Sensitivity analysis of fracture scattering

Abstract

We use a 2-D finite difference method to numerically calculate the seismic response of a single finite fracture in a homogeneous media. In our experiments, we use a point explosive source and ignore the free surface effect, so the fracture scattering wave field contains two parts: P-to-P scattering and P-to-S scattering. We vary the fracture compliance within a range considered appropriate for field observations, 10-12 m/Pa to 10-9 m/Pa, and investigate the variation of the scattering pattern of a single fracture as a function of normal and tangential fracture compliance. We show that P-to-P and P-to-S fracture scattering patterns are sensitive to the ratio of normal to tangential fracture compliance and different incident angle, while radiation pattern amplitudes scale as the square of the compliance. We find that, for a vertical fracture system, if the source is located at the surface, most of the energy scattered by a fracture propagates downwards, specifically, the P-to-P scattering energy propagates down and forward while the P-to-S scattering energy propagates down and backward. Therefore, most of the fracture scattered waves observed on the surface are, first scattered by fractures, and then reflected back to the surface by reflectors below the fracture zone, so the fracture scattered waves have complex ray paths and are contaminated by the reflectivity of matrix reflectors.

Fracture clustering effect on amplitude variation with offset and azimuth analyses

“…The Fresnel zone for the bottom reflections (red) is much wider than that for the top reflections (gray), indicating that the bottom reflections interfere with fracture-scattered waves that are generated from fractures spread over a broader region. Moreover, fracture scattering becomes stronger when it occurs further away from the midpoint because Pto-P fracture scattering generally becomes stronger when the incident angle with respect to the fracture plane increases (Fang et al, 2013a). Therefore, it is more difficult to analyze the AVAz of the bottom reflections.…”

Sensitivity of time lapse seismic data to the compliance of hydraulic fractures

“…Fang et al (2013) found the same linear relationship between fracture scattering strength and fracture compliance when compliance is less than 10 -10 m/Pa, and they argued that the departure of this linear relationship at large compliance is due to the breakdown of the Born approximation. We here demonstrate that Z ξ <<η ξ is the necessary condition for the Born approximation (or weak scattering) to be valid for scattering from fractures.…”

“…The Z N /Z T ratio is strongly influenced by the way the fracture surfaces interact and it can be taken as an indicator representing the fracture saturation condition (Dubos-Sallée and Rasolofosaon, 2008;Fang et al, 2013). Both numerical simulations (Sayers et al, 2009;Gurevich et al, 2009) and laboratory measurements (Lubbe et al, 2008;Gurevich et al, 2009) suggest that Z N is generally smaller than Z T for reservoir fractures.…”

“…Previous studies have mainly focused on characteristics of scattering from fractures as a means of fracture characterization (e.g. Chen et al, 2012;Fang et al, 2013). In this paper, we propose an analysis of the sensitivity of time-lapse seismic data to the fracture compliance.…”

Sequential approach to joint flow‐seismic inversion for improved characterization of fractured media

“…We first run a forward seismic simulation on the true compliance field (C T ) to generate the detailed wavefield [Schoenberg, 1980;Coates and Schoenberg, 1995;Fang et al, 2013]. The seismic response is affected by the underlying fracture mechanics parameters, such as fracture orientation, spacing, and compliance.…”