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Mulder, W.A. (author), Geevers, S. (author), van der Vegt, J. (author)Masslumped 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 present new and efficient quadrature rules for computing the stiffness matrices of masslumped tetrahedral elements for wave propagation modeling. These quadrature rules allow for a more efficient implementation of the masslumped finite element method and can handle materials that are heterogeneous within the element without loss of the...journal article 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 masslumped 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 fullwaveform 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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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 masslumped elements. This condition is less restrictive than the one currently used and enabled us to construct new masslumped tetrahedral elements of degrees 2 to 4. The new degree2 and degree3 tetrahedral elements require 15 and 32 nodes per element, respectively, while...journal article 2018
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Shamasundar, R. (author), Mulder, W.A. (author)Finite elements can, in some cases, outperform finitedifference 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 secondorder form, the firstorder 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)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 nearsurface shearvelocity profile. The inverse problem is solved for the locally onedimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a Pwave velocity profile, the Pguided 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 finitedifference 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 finitedifference 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 fullwaveform 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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Kadu, Ajinkya (author), Mulder, W.A. (author), van Leeuwen, Tristan (author)Fullwaveform inversion attempts to estimate a highresolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains highcontrast 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
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Bharadwaj, Pawan (author), Drijkoningen, G.G. (author), Mulder, W.A. (author), Thorbecke, J.W. (author), Neducza, Boriszlav (author), Jenneskens, R (author)In the near surface with unconsolidated soils, shearwave properties can often be characterised better and with a higher resolution than compressionalwave properties. To enable imaging ahead of a tunnelboring machine, we developed a seismic prediction system with a few shearwave vibrators and horizontal receivers. The boring process is...journal article 2017
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Mulder, W.A. (author), Huiskes, M.J. (author)One approach to incorporate topography in seismic finitedifference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constantdensity acoustic finitedifference code, based on the secondorder formulation of the wave equation that only...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 lowfrequency and wideaperture data, the longtointermediate wavelength components of the velocity model can be recovered by fullwaveform inversion. Standard static corrections to handle the topography do not work satisfactorily on longoffset...conference paper 2017
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Shamasundar, R. (author), Mulder, W.A. (author)For seismic modelling, imaging and inversion, finitedifference 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 stressvelocity formulation with linear elements and...conference paper 2017
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Mulder, W.A. (author)Storage of the source wavefield during reversetime migration and fullwaveform inversion can be avoided by reconstructing that wavefield during reversetime 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
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Ishiyama, T. (author), Blacquière, G. (author), Verschuur, D.J. (author), Mulder, W.A. (author)Surface waves in seismic data are often dominant in a land or shallowwater environment. Separating them from primaries is of great importance either for removing them as noise for reservoir imaging and characterization or for extracting them as signal for nearsurface characterization. However, their complex properties make the surfacewave...journal article 2016
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Bharadwaj, Pawan (author), Mulder, W.A. (author), Drijkoningen, G.G. (author)Leastsquares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the leastsquares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an...journal article 2016
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Geevers, Sjoerd (author), van der Vegt, Jaap (author), Mulder, W.A. (author)We present and analyse a Symmetric Interior Penalty Discontinuous Galerkin (SIPDG) method combined with an explicit hybrid Local Time Stepping (LTS) scheme for solving seismic wave problems in heterogeneous anisotropic elastic media. The discontinuous Galerkin method allows for local adjustment of the mesh size and approximation order, and can...abstract 2016
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Huiskes, M.J. (author), Plessix, RE (author), Mulder, W.A. (author)We propose a finitedifference scheme for the simulation of seismic waves interacting with 3D freesurface topography. The intended application is velocity model building by acoustic fullwaveform inversion (FWI). The scheme follows an immersed boundary approach for wave equations in the firstorder stressvelocity formulation, discretized on a...conference paper 2016