HR: 0830h
AN: S11F-0359    [PDF]
TI: Self-Affine Fracture Surface Topography and its Implications on Seismic Wave Propagation
AU: * Nakagawa, S
EM: snakagawa@lbl.gov
AF: Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS90-1116, Berkeley, CA 94720 United States
AU: Nihei, K T
EM: ktnihei@lbl.gov
AF: Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS90-1116, Berkeley, CA 94720 United States
AU: Larry, M R
EM: lrmyer@lbl.gov
AF: Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS90-1116, Berkeley, CA 94720 United States
AB: Over the past two decades, many field and laboratory observations have been made on the self-affine (fractal) properties of fracture surface geometry. In many cases, particularly for fractures in crystalline and granular rocks, the power spectrum of a fracture surface can be described by the power law with exponents limited to a relatively narrow range (e.g., Schmittbuhl et al., 1995). This number is directly related to the Hurst exponent which characterizes the self-affine properties of the fracture, i.e., the scaling relationship of the surface topography between the fracture-normal coordinate and the fracture-parallel coordinates. In this presentation, we will discuss the effect of self-affine fracture geometry on the scaling relationships of fracture compliance and, therefore, on the reflection and transmission of seismic (elastic) waves. The opening width of the fracture is assumed to have either 1) the same self-affine distribution as the fracture surfaces or 2) a distribution resulting from shear displacement across the fracture. Fracture compliances of three-dimensional, self-affine fractures subjected to stress are computed using a numerical model modified from the work of Hopkins (2000). Our preliminary study showed that for a self-affine fracture, normal fracture compliance is proportional to the scale of the fracture in the fracture-normal direction, and hence the fracture compliance follows a scaling relationship log(S/S0)=H log(L/L0). Here, S and L are the normal fracture compliance and the characteristic length of observation, respectively, H is the Hurst exponent, and 0 indicates the quantities measured at the reference scale L0. By introducing this relationship to the seismic displacement discontinuity model (Schoenberg, 1980; Pyrak-Nolte et al., 1990), transmission and reflection coefficients of fractures at different scales and frequencies can be computed. The scaling relationship of fracture properties as shown in this paper is significant because it allows us to estimate the geometry and constitutive relationships of fractures in the field from laboratory measurements on small core and block samples. Once this is done, properties of interests such as stress state and gas and fluid contents of the fractures can be evaluated from field seismic measurements on the fractures.
DE: 3210 Modeling
DE: 3250 Fractals and multifractals
DE: 7260 Theory and modeling
SC: Seismology [S]
MN: 2003 Fall Meeting