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Average elastic properties of a fluid-saturated fractured rock are discussed in association with the extremely slow and dispersive Krauklis wave propagation within individual fractures. The presence of the Krauklis wave increases P-wave velocity dispersion and attenuation with decreasing frequency. Different laws (exponential, power, fractal, and gamma laws) of distribution of the fracture length within the rock show more velocity dispersion and attenuation of the P-wave for greater fracture density, particularly at low seismic frequencies. The results exhibit a remarkable difference in the P-wave reflection coefficient for frequency and angular dependency from the fractured layer in comparison with the homogeneous layer. The biggest variation in behaviour of the reflection coefficient versus incident angle is observed at low seismic frequencies. The proposed approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behaviour of reflection coefficients versus frequency and angle of incidence as the indicators of fractures. [ABSTRACT FROM AUTHOR]

The purpose of this study is to experimentally investigate the stress effect on normally incident P-wave attenuation through coal specimens. Laboratory tests were carried out using a Split Hopkinson pressure bar (SHPB) system, and a modified method was proposed to determine the quality factor ( Q ) of P-waves through coal specimens. Larger quality factor denotes less energy attenuated during P-wave propagating through coal. Experimental results indicate that the quality factor and stress ( σ ) within coal specimens are positively correlated. The P-wave propagation through coal specimens causes crack closure at the beginning of the coal fracture process in SHPB tests, an innovative model was thus proposed to describe the relationship between the crack closure length and the dynamic stress induced by P-wave. Finally, the stress effect on P-wave attenuation through coal was quantitatively represented by a power function Q = a ( c – bσ ) − 6 , and the material constants a , b , and c were determined as 1.227, 1.314, and 0.005, respectively. The results obtained in this study would be helpful for engineers to estimate seismic energy attenuation and coal mass instability in coal mines. [ABSTRACT FROM AUTHOR]

We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot's equations and Johnson's bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot's theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius. [ABSTRACT FROM AUTHOR]

We used the seismic physical modelling approach to study the effect of fracture thickness or aperture on P-wave attenuation, using a laboratory scale model of two horizontal layers. The first layer is isotropic while the second layer has six fractured blocks, each consisting of thin penny-shaped chips of 3 mm fixed diameter and same thickness to simulate a set of aligned vertical fractures. The thickness of the chips varies according to the blocks while the fracture density remains the same in each block. 2D reflection data were acquired with the physical model submerged in a water tank in a direction perpendicular to the fracture strikes using the pulse and transmission method. The induced attenuation was estimated from the preprocessed CMP gathers using the QVO method, which is an extension of the classical spectral ratio method of attenuation measurement from seismic data. The results of our analysis show a direct relationship between attenuation and the fracture thickness or aperture. The induced attenuation increases systematically with fracture thickness, implying more scattering of the wave energy in the direction of increasing aperture. This information may be useful to differentiate the effect caused by thin microcracks from that of large open fractures. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this study is to analytically predict and to experimentally investigate the seismic response of adjacent filled parallel rock fractures with dissimilar properties (e.g., fracture thickness and stiffness). The time-domain recursive method is extended to predict that a P-wave propagates normally across the filled parallel fractures using the specific stiffness of each filled fracture and considering multiple wave reflections between the parallel fractures. The split Hopkinson rock bar technique is modified to simulate P-wave propagation normally across the sand-filled parallel fractures and to characterize the stress-closure relation of each sand-filled fracture. The P-wave transmission and the seismic response of the filled parallel fractures are an interactive process. The experimental results show the decreases of loading rate and dominant frequency when the P-wave propagates across each sand-filled fracture. The P-wave transmitted from the first sand-filled fracture strongly affects the seismic response of the second one. The P-wave attenuation in the filled parallel fractures is mainly due to the dynamic compaction of the filling sands. By comparison, the analytical method provides a satisfactory prediction to the experimental result. This study suggests considering the specific stiffness of each filled fracture to precisely predict the seismic response of filled parallel rock fractures. [Copyright &y& Elsevier]

Abstract: The attenuation of P and S waves caused by quarry blasts in south and southeast Tehran was estimated using the extended coda-normalization method. The analysis used 230 seismic events from quarry blasts recorded in a range of 3–50km using a network of 13 seismic stations. To estimate the frequency-dependent Q-value, the seismograms were band-pass filtered at the central frequencies (f i ) of 1, 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 10 and 12Hz using a phaseless eight-pole Butterworth band pass filter with a bandwidth of f i /√2 to f i √2. We showed that geometrical spreading exponent value (γ) is a variable depending on the propagation distance. The attenuation parameters were: Q p −1=(100±6) ×10 −3 (f −1±0.07) and Q s −1=(73±2)×10 −3 (f −1.06±0.03) indicating that the strong frequency dependency of Q p −1 and Q s −1 can propose heterogeneity of the medium. The ratio of Q p −1 /Q s −1 obtained in this study is larger than unity and less than 2 for the entire frequency range. Also, Q s ≥Q p indicates that the region is composed of half-saturated rocks. [Copyright &y& Elsevier]