Wave Attenuation In Rocks Research Articles

Low-Amplitude Wave Propagation and Attenuation Through Damaged Rock and a Classification Scheme for Rock Fracturing Degree

Damaged rock mass contains a great number of microstructures and defects at various scales, which could influence wave propagation significantly. In this paper, investigation of low-amplitude stress wave attenuation in rocks with different damage degrees was undertaken to determine the effects of parameters including damage degree, heterogeneity and type of waveforms on wave propagation, attenuation and slowness. The numerical method was validated through comparison with laboratory measurements. The damage was induced by conducting uniaxial compression tests on the intact rocks and was defined with the acoustic emission. The results showed that the attenuation ratio of low-amplitude stress wave increases with increasing rock damage degree. The rock heterogeneity was incorporated into the numerical model using a digital image processing technique with the combination of X-ray micro-computerized tomography. We found that the rock heterogeneity has great influence on the wave amplitude attenuation. Three types of waveforms, i.e., half-sine wave, square wave and exponential decay wave, were utilized to analyze influences of waveforms on attenuation characteristics in damaged rock specimens. The attenuation ratio of the exponential decay wave is the highest for rock specimens with the same damage degree, attributed to its highest dominant frequency. Moreover, detailed spectrum analysis suggested that the dominant frequency of the wave signal decreases with increasing damage degree. Based on derived simulating results, an improved classification scheme for determining rock fracturing degree, which groups the rock into zones of slightly fractures, moderately fractured and strongly fractured, was established by considering the relationship between wave amplitude and damage, since wave amplitude, other than wave velocity, is more sensitive to rock damage. The findings in this paper could facilitate a better understanding of wave propagation through rock and provide another means to determine rock fracturing degree.

Elastic Wave Attenuation Characteristics and Relevance for Rock Microstructures

We investigated elastic wave attenuation characteristics using a PCI-2 acoustic emission system. A lead-break test was employed to carry out attenuation experiments in granite, marble, red sandstone, and limestone. Because the centroid frequency variation of the red sandstone differs significantly from the other rocks, a pendulum steel ball impact test was also performed to study the attenuation characteristics of elastic waves in red sandstone. The results show that the elastic wave signal amplitude decreases with increasing propagation distance for all four rock types. In granite and red sandstone, the peak frequency of the elastic wave declines abruptly after the propagation exceeds 800 and 100 mm, respectively, and remains almost unchanged in marble and limestone. The attenuation of centroid frequency in granite, limestone, and marble shows the same trend; however, in red sandstone, when the elastic wave propagation exceeds a certain distance, the variation of centroid frequency shows an upward tendency. The main influence of elastic wave attenuation in rock is the packing state of mineral particles: less tightly packed rocks consistently have a higher attenuation coefficient. The secondary cause of attenuation is the development of structures such as joints and stratifications. More developed interior structures lead to higher attenuation coefficients. Sensor selection is also very important in rock attenuation tests. We recommend use of a wide resonant frequency sensor or sensors with different resonant frequencies along the elastic wave propagation path.

Anomalies of low-intensity acoustic wave attenuation in rocks

It is experimentally established that acoustic waves in rocks attenuate abnormally depending on varying amplitude. The amplitude growth results in the increase in elastic wave velocities and decrease in the attenuation decrement. The attenuation rather than wave velocity is more sensitive to the amplitude variations. The obtained data are applicable to diagnose the states of fractured and porous rocks.

Elastic wave attenuation in rocks containing fluids

The low-frequency limit of Biot’s theory of fluid-saturated porous media predicts that the coefficients for viscous attenuation of shear waves and of the fast compressional wave are proportional to the fluid permeability. Although the observed attenuation is generally in qualitative agreement with the theory, the magnitude of the observed attenuation coefficient in rocks is often more than an order of magnitude higher than expected. This apparent dilemma can be resolved without invoking other attenuation mechanisms if the intrinsic permeability of the rock is inhomogeneous and varies widely in magnitude. A simple calculation of the overall behavior of a layered porous material using local-flow Biot theory shows that the effective permeability for attenuation is the mean of the constituent permeabilities while the effective permeability for fluid flow is the harmonic mean. When the range of variation in the local permeability is one or more orders of magnitude, this difference in averaging method can easily explain some of the observed discrepancies.

Seismic attenuation: Effects of pore fluids and frictional‐sliding

Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in terms of wave induced pore fluid flow. The ratio of compressional to shear attenuation is found to be a more sensitive and reliable indicator of partial gas saturation than is the corresponding velocity ratio. Potential applications may exist in exploration for natural gas and geothermal steam reservoirs.

Thermal cracking and amplitude dependent attenuation

The role of crack and grain boundary contacts in determining seismic wave attenuation in rock is investigated by examining Q as a function of thermal cycling (cracking) and wave strain amplitude. Q values are obtained using a longitudinal resonant bar technique in the 10‐ to 20‐kHz range for maximum strain amplitudes varying from roughly 10−8 to 10−5. The samples studied include the Berea and Navajo sandstones, Plexiglas, Westerly granite, Solenhofen limestone, and Frederick diabase, the latter two relatively crack free in their virgin state. Measurements were made at room temperature and pressure in air. Q values for both sandstones are constant at low strains (<10−) but decrease rapidly with amplitude at higher strains. There is no hysteresis of Q with amplitude. Q values for Plexiglas show no indication of amplitude dependent behavior. The granite, limestone, and diabase are thermally cycled at both fast and slow heating rates in order to induce cracking. Samples slowly cycled at 400°C show a marked increase in Q that cannot be entirely explained by outgassing of volatiles. Cycling may also widen thin cracks and grain boundaries, reducing contact areas. Samples heated beyond 400°C, or rapidly heated, result in generally decreasing Q values. The amplitude dependence of Q is found to be coupled to the effects of thermal cycling. For rocks slowly cycled to 400°C or less, the transition from low‐amplitude contant Q to high‐amplitude variable Q behavior decreases to lower amplitudes as a function of maximum temperature. Above 400°C, and possibly in the rapidly heated samples also, the transition moves to higher amplitudes.

Seismic wave attenuation in rock due to friction

The total attenuation in rock is probably due to a number of sources of dissipation. The mechanism proposed here as one source of attenuation is based on the frictional dissipation as crack surfaces in contact slide relative to one another during passage of a seismic wave. The attenuation due to friction at cracks is derived for dilatation and shear waves under the assumption that the cracks may be approximated as elliptical slits in plane strain. The results cannot be evaluated on an absolute basis; however, the ratio Qα/Qβ of the quality factor for longitudinal waves to that for transverse waves predicted by the theory agrees reasonably well with published values (all of which equal approximately 0.5) found in laboratory experiments on granite and limestone.