Hartmut Spetzler

Structure and elasticity of single‐crystal (Mg,Fe)O and a new method of generating shear waves for gigahertz ultrasonic interferometry

investigated Fe 3+ -bearing (Mg,Fe)O single crystals prepared by interdiffusion having Fe/(Fe + Mg) = 0.06, 015, 0.24, 0.27, 0.37, 0.53, 0.56, 0.75, and 0.79, with ferric iron contents ranging from � 1 to 12% of the total Fe. The elastic constants (c11, c12, c44) are determined from compressional and shear wave velocities in the (100) and (111) propagation directions in the range of 0.5-1.2 GHz. The c11 and c44 elastic constants soften from periclase to wustite, whereas the c12 elastic constant increases. The rate of change in the elastic constants with composition (@cij/@x) is greatest between MgO and (Mg,Fe)O with � 25 mol % FeO implying that substitution of Fe into periclase has a greater effect on the elastic properties than adding Mg to wustite. The elastic anisotropy of (Mg,Fe)O has rather unusual behavior, being essentially constant for the range 0-25 mol % FeO but then decreases linearly with Fe content such that wustite is elastically isotropic. The elastic properties of (Mg,Fe)O having similar total Fe but varying Fe 3+ contents are identical within uncertainty. The isothermal compressibility of samples with Fe/(Fe + Mg) = 0.27, 0.56, and 0.75 is determined by single-crystal X-ray diffraction in a diamond anvil cell to � 9 GPa. For these samples, K0T = 158.4(4), 155.8(9), and 151.3(6) GPa with @KT/@P = 5.5(1), 5.5(1), and 5.6(2), respectively (where values in parentheses indicate standard deviations). The deviation of @KT/@P from 4.0 corresponds to a difference in calculated density of about one percent for ferropericlase (Mg0.8Fe0.2)O at 30 GPa from the value predicted by second-order truncation of the Birch- Murnaghan equation of state. INDEX TERMS: 3620 Mineralogy and Petrology: Crystal chemistry; 3909 Mineral Physics: Elasticity and anelasticity; 3919 Mineral Physics: Equations of state; 3924 Mineral Physics: High-pressure behavior; KEYWORDS: magnesiowustite, elastic constants, ultrasonics, crystal chemistry, bulk moduli

Permeability dependence of seismic amplitudes

Can permeability be determined from seismic data? This question has been around since Maurice Biot, working for Shell in the 1950s, introduced the idea that seismic waves induce fluid flow in saturated rocks due to fluid-pressure equilibration between the peaks and troughs of a compressional wave (or due to grain accelerations in the case of a shear wave). Biot (1956) established a frequency-dependent analytical relation between permeability and seismic attenuation. However, laboratory, sonic log, crosswell, VSP, and surface seismic have all demonstrated that Biots predictions often greatly underestimate the measured levels of attenuation—dramatically so for the lower-frequency measurements. Yet, if an unresolved link truly exists between seismic amplitudes and permeability, the potential benefit to the oil industry is enormous. For this reason, the Department of Energy (DOE) brought together 15 participants from industry, national laboratories, and universities to concentrate for two days on whether permeability information is conceivably contained in and retrievable from seismic data. The present article represents much of the workshop discussion (which took place 5–6 December 2001 in Berkeley, California), but is not strictly limited to it. Not all connections between hydrological and seismic properties are considered. Three-dimensional seismic images and time-lapse seismic monitoring are routinely used by reservoir engineers in constructing and constraining their reservoir model. Such imaging applications of seismic surveys to hydrological modeling are not discussed. Furthermore, in fractured reservoirs it is reasonable to postulate that any locally determined seismic anisotropy defines a symmetry class for the geologic material that must also be satisfied by the permeability tensor. Neither are such material-symmetry constraints discussed. The focus here is only on whether the permeability of the rocks through which seismic waves propagate directly influences the decay of the wave amplitudes with distance. Key to addressing this question is an up-to-date discussion of the likely attenuation …

A New Ultrasonic Interferometer for the Determination of Equation of State Parameters of Sub-millimeter Single Crystals

A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 105 in travel time measurements is achievable in single crystals (thickness of ∼200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities.The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting andSpetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.

A new conceptual model for fluid flow in discrete fractures : An experimental and numerical study

A fundamental understanding of flow within single, or discrete, fractures is necessary so that fluid flow and chemical transport in fractured rocks can be accurately characterized. To explore discrete fracture flow, we conducted a series of experiments to study the movement of water through four artificial fractures, each with a different two-dimensional surface topography. We then performed fluid flow simulations using a lattice gas automata (LGA) numerical model to compare with the experimental results and to obtain detailed pictures of the fluid velocity fields within these fractures. The flow experiments and LGA simulations, all performed under fully saturated and laminar flow conditions, used fracture aperture values ranging from 0.25 to 1.80 mm. Our main focus was to determine how the cubic law, derived for fluid flow through parallel plates, could be modified to accommodate a tortuous fracture geometry. Our experimental and numerical results led to the proposal of a new conceptual model. This model states that when the aperture is measured normal to the flow path and is harmonically averaged and when the tortuosity of the flow path is included in the calculation of the pressure gradient, the cubic law can adequately predict the flow rate through fractures with a nonparallel geometry. Our study has implications for interpreting laboratory fracture flow data and for improving predictive numerical models.

Transient creep in natural and synthetic, iron-bearing olivine single crystals: Mechanical results and dislocation microstructures

Abstract This study examines transient creep of single crystals of both natural and synthetic iron-bearing olivine under uniaxial compression (0.1 MPa confining pressure and loads of 25–30 MPa) at high temperature (1650 K) and controlled oxygen fugacity. Natural samples were obtained from San Carlos, Arizona and synthetic crystals were grown at Lawrence Livermore National Laboratory. Samples were deformed in the [110] c and [101] c orientations, corresponding to the softest and intermediate strength orientations, respectively, as determined from steady-state creep tests. Dislocation microstructures were examined for samples unloaded at 0%, 0.1%, 0.5% and 5% strain. At 0% strain the dislocation density and morphology were lower and less complex in the synthetic olivine than in San Carlos samples. Nearly all microstructures initially present in undeformed material were overwritten by 0.1% strain. With further straining, little change in microstructure occurred to the 5% strain limit tested here. Dislocation microstruc- tures in [101] c samples were consistent with the activation of the [100](001) and [001](100) slip systems. Microstruc- tures formed in [110] c samples matched those expected from activation of a single slip system, [100](010). These slip systems are the same as those identified as responsible for steady-state creep under similar temperature, oxygen fugacity and stress conditions. Both natural and synthetic crystals deformed under constant stress in [101] c showed normal strain hardening with initial strain rates about an order of magnitude higher than those at 5% strain. After an initial high strain rate that was roughly equal in both sample types, the synthetic samples deformed at higher rates than the natural crystals. Crystals in the [110] c orientation deformed in a strikingly different manner. San Carlos olivine showed inverse or strain-softening creep in the first 1–2% strain, after which there is weak evidence suggesting a change to strain-hardening behavior. The temporal strain behavior of synthetic olivine in [110] c is strongly sigmoidal. An inflection point at 1% strain marks the change from inverse to normal transient creep. In the [110] c orientation, steady-state creep was not attained for synthetic samples in the 5% strain limit tested here. These results imply that anisotropic transient creep may exist in the upper mantle, complicating rheological models of post-glacial rebound. The transient creep observed in the [110] c orientation illustrates that the strain- hardening Burgers body model is not universally applicable. The (100)[010] slip system is not always the softest system in the transient regime. Strain may initially be accommodated primarily in the [100](001), [001](100) duplex system. Finally, the transient regime has been shown to extend to several percent strain (in the [110] c . orientation), making transient creep potentially important in modelling initial post-glacial rebound.

The effect of surface geometry on fracture permeability: A case study using a sinusoidal fracture

Measurements of water flow through a sinusoidal fracture were undertaken to compare sinusoidal flow with parallel plate flow. Flow rates were measured through a fracture with an amplitude of 1.02 mm and a wavelength of 5.08 mm, with vertical separation ranging from 0.21 mm to 0.71 mm, and for Reynolds numbers (Re) ranging from 0.05 to 58. In addition, a series of lattice gas automata flow simulations of water flow through a sinusoidal fracture with the same dimensions were performed. Results from both the experiments and the numerical simulations reflect that, compared to a parallel plate channel, a sinusoidal channel has a significantly lower ability to transmit fluid. This is proposed to be due to the variation in the aperture measured normal to the flow path, the tortuosity of the flow path, and potential instabilities within the flow field.

Shear attenuation and dispersion in MgO

Abstract An understanding of anelastic effects on seismic wave propagation is crucial for developing accurate seismic models of the mantle. The lower mantle is thought to contain a significant volume fraction, approximately 20%, of magnesiowustite, (Mg,Fe)O, in addition to the dominant silicate perovskite. Weaker magnesiowustite may dominate the rheological response of the lower mantle. It may also account for the shear attenuation observed in the lower mantle. We have measured the complex torsional modulus of a single crystal of the magnesiowustite end member periclase, MgO, at small strains, seismic frequencies, and high temperature. The attenuation is approximately 0.030 ( Q approximately 33) at 0.003 Hz and 1500 K with a dislocation density of approximately 5 × 109 m−2. The corresponding dispersion reduces the shear velocity of MgO at 0.001 Hz and 1500 K by approximately 4% relative to ultrasonic values. To the extent that magnesiowustite behaves similarly to MgO, it appears to be a good candidate to account for a major portion of lower-mantle attenuation.

Ultrasonic measurements in a diamond anvil cell

Abstract Advances in ultrasonic and electronic technology have made it practical to make elastic wave measurements with wavelengths which are near the optical range, i.e. in the micro meter range. Ultrasonic interferometry has been adapted to a diamond anvil cell and thus expands the tools available for material property measurements under high pressure and temperature. Sound waves with a frequency of 1 GHz were propagated through an H2O sample in a diamond anvil cell. Starting at room temperature and a pressure of approximately 1.2 GPa a single crystal of ice VI was heated until it was completely liquid. Good signal transmission was observed in the solid, two phase and liquid states. While the sample was in the two phase region the velocity of propagation of the phase boundary between the solid and the liquid and its roughness were observed. At a propagation velocity of 2 μ s−1 the phase boundary is smooth on the order of 1 μ. Compressional wave travel time measurements at ∼ 2.5 GPa through a ∼ 200-μ thick garnet sample illustrate the capability of the technique for solids. No frequency dispersion in the travel time is observed for this sample from 600 MHz to 1.3 GHz.

Gigahertz ultrasonic interferometry at high P and T: new tools for obtaining a thermodynamic equation of state

A new method of generating shear waves with near-optical wavelength has been developed for gigahertz ultrasonic interferometry. The new acoustic technique features a P-to-S conversion upon reflection inside an MgO buffer rod, and is used first to determine the full set of ambient P–T elastic constants (cij) of magnesiowustite—(Mg, Fe)O. In addition, P-wave travel times have been measured in olivine to 250oC at ~ 2.5 GPa in a resistance-heated ultrasonic diamond anvil cell, demonstrating that acoustic coupling can be maintained at high temperature in a hydrostatic (alcohol) pressure medium. The new methodology brings us closer to obtaining a complete travel-time equation of state for single-crystal samples.

Seismic attenuation in artificial glass cracks: Physical and physicochemical effects of fluids

Attenuation and stiffness of artificial, fluid containing cracks are measured from 3 mHz to 10 Hz. The cracks are wedge-shaped; made from glass microscope slides. To explain the frequency dependence of both the attenuation and the stiffness (akin to a modulus), we need to appeal to well known fluid flow mechanisms and to the physicochemical interaction between the fluid and crack surface. By altering the wettability of the crack surfaces, surfactants change the mobility of water and thereby change the frequency dependence of the fluid flow effects by several orders of magnitude.