirs, salt slabs, anhydrite or basalt layers. Salt geometries are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. This...conference paper 2016
- document
-
Bharadwaj, Pawan (author), Drijkoningen, G.G. (author), Mulder, W.A. (author), Tscharner, Thomas (author), Jenneskens, Rob (author)The Earth’s properties, composition and structure ahead of a tunnel boring machine (TBM) should be mapped for hazard assessment during excavation. We study the use of seismic-exploration techniques for this purpose. We focus on a seismic system for soft soils, where shear waves are better and easier to interpret than compressional waves, as has...conference paper 2016
- document
-
Shamasundar, R. (author), Mulder, W.A. (author)The second-order formulation of the wave equation is often used for spectral-element discretizations. For some applications, however, a first-order formulation may be desirable. It can, in theory, provide much better accuracy in terms of numerical dispersion if the consistent mass matrix is used and the degree of the polynomial basis functions...conference paper 2016
- document
-
Shamasundar, R. (author), Al-Khoury, R.I.N. (author), Mulder, W.A. (author)We investigated one-dimensional numerical dispersion curves and error behaviour of four finite-element schemes with polynomial basis functions: the standard elements with equidistant nodes, the Legendre-Gauss-Lobatto points, the Chebyshev-Gauss-Lobatto nodes without a weighting function and with. Mass lumping, required for efficiency reasons and...conference paper 2015