William Waite | University of Colorado, Boulder (original) (raw)

Papers by William Waite

Nat Geosci, 2010

Marine sediments contain about 500-10,000Gt of methane carbon, primarily in gas hydrate. This res... more Marine sediments contain about 500-10,000Gt of methane carbon, primarily in gas hydrate. This reservoir is comparable in size to the amount of organic carbon in land biota, terrestrial soils, the atmosphere and sea water combined, but it releases relatively little methane to the ocean and atmosphere. Sedimentary microbes convert most of the dissolved methane to carbon dioxide. Here we show

Seismic wave attenuation analysis, the study of how seismic waves lose their energy while they tr... more Seismic wave attenuation analysis, the study of how seismic waves lose their energy while they travel, relies on models to transform measured data into descriptions of the subsurface environment. Seismic attenuation in fluid bearing rock is dominated by interactions between the fluid and the rock. Standard attenuation theories model attenuation due to viscous shear within the flowing fluid (local fluid flow), shear between the pore fluid and pore walls (global fluid flow), or fluid-assisted thermal diffusion. All of these models rely solely on physical and geometrical properties of the system to describe the mechanism by which attenuation occurs. These models do not account for attenuative physicochemical interactions between the pore fluid and pore walls. Effects of physicochemical interactions between the pore fluid and pore walls are considered in this work. Physicochemical interactions between the solid crack surface and the fluid meniscus can restrict contact line motion (motion of the three phase boundary) across the solid surface. In partially saturated cracks subjected to seismic deformation, two consequences of restricted contact line motion are crack stiffening and energy loss. Fluid redistribution in a deforming, partially saturated crack occurs via meniscus deformation or contact line motion or both. If there is some resistance to contact line motion, during the initial response to fluid redistribution the contact lines remain stationary while the meniscus deforms. The meniscus deforms because the fluid pressure is changing, and these fluid pressure changes always act against further crack deformation. The fluid pressurization makes the crack more stiff than a dry crack or a crack in which only stiffening due to viscous flow is considered. If crack deformation pressurizes the fluid enough that the force applied by the deforming meniscus on a contact line exceeds the resistive force holding the contact line stationary, contact line motion occurs. Contact line motion against the resistive force requires energy, which is lost from the seismic wave causing the original crack deformation. This friction-like energy loss mechanism is responsible for the attenuation in the restricted meniscus motion model. The restricted meniscus motion model interprets attenuation and stiffness data which can not be described by attenuation theories relying solely on the physical and geometrical parameters (pore fluid viscosity, fluid and solid compressibilities) used in the standard models. The restricted geometry, meniscus motion model, born from attenuation and stiffening observations in an artificial glass crack sample, is itself composed of parameters which can be measured or estimated using experiments which are distinct from the attenuation and stiffness measurements. These independently measured model parameters are in general agreement with the model parameters used to fit attenuation and stiffness results measured on the artificial glass crack samples.

Scientific Investigations Report, 2010

Scientific Investigations Report, 2009

The Journal of the Acoustical Society of America, 2011

Geophysical Research Letters, 2007

Geochemistry, Geophysics, Geosystems, 2008

Agu Fall Meeting Abstracts, Dec 1, 2006

Physical property measurements on cores containing natural gas hydrate are typically performed on... more Physical property measurements on cores containing natural gas hydrate are typically performed on material exposed to non-in situ conditions at least briefly during recovery. In situ temperature and effective stress are difficult to maintain during core recovery, but pressure-coring systems such as the HYACINTH, Fugro, and IODP PCS can maintain in situ hydrostatic pressure during core retrieval. To simulate effects of transferring pressure-core samples to storage vessels, the USGS conducted physical property measurements on Ottawa sand samples containing methane gas and gas hydrate before and after samples were depressurized out of, then repressurized back into, the gas hydrate stability field. For measurements made along a sample's cylindrical axis, compressional and shear wave speed, shear strength, and thermal conductivity increased 10 to 30 percent following a 5 minute excursion from the gas hydrate stability field. Experiments were conducted in unsaturated sand in the presence of methane gas, and increases in measured physical property values resulting from the repressurization cycle can be attributed to a redistribution of water and gas hydrate within the sample. Redistribution of water and re-formation of gas hydrate is inferred from X- Ray Computed Tomography of a cylindrical hydrate-bearing Ottawa sand sample similar to the USGS samples. During the excursion from the gas hydrate stability field, images collected at the Lawrence Berkeley National Laboratory demonstrate gas hydrate dissociates first at the outer surface, where heat is efficiently transferred from a temperature-controlled bath. Upon repressurizing to stable conditions, gas hydrate remaining near the sample's central axis draws water away from the outer part of the sediment sample, and new gas hydrate grows most rapidly close along the central axis, where the original gas hydrate never dissociated during depressurization. These results can be compared to those obtained by Georgia Tech on water-saturated, natural sediment cores collected in the Gulf of Mexico. Pressure cores that never experienced a depressurization cycle and were analyzed in the Georgia Tech Instrumented Pressure Testing Chamber (IPTC) yielded significantly higher seismic velocities than conventional cores recovered at the same depth and tested at atmospheric pressure. This effect was observed even though the cores did not contain gas hydrate, attesting to the importance of maintaining pressure if the goal is to constrain in situ physical properties. A second set of measurements at Georgia Tech focused on natural samples with pore space 100 percent saturated with synthetic hydrate at low confining pressures. These samples also produced seismic velocities closer to those obtained from borehole logs, but this effect is sediment-dependent, and therefore difficult to correlate with in situ properties. Though laboratory facilities continue to provide insight via controlled studies of model systems, confidently characterizing in situ mechanical and thermal properties of hydrate-bearing material will require emphasis not on repressurized samples, but on cores that have never experienced a depressurization cycle. The consequences of releasing effective stress during pressure coring is unknown, and currently under investigation.

Agu Fall Meeting Abstracts, Dec 1, 2008

A comprehensive description of hydrate morphological evolution is related to observations, crysta... more A comprehensive description of hydrate morphological evolution is related to observations, crystal growth theory and formation thermodynamics. Transient hydrate morphologies vary significantly even under pressure, temperature and chemical concentration conditions known to be thermodynamically stable. This is in part because methane dissolves from hydrate into surrounding water or precipitates from supersaturated water to hydrate until it reaches an equilibrium saturation level. The degree of supersaturation, S, is a primary parameter for describing crystal formation from a fluid solution. Once formed, it is the change in S that guides the crystal's morphological evolution, which develops by reducing the degree of supersaturation to achieve the lowest possible energy state. This work provides examples and a comprehensive framework for understanding how the variety of initial hydrate crystal morphologies ranging from large, smoothly-surfaced, slow-growth crystals to small, dendritic, rapidly grown crystals, evolve through Oswald ripening, annealing, and Oswald series processes to a final, stable product. Understanding the causes and timescales of these growth patterns are important for interpreting macro-scale property measurements such as wave speed or shear strength that depend on hydrate morphology and contacts between hydrate and sediment grains.

Canadian Journal of Physics, 2003

Agu Fall Meeting Abstracts, Dec 1, 2001

We report on laboratory measurements of compressional and shear wave speeds in compacted, polycry... more We report on laboratory measurements of compressional and shear wave speeds in compacted, polycrystalline sI methane and sII methane-ethane hydrates and ice Ih. The hydrate samples were made from granulated ice warmed to 290 K in the presence of methane or methane-ethane gas at high pressure. The resulting porous gas hydrate samples were uniaxially compacted within the synthesis pressure vessel using a hydraulic ram with a moving piston and fixed end plug fitted with shear transducers. Once the samples were fully compacted, the temperature was cycled in steps from 258 to 288 K while the uniaxial pressure was held constant at 60 MPa. After temperature cycling was completed, the uniaxial pressure was varied between 30 and 90 MPa at 283, 273, 263 and 253 K. At the end of each experiment, the uniaxial pressure was slowly decreased to 1 atm at 253 K. Shear and compressional wave speed measurements were made throughout each experiment. For ice Ih, the sample was evacuated before compaction, the measurement temperature range was 253 to 268 K and the applied uniaxial pressure did not exceed 42 MPa. Analysis of the data produces several interesting observations. Among them are: 1) sI and sII gas hydrate resist compaction much more than ice. A pressure of 42 MPa fully compacted the ice sample at 268 K, but a pressure of 105 MPa had to be applied for several days (at temperatures of 253, 278 and 288 K) to fully compact the hydrate samples. 2) Wave speed increases at constant sample length strongly suggest grain to grain bonds form between adjacent ice or gas hydrate grains. The relative wave speed increases with time show this process is more efficient in ice samples, perhaps due to the higher mobility of water in ice's crystal lattice. 3) Within the pressure and temperature conditions studied, the wave speed based calculations of Poisson's ratio are 5 to 6% smaller in sI and sII gas hydrate than in ice. 4) Shear wave speed decreases with increasing uniaxial pressure in Ice Ih, sI methane and sII methane-ethane hydrate. This unusual behavior was well known in ice Ih but was not known to apply to gas hydrates because no independent measurements of shear wave speed versus pressure in gas hydrates were previously available.

Can J Phys, 2003

We report on compressional- and shear-wave-speed measurements made on compacted polycrystalline s... more We report on compressional- and shear-wave-speed measurements made on compacted polycrystalline sI methane and sII methane-ethane hydrate. The gas hydrate samples are synthesized directly in the measurement apparatus by warming granulated ice to 17degreesC in the presence of a clathrate-forming gas at high pressure (methane for sI, 90.2% methane, 9.8% ethane for sII). Porosity is eliminated after hydrate synthesis by compacting the sample in the synthesis pressure vessel between a hydraulic ram and a fixed end-plug, both containing shear-wave transducers. Wave-speed measurements are made between -20 and 15degreesC and 0 to 105 MPa applied piston pressure.

The American Mineralogist, Aug 1, 2004

ABSTRACT This paper presents results of shear strength and acoustic velocity (p-wave) measurement... more ABSTRACT This paper presents results of shear strength and acoustic velocity (p-wave) measurements performed on: (1) samples containing natural gas hydrate from the Mallik 2L-38 well, Mackenzie Delta, Northwest Territories; (2) reconstituted Ottawa sand samples containing methane gas hydrate formed in the laboratory; and (3) ice-bearing sands. These measurements show that hydrate increases shear strength and p-wave velocity in natural and reconstituted samples. The proportion of this increase depends on (1) the amount and distribution of hydrate present, (2) differences, in sediment properties, and (3) differences in test conditions. Stress-strain curves from the Mallik samples suggest that natural gas hydrate does not cement sediment grains. However, stress-strain curves from the Ottawa sand (containing laboratory-formed gas hydrate) do imply cementation is present. Acoustically, rock physics modeling shows that gas hydrate does not cement grains of natural Mackenzie Delta sediment. Natural gas hydrates are best modeled as part of the sediment frame. This finding is in contrast with direct observations and results of Ottawa sand containing laboratory-formed hydrate, which was found to cement grains (Waite et al. 2004). It therefore appears that the microscopic distribution of gas hydrates in sediment, and hence the effect of gas hydrate on sediment physical properties, differs between natural deposits and laboratory-formed samples. This difference may possibly be caused by the location of water molecules that are available to form hydrate. Models that use laboratory-derived properties to predict behavior of natural gas hydrate must account for these differences.

Cracking within gas hydrate-bearing sediment can occur in the field at core-scales, due to unload... more Cracking within gas hydrate-bearing sediment can occur in the field at core-scales, due to unloading as material is brought to the surface during conventional coring, and at reservoir scales if the formation is fractured prior to production. Cracking can weaken hydrate-bearing sediment, but can also provide additional surface area for dissociation and permeability pathways for enhanced gas and fluid flow. In pulse-transmission wave speed measurements, we observe cracking in laboratory-formed pure sI methane and sII methane-ethane hydrates when samples are axially unloaded while being held under gas pressure to maintain hydrate stability. Cracking events are inferred from repeated, sharp decreases in shear wave speed occurring concurrently with abrupt increases in sample length. We also visually observe cracks in the solid samples after their recovery from the apparatus following each experiment. Following a cracking event, we observe evidence of rapid crack healing, or annealing expressed as nearly complete recovery of the shear wave speed within approximately 20 minutes. Gas hydrate recrystallization, grain growth, and annealing have also been observed in optical cell experiments and SEM imagery over a similar time frame. In a recovered hydrate-bearing core that is repressurized for storage or experimentation, rapid crack healing and recrystallization can partly restore lost mechanical strength and raise wave speeds. In a fractured portion of a hydrate-bearing reservoir, the rapid healing process can close permeable cracks and reduce the surface area available for dissociation.

The American Mineralogist, 2004

Nat Geosci, 2010

Marine sediments contain about 500-10,000Gt of methane carbon, primarily in gas hydrate. This res... more Marine sediments contain about 500-10,000Gt of methane carbon, primarily in gas hydrate. This reservoir is comparable in size to the amount of organic carbon in land biota, terrestrial soils, the atmosphere and sea water combined, but it releases relatively little methane to the ocean and atmosphere. Sedimentary microbes convert most of the dissolved methane to carbon dioxide. Here we show

Seismic wave attenuation analysis, the study of how seismic waves lose their energy while they tr... more Seismic wave attenuation analysis, the study of how seismic waves lose their energy while they travel, relies on models to transform measured data into descriptions of the subsurface environment. Seismic attenuation in fluid bearing rock is dominated by interactions between the fluid and the rock. Standard attenuation theories model attenuation due to viscous shear within the flowing fluid (local fluid flow), shear between the pore fluid and pore walls (global fluid flow), or fluid-assisted thermal diffusion. All of these models rely solely on physical and geometrical properties of the system to describe the mechanism by which attenuation occurs. These models do not account for attenuative physicochemical interactions between the pore fluid and pore walls. Effects of physicochemical interactions between the pore fluid and pore walls are considered in this work. Physicochemical interactions between the solid crack surface and the fluid meniscus can restrict contact line motion (motion of the three phase boundary) across the solid surface. In partially saturated cracks subjected to seismic deformation, two consequences of restricted contact line motion are crack stiffening and energy loss. Fluid redistribution in a deforming, partially saturated crack occurs via meniscus deformation or contact line motion or both. If there is some resistance to contact line motion, during the initial response to fluid redistribution the contact lines remain stationary while the meniscus deforms. The meniscus deforms because the fluid pressure is changing, and these fluid pressure changes always act against further crack deformation. The fluid pressurization makes the crack more stiff than a dry crack or a crack in which only stiffening due to viscous flow is considered. If crack deformation pressurizes the fluid enough that the force applied by the deforming meniscus on a contact line exceeds the resistive force holding the contact line stationary, contact line motion occurs. Contact line motion against the resistive force requires energy, which is lost from the seismic wave causing the original crack deformation. This friction-like energy loss mechanism is responsible for the attenuation in the restricted meniscus motion model. The restricted meniscus motion model interprets attenuation and stiffness data which can not be described by attenuation theories relying solely on the physical and geometrical parameters (pore fluid viscosity, fluid and solid compressibilities) used in the standard models. The restricted geometry, meniscus motion model, born from attenuation and stiffening observations in an artificial glass crack sample, is itself composed of parameters which can be measured or estimated using experiments which are distinct from the attenuation and stiffness measurements. These independently measured model parameters are in general agreement with the model parameters used to fit attenuation and stiffness results measured on the artificial glass crack samples.

Scientific Investigations Report, 2010

Scientific Investigations Report, 2009

The Journal of the Acoustical Society of America, 2011

Geophysical Research Letters, 2007

Geochemistry, Geophysics, Geosystems, 2008

Agu Fall Meeting Abstracts, Dec 1, 2006

Physical property measurements on cores containing natural gas hydrate are typically performed on... more Physical property measurements on cores containing natural gas hydrate are typically performed on material exposed to non-in situ conditions at least briefly during recovery. In situ temperature and effective stress are difficult to maintain during core recovery, but pressure-coring systems such as the HYACINTH, Fugro, and IODP PCS can maintain in situ hydrostatic pressure during core retrieval. To simulate effects of transferring pressure-core samples to storage vessels, the USGS conducted physical property measurements on Ottawa sand samples containing methane gas and gas hydrate before and after samples were depressurized out of, then repressurized back into, the gas hydrate stability field. For measurements made along a sample's cylindrical axis, compressional and shear wave speed, shear strength, and thermal conductivity increased 10 to 30 percent following a 5 minute excursion from the gas hydrate stability field. Experiments were conducted in unsaturated sand in the presence of methane gas, and increases in measured physical property values resulting from the repressurization cycle can be attributed to a redistribution of water and gas hydrate within the sample. Redistribution of water and re-formation of gas hydrate is inferred from X- Ray Computed Tomography of a cylindrical hydrate-bearing Ottawa sand sample similar to the USGS samples. During the excursion from the gas hydrate stability field, images collected at the Lawrence Berkeley National Laboratory demonstrate gas hydrate dissociates first at the outer surface, where heat is efficiently transferred from a temperature-controlled bath. Upon repressurizing to stable conditions, gas hydrate remaining near the sample's central axis draws water away from the outer part of the sediment sample, and new gas hydrate grows most rapidly close along the central axis, where the original gas hydrate never dissociated during depressurization. These results can be compared to those obtained by Georgia Tech on water-saturated, natural sediment cores collected in the Gulf of Mexico. Pressure cores that never experienced a depressurization cycle and were analyzed in the Georgia Tech Instrumented Pressure Testing Chamber (IPTC) yielded significantly higher seismic velocities than conventional cores recovered at the same depth and tested at atmospheric pressure. This effect was observed even though the cores did not contain gas hydrate, attesting to the importance of maintaining pressure if the goal is to constrain in situ physical properties. A second set of measurements at Georgia Tech focused on natural samples with pore space 100 percent saturated with synthetic hydrate at low confining pressures. These samples also produced seismic velocities closer to those obtained from borehole logs, but this effect is sediment-dependent, and therefore difficult to correlate with in situ properties. Though laboratory facilities continue to provide insight via controlled studies of model systems, confidently characterizing in situ mechanical and thermal properties of hydrate-bearing material will require emphasis not on repressurized samples, but on cores that have never experienced a depressurization cycle. The consequences of releasing effective stress during pressure coring is unknown, and currently under investigation.

Agu Fall Meeting Abstracts, Dec 1, 2008

A comprehensive description of hydrate morphological evolution is related to observations, crysta... more A comprehensive description of hydrate morphological evolution is related to observations, crystal growth theory and formation thermodynamics. Transient hydrate morphologies vary significantly even under pressure, temperature and chemical concentration conditions known to be thermodynamically stable. This is in part because methane dissolves from hydrate into surrounding water or precipitates from supersaturated water to hydrate until it reaches an equilibrium saturation level. The degree of supersaturation, S, is a primary parameter for describing crystal formation from a fluid solution. Once formed, it is the change in S that guides the crystal's morphological evolution, which develops by reducing the degree of supersaturation to achieve the lowest possible energy state. This work provides examples and a comprehensive framework for understanding how the variety of initial hydrate crystal morphologies ranging from large, smoothly-surfaced, slow-growth crystals to small, dendritic, rapidly grown crystals, evolve through Oswald ripening, annealing, and Oswald series processes to a final, stable product. Understanding the causes and timescales of these growth patterns are important for interpreting macro-scale property measurements such as wave speed or shear strength that depend on hydrate morphology and contacts between hydrate and sediment grains.

Canadian Journal of Physics, 2003

Agu Fall Meeting Abstracts, Dec 1, 2001

We report on laboratory measurements of compressional and shear wave speeds in compacted, polycry... more We report on laboratory measurements of compressional and shear wave speeds in compacted, polycrystalline sI methane and sII methane-ethane hydrates and ice Ih. The hydrate samples were made from granulated ice warmed to 290 K in the presence of methane or methane-ethane gas at high pressure. The resulting porous gas hydrate samples were uniaxially compacted within the synthesis pressure vessel using a hydraulic ram with a moving piston and fixed end plug fitted with shear transducers. Once the samples were fully compacted, the temperature was cycled in steps from 258 to 288 K while the uniaxial pressure was held constant at 60 MPa. After temperature cycling was completed, the uniaxial pressure was varied between 30 and 90 MPa at 283, 273, 263 and 253 K. At the end of each experiment, the uniaxial pressure was slowly decreased to 1 atm at 253 K. Shear and compressional wave speed measurements were made throughout each experiment. For ice Ih, the sample was evacuated before compaction, the measurement temperature range was 253 to 268 K and the applied uniaxial pressure did not exceed 42 MPa. Analysis of the data produces several interesting observations. Among them are: 1) sI and sII gas hydrate resist compaction much more than ice. A pressure of 42 MPa fully compacted the ice sample at 268 K, but a pressure of 105 MPa had to be applied for several days (at temperatures of 253, 278 and 288 K) to fully compact the hydrate samples. 2) Wave speed increases at constant sample length strongly suggest grain to grain bonds form between adjacent ice or gas hydrate grains. The relative wave speed increases with time show this process is more efficient in ice samples, perhaps due to the higher mobility of water in ice's crystal lattice. 3) Within the pressure and temperature conditions studied, the wave speed based calculations of Poisson's ratio are 5 to 6% smaller in sI and sII gas hydrate than in ice. 4) Shear wave speed decreases with increasing uniaxial pressure in Ice Ih, sI methane and sII methane-ethane hydrate. This unusual behavior was well known in ice Ih but was not known to apply to gas hydrates because no independent measurements of shear wave speed versus pressure in gas hydrates were previously available.

Can J Phys, 2003

We report on compressional- and shear-wave-speed measurements made on compacted polycrystalline s... more We report on compressional- and shear-wave-speed measurements made on compacted polycrystalline sI methane and sII methane-ethane hydrate. The gas hydrate samples are synthesized directly in the measurement apparatus by warming granulated ice to 17degreesC in the presence of a clathrate-forming gas at high pressure (methane for sI, 90.2% methane, 9.8% ethane for sII). Porosity is eliminated after hydrate synthesis by compacting the sample in the synthesis pressure vessel between a hydraulic ram and a fixed end-plug, both containing shear-wave transducers. Wave-speed measurements are made between -20 and 15degreesC and 0 to 105 MPa applied piston pressure.

The American Mineralogist, Aug 1, 2004

ABSTRACT This paper presents results of shear strength and acoustic velocity (p-wave) measurement... more ABSTRACT This paper presents results of shear strength and acoustic velocity (p-wave) measurements performed on: (1) samples containing natural gas hydrate from the Mallik 2L-38 well, Mackenzie Delta, Northwest Territories; (2) reconstituted Ottawa sand samples containing methane gas hydrate formed in the laboratory; and (3) ice-bearing sands. These measurements show that hydrate increases shear strength and p-wave velocity in natural and reconstituted samples. The proportion of this increase depends on (1) the amount and distribution of hydrate present, (2) differences, in sediment properties, and (3) differences in test conditions. Stress-strain curves from the Mallik samples suggest that natural gas hydrate does not cement sediment grains. However, stress-strain curves from the Ottawa sand (containing laboratory-formed gas hydrate) do imply cementation is present. Acoustically, rock physics modeling shows that gas hydrate does not cement grains of natural Mackenzie Delta sediment. Natural gas hydrates are best modeled as part of the sediment frame. This finding is in contrast with direct observations and results of Ottawa sand containing laboratory-formed hydrate, which was found to cement grains (Waite et al. 2004). It therefore appears that the microscopic distribution of gas hydrates in sediment, and hence the effect of gas hydrate on sediment physical properties, differs between natural deposits and laboratory-formed samples. This difference may possibly be caused by the location of water molecules that are available to form hydrate. Models that use laboratory-derived properties to predict behavior of natural gas hydrate must account for these differences.

Cracking within gas hydrate-bearing sediment can occur in the field at core-scales, due to unload... more Cracking within gas hydrate-bearing sediment can occur in the field at core-scales, due to unloading as material is brought to the surface during conventional coring, and at reservoir scales if the formation is fractured prior to production. Cracking can weaken hydrate-bearing sediment, but can also provide additional surface area for dissociation and permeability pathways for enhanced gas and fluid flow. In pulse-transmission wave speed measurements, we observe cracking in laboratory-formed pure sI methane and sII methane-ethane hydrates when samples are axially unloaded while being held under gas pressure to maintain hydrate stability. Cracking events are inferred from repeated, sharp decreases in shear wave speed occurring concurrently with abrupt increases in sample length. We also visually observe cracks in the solid samples after their recovery from the apparatus following each experiment. Following a cracking event, we observe evidence of rapid crack healing, or annealing expressed as nearly complete recovery of the shear wave speed within approximately 20 minutes. Gas hydrate recrystallization, grain growth, and annealing have also been observed in optical cell experiments and SEM imagery over a similar time frame. In a recovered hydrate-bearing core that is repressurized for storage or experimentation, rapid crack healing and recrystallization can partly restore lost mechanical strength and raise wave speeds. In a fractured portion of a hydrate-bearing reservoir, the rapid healing process can close permeable cracks and reduce the surface area available for dissociation.

The American Mineralogist, 2004