In this paper, we investigate effects of fracture scale on seismic P wave attenuation by three sets of physical models. These models are constructed from a solid background of epoxy resin with inclusions of silicon rubber chips of different numbers, diameter and thickness, which simulate fractures with different crack density (CD), length and aperture. P wave propagating parallel and perpendicular to the fractures are then recorded using a pulse transmission method. Besides of analysis on the amplitude, we get quality factor Q using classic spectral ratio method for determining attenuation. And obvious anisotropy can be observed by calculating Thomsen parameter e and attenuation parameter Q e . We conclude that attenuation anisotropy is a potential exploration tool in fracture detection.
Seismic anisotropy has become a potential tool for the detection of natural fractures. In recent times, there has been an increasing use of the P-wave data to detect natural fractures ,especially using azimuthal variations in P wave amplitude, travel-times, velocity, AVO gradient and attenuation to be diagnostic of the presence of aligned fractures (e.g. Li, 1997, Wang et al, 2007; Rathore et al, 1994; Luo et al, 2006; etc). It is for this reason that we focus on investigating the relationship between fracture scale and P wave attenuation. Equivalent medium theories, such as Hudson (1981), are often used to model seismic wave propagation in fractured media. The construction of our fractured models is based on Hudson’s fracture medium theory. Three sets of fractured models are constructed with different CD, fracture length and aperture. And we use the pulse transmission method to do P wave test on them separately. Furthermore, we calculate Q from our amplitude data and see obvious anisotropy from Thomsen parameter e and attenuation parameter Q e.
The construction is based on Hudson’s theoretic hypothesis of thin penny-shaped cracks. The models consist of a solid base with inclusions of low velocity thin penny-shaped materials (Figure 1a). For each model, the crack density (CD) is given by CD=Nr3/V, where V denotes the volume of the base material, r denotes the radius of the round chips and N is the total number of chips in the base material. The crack density changes when we alter N or r. The density of the solid base material is 1.18g/cm3, the Pwave velocity is 2630m/s and the S-wave velocity is 1200m/s. The round chip simulating the fracture is made from a mixture of silicon rubber. Its density is 1.09g/cm3, P-wave velocity is 1360m/s and S-wave velocity is too small to be received. Each fractured model is made of 35 layers of epoxy resin with equal weight to ensure that the separation between two neighboring layers is kept the same. The thickness of each layer is 1.72mm. Once a layer is laid, silicon rubber chips with random distribution are embedded into the layer, and another layer of epoxy resin is then added on the top. Figure 2 is the picture of one set of models.