Modeling elastic fields across irregular boundaries

Muir, Francis; Dellinger, Joe; Etgen, John; Nichols, Dave

doi:10.1190/1.1443332

Cited by 100 publications

(49 citation statements)

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“…This means that we increase the velocity in some regions of the original model as well as decrease it in other regions of the original model. The volumetric averaging of slowness (Muir et al, 1992;Moczo et al, 2000) is the most appropriate method to discretize an isotropic model to an isotropic model.…”

Section: Discussion Of the Algorithm For A 3d Isotropic Modelmentioning

confidence: 99%

Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

Eisner

Clayton

2002

Bulletin of the Seismological Society of America

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We have developed a methodology to discretize an isotropic velocity model with low velocities near the free surface for full waveform numerical modeling. The method modifies the near-surface minimum velocity in a given (original) model by replacing parts of the model with equivalent medium parameters (EMP). The discretized model (with EMP) has a higher minimum velocity and minimizes the difference between the seismograms evaluated for the original model and the model with EMP. The method is suitable for studies requiring full waveform numerical modeling with a limited frequency range (such as a finite-difference full waveform modeling in a sedimentary basin). The discretized model with EMP is set to match locally surface-wave velocities evaluated in the original model over the frequency range of interest. The difference in group velocity calculated for the original vertical profile and the vertical profile with EMP provides an estimate of the error due to the modification of the original model.Online material: source code for the discussed algorithm.

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Section: Discussion Of the Algorithm For A 3d Isotropic Modelmentioning

confidence: 99%

Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

Eisner

Clayton

2002

Bulletin of the Seismological Society of America

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“…derived the effective properties of a finely layered medium based on this long-wavelength equivalent medium theory. In order to accurately model wave propagation through boundaries in an elastic solid with a Finite-Difference (FD) scheme, Muir et al (1992) extended Schoenberg and Muir's derivation to represent the stiffness coefficient of a grid cell traversed by a boundary. developed this idea further to represent fractures with linear slip behavior in a FD scheme.…”

Section: Modeling Methodsmentioning

confidence: 99%

Characterization of In-Situ Stress and Permeability in Fractured Reservoirs

Burns¹,

Toksoz²

2006

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Fracture orientation and spacing are important parameters in reservoir development. This project resulted in the development and testing of a new method for estimating fracture orientation and two new methods for estimating fracture spacing from seismic data. The methods developed were successfully applied to field data from fractured carbonate reservoirs. Specific results include: the development a new method for estimating fracture orientation from scattered energy in seismic data; the development of two new methods for estimating fracture spacing from scattered energy in seismic data; the successful testing of these methods on numerical model data and field data from two fractured carbonate reservoirs; and the validation of fracture orientation results with borehole data from the two fields.Researchers developed a new method for determining the reflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations made from 3D finite difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fractures impart a ringing coda type signature to seismic energy that is transmitted through or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1) the difference in angle between the orientation of the fractures and the acquisition direction, 2) the fracture spacing, 3) the wavelength of the illuminating seismic energy, and 4) the compliance, or stiffness, of the fractures. This coda energy is the most coherent when the acquisition direction is parallel to the strike of the fractures. It has the largest amplitude when the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. The method uses surface seismic reflection traces to derive a transfer function that quantifies the change in the apparent source wavelet before and after propagating through a fractured interval. When a 3D seismic survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows identification of subsurface areas with high fracturing and determines the strike of those fractures. The method was calibrated with model data and then applied it to data from two fractured carbonate reservoirs giving results that agree with well data and fracture orientations derived from other measurements.In addition, two approaches for estimating fracture spacing from scattered seismic energy were developed. The first method relates notches in the amplitude spectra of the scattered wavefield to the dominant fracture spacing that caused the scattering. The second uses conventional frequency-wavenumber (FK) filtering to isolate the backscattered signals and then recovers an estimate of the fracture spacing from the dominant wavelength of those signals. The methods were applied to Emilio Field data, resulting in the fracture spacing estimates of about 30-40 meters ...

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“…Based on this theory, smoothing the grid points around the interface can give second-order accuracy to approximate the boundary conditions of the interface [5]. Muir et al [34] applied the S-M calculus [40], which is a general formulation of Backus averaging [2], to compute the equivalent value of elastic parameters for the grid points near the discontinuous interfaces [34]. Their results demonstrated that the averaging method can effectively suppress the spurious diffractions [34].…”

Section: Introductionmentioning

confidence: 99%

“…Muir et al [34] applied the S-M calculus [40], which is a general formulation of Backus averaging [2], to compute the equivalent value of elastic parameters for the grid points near the discontinuous interfaces [34]. Their results demonstrated that the averaging method can effectively suppress the spurious diffractions [34]. The idea of averaging for dealing with discontinuous interfaces has also been applied with the finite-element methods with a lumped mass matrix, which leads to an effective interface-smoothing scheme by summing the rows of the mass matrix for constant-density acoustic media [41].…”

Section: Introductionmentioning

confidence: 99%

Accurate seabed modeling using finite difference methods

et al. 2017

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Finite difference is the most widely used method for seismic wavefield modeling. However, most finitedifference implementations discretize the Earth model over a fixed grid interval. This can lead to irregular model geometries being represented by 'staircase' discretization, and potentially causes mispositioning of interfaces within the media. This misrepresentation is a major disadvantage to finite difference methods, especially if there exist strong and sharp contrasts in the physical properties along an interface. The discretization of undulated seabed bathymetry is a common example of such misrepresentation of the physical properties in finite-difference grids, as the seabed is often a particularly sharp interface owing to the rapid and considerable change in material properties between fluid seawater and solid rock. There are two issues typically involved with seabed modeling using finite difference methods: firstly, the travel times of reflections from the seabed are inaccurate as a consequence of its spatial mispositioning; secondly, artificial diffractions are generated by the staircase representation of dipping seabed bathymetry. In this paper, we propose a new method that provides a solution to these two issues by positioning sharp interfaces at fractional grid locations. To achieve this, the velocity The Unconventional Natural Gas Institute, China University of Petroleum (Beijing), Beijing 102249, China model is first sampled in a model grid that allows the center of the seabed to be positioned at grid points, before being interpolated vertically onto a regular modeling grid using the windowed sinc function. This procedure allows undulated seabed bathymetry to be represented with improved accuracy during modeling. Numerical tests demonstrate that this method generates reflections with accurate travel times and effectively suppresses artificial diffractions.

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Modeling elastic fields across irregular boundaries

Cited by 100 publications

References 0 publications

Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

Characterization of In-Situ Stress and Permeability in Fractured Reservoirs

Accurate seabed modeling using finite difference methods

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