Numerical simulation of wave propagation in media with discrete distributions of fractures: effects of fracture sizes and spatial distributions

Vlastos, S.; Liu, E.; Main, Ian; Li, X.-Y.

doi:10.1046/j.1365-246x.2003.01876.x

Cited by 95 publications

(67 citation statements)

References 32 publications

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“…If, however, the fractures and fracture spacing are closer in size to the seismic wavelength, then the fractures will scatter the seismic energy causing a more complex seismic signature Nakagawa et al, 2003;Vlastos et al, 2003;Willis et al, 2004). These larger scale features are the major fracture corridors within a reservoir.…”

Section: Fracture Systems -Numerical Models and Analysis Methodsmentioning

confidence: 99%

Fracture properties from seismic scattering

Burns¹,

Willis²,

Toksöz³

et al. 2007

The Leading Edge

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Fractures scatter seismic energy and this energy can be analyzed to provide information about fracture direction and density. Laboratory and numerical (finite difference) models of fractures show that scattered energy varies with the seismic acquisition direction relative to the orientation of parallel fracture sets. Data acquired normal to fracture strike displays forward and backscattered energy that is canceled in the stacking process, while data acquired parallel to the fracture strike contains forward scattered and guided waves that are enhanced by stacking. The Scattering Index method estimates the fracture orientation by comparing wavelet changes in the data from azimuthal stacks. Fracture density or spacing can be estimated by spectral methods that include f-k analysis of backscattered energy or analysis of spectral notches as functions of azimuth. Application of these methods to data from a fractured carbonate field results in fracture orientation and density estimates that are consistent with borehole measurements. II. IntroductionThe seismic trace is a complex aggregate of reflected and scattered signals from subsurface formation interfaces and heterogeneities. Although many varieties of random noise may also be present in the trace, we know from reacquiring the same seismic survey that seismic data are highly repeatable, indicating that significant information about the subsurface is contained in the trace yet not used by our standard analysis methods. Seismic scattering is a type of signal contained in the data that is generally not utilized. Most of our processing methods are focused on optimizing the specular reflections from subsurface lithology or fluid boundaries for structural and stratigraphic interpretation. The presence of small-scale heterogeneities, creating variability in seismic properties that are on the order of a wavelength or less, will also generate seismic signatures. However, the scattered signals will appear to be less coherent and not be correlated over long distances. Such signals are generally treated as 'random noise' in the sense that stacking and deconvolutional processes may effectively remove them in many situations. Because these signals contain information about the subsurface at smaller scales it would be beneficial to find ways to extract and utilize them. One particular application where this is true is in the area of fracture characterization. Fractures can cause significant scattering since they generally have large contrasts in elastic properties compared to the surrounding rock. In addition this contrast will be greatest for those fractures that 'open', and therefore have the largest impact on reservoir productivity. Although fractures may exist with a variety of orientations in the subsurface due to changing stress regimes over time, those fractures that are oriented 2 parallel to the present day maximum horizontal stress direction will be open and generate the most scattering. Over the past several years we have developed several methods for using scat...

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Section: Fracture Systems -Numerical Models and Analysis Methodsmentioning

confidence: 99%

Fracture properties from seismic scattering

Burns¹,

Willis²,

Toksöz³

et al. 2007

The Leading Edge

View full text Add to dashboard Cite

show abstract

“…Some authors modeled cracks in indirect manners, such as thin layers of equivalent homogeneous anisotropic materials (Vlastos et al, 2003) or arrayed point sources (van Antwerpen et al, 2002). In contrast, Saenger et al (2000) modeled cracks as a thin inclusion with zero elastic constants and small mass density within the "rotated staggered grid" developed by them.…”

Section: Introductionmentioning

confidence: 99%

Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method

et al. 2013

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We simulate P-SV wave scattering by 2-D parallel cracks using the finite difference method (FDM). Here, special emphasis is put on simplicity; we apply a standard FDM (second-order velocity-stress scheme with a staggered grid) to media including traction-free, infinitesimally thin cracks, which are expressed in a simple manner. As an accuracy test of the present method, we calculate the displacement discontinuity along an isolated crack caused by harmonic waves using the method, which is compared with the corresponding results based on a reliable boundary integral equation method. The test resultantly indicates that the present method yields sufficient accuracy. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation, if the crack density is sufficiently low. The theory appears valid with a crack density up to at least 0.1 for SV wave incidence, whereas the validity limit appears lower for P wave incidence.

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“…Pointer et al (1998) treated the set of fractures as if it was a single fracture and they were able to detect its shape and size studying diffraction in the Rayleigh regime. On the other hand, Vlastos et al (2003) and Murai (2007) showed that length and spatial distribution of fractures cannot be seen in the Rayleigh regime.…”

Section: Introductionmentioning

confidence: 99%