The effect of the extent of freezing on seismic velocities in unconsolidated permafrost

Geophysics ◽  
1986 ◽  
Vol 51 (6) ◽  
pp. 1285-1290 ◽  
Author(s):  
Robert W. Zimmerman ◽  
Michael S. King
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Compressional Wave ◽  
Seismic Velocities ◽  
Wave Speeds ◽  
Direct Measurements ◽  
Two Parameters ◽  
Decreasing Functions ◽  
Increasing Function ◽  
Quartz Grains

We develop a model to relate velocities of seismic waves in unconsolidated permafrost is idealized as an assemblage of spherical quartz grains imbedded in a matrix composed of spherical water inclusions in ice. The theory of Kuster and Toksöz, based on wave‐scattering considerations, is used to determine the effective elastic moduli, and hence the wave speeds. The Hasin-Shtrikman theoretical bounds on the elastic moduli of heterogeneous materials and considerations establish the plausibility of the model. The model predicts [Formula: see text] and [Formula: see text] to be decreasing functions of both the porosity and the water‐to‐ice ratio, and the ratio [Formula: see text] to be an increasing function of these two parameters. The theory is then applied to laboratory measurements of shear‐ and compressional‐wave velocities in 23 permafrost samples from different sites in the Beaufort Sea, Mackenzie River Valley, and Canadian Arctic islands. Although no direct measurements were made of the extents of freezing in these samples, the data are consistent with the predictions of the model. We show the theory can be used to predict the extent of freezing of the water in the pore spaces, based on knowledge of the porosity and either of the two wave speeds.

VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS

Geophysics ◽  
1974 ◽  
Vol 39 (5) ◽  
pp. 587-606 ◽  
Author(s):  
Guy T. Kuster ◽  
M. Nafi Toksöz
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Matrix Material ◽  
Composite Medium ◽  
Solid Matrix ◽  
Seismic Velocities ◽  
Displacement Fields ◽  
Two Phase ◽  
The Matrix ◽  
In Series

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. It is found that the concentration, shapes, and properties of the inclusions are important parameters. A concentration of a fraction of one percent of thin (small aspect ratio) inclusions could affect the compressional and shear velocities by more than ten percent. For both sedimentary and igneous rock models, the calculations for “dry” (i.e.,air‐saturated) and water‐saturated states indicate that the compressional velocities change significantly while the shear velocities change much less upon saturation with water.

Accounting for pressure-dependent ultrasonic beam skew in transversely isotropic rocks: combining modelling and measurement of anisotropic wave speeds

2020 ◽  
Vol 221 (1) ◽  
pp. 231-250 ◽  
Author(s):  
Wei Li ◽  
Douglas R Schmitt ◽  
Xiwei Chen
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
Confining Pressure ◽  
P Wave ◽  
Diffraction Effect ◽  
Finite Width ◽  
Ultrasonic Beam ◽  
Wave Speeds ◽  
Dynamic Elastic Moduli

SUMMARY The intrinsic anisotropy of rock influences the paths of propagating seismic waves and indicates mineralogical texture and strains; and as such it is important that laboratory measurements of such properties be fully understood. Usually, when studying anisotropy, ultrasonic wave speeds are measured in a variety of strategic directions and, subsequently transformed to the dynamic elastic moduli using symmetry-appropriate formula. For transversely isotropic rocks the moduli are ideally found by measuring wave speeds in directions vertical, parallel and oblique to the foliation or bedding using finite-width ultrasonic transducers. An important, but ignored, complication is that at oblique angles the ultrasonic beam unavoidably deviates, or skews, away from the transmitter's normal axis making proper wave speed determinations difficult. The pressure dependence of the wave speeds further confounds finding a solution as skew angles, too, vary with confining pressure. We develop a new technique that incorporates dual ultrasonic receivers to account for and mitigate the effects of the pressure-dependent beam skew problem. Anisotropy measurements to 200 MPa hydrostatic confining pressure combined with recent beam modeling algorithms illustrate the errors obtained in the determined wave speeds that are subsequently magnified in calculating the full set of elastic stiffnesses. In materials with P-wave anisotropies near 30 per cent the error introduced by ignoring beam skew exceeds the transit time picking errors by more than a factor of three, these propagate to much larger errors in the stiffnesses particularly for C13 and the dynamic elastic moduli referred to C13. Meanwhile, shortening the sample or enlarging the transmitter size is not suggested to counter the beam skew issue because it reduces the beam skew effect but increases the diffraction effect.

scholarly journals Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

2015 ◽  
Vol 9 (1) ◽  
pp. 367-384 ◽  
Author(s):  
A. Diez ◽  
O. Eisen
Keyword(s):  
Seismic Waves ◽  
Dynamic Behaviour ◽  
Ice Core ◽  
Ice Cores ◽  
Seismic Wave Propagation ◽  
Elasticity Tensor ◽  
Reflection Coefficients ◽  
Seismic Velocities ◽  
Crystal Anisotropy ◽  
Elasticity Tensors

Abstract. A preferred orientation of the anisotropic ice crystals influences the viscosity of the ice bulk and the dynamic behaviour of glaciers and ice sheets. Knowledge about the distribution of crystal anisotropy is mainly provided by crystal orientation fabric (COF) data from ice cores. However, the developed anisotropic fabric influences not only the flow behaviour of ice but also the propagation of seismic waves. Two effects are important: (i) sudden changes in COF lead to englacial reflections, and (ii) the anisotropic fabric induces an angle dependency on the seismic velocities and, thus, recorded travel times. A framework is presented here to connect COF data from ice cores with the elasticity tensor to determine seismic velocities and reflection coefficients for cone and girdle fabrics. We connect the microscopic anisotropy of the crystals with the macroscopic anisotropy of the ice mass, observable with seismic methods. Elasticity tensors for different fabrics are calculated and used to investigate the influence of the anisotropic ice fabric on seismic velocities and reflection coefficients, englacially as well as for the ice–bed contact. Hence, it is possible to remotely determine the bulk ice anisotropy.

FLUID SATURATION EFFECTS ON DYNAMIC ELASTIC PROPERTIES OF SEDIMENTARY ROCKS

Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 895-921 ◽  
Author(s):  
A. R. Gregory
Keyword(s):  
Shear Wave ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Compressional Wave ◽  
Reflection Coefficients ◽  
High Porosity ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Fluid Saturation ◽  
Saturation Effects

The influence of saturation by water, oil, gas, and mixtures of these fluids on the densities, velocities, reflection coefficients, and elastic moduli of consolidated sedimentary rocks was determined in the laboratory by ultrasonic wave propagation methods. Twenty rock samples varying in age from Pliocene to early Devonian and in porosity from 4 to 41 percent were tested under uniform pressures equivalent to subsurface depths of 0 to 18,690 ft. Fluid saturation effects on compressional‐wave velocity are much larger in low‐porosity than in high‐porosity rocks; this correlation is strengthened by elevated pressures but is absent at atmospheric pressure. At a frequency of 1 MHz, the shear‐wave velocities do not always decrease when liquid pore saturants are added to rocks as theorized by Biot; agreement with theory is dependent upon pressure, porosity, fluid‐mineral chemical interactions, and the presence of microcracks in the cementing material. Experimental results support the belief that lower compressional‐wave velocities and higher reflection coefficients are obtained in sedimentary rocks that contain gas. Replacing pore liquids with gas markedly reduces the elastic moduli of rocks, and the effect is enhanced by decreasing pressure. As a rule, the moduli decrease as the porosity increases; Poisson’s ratio is an exception to the rule. Liquid and gas saturation in consolidated rocks can also be distinguished by the ratio of compressional and shear wave velocities [Formula: see text]. The potential diagnostic value of elastic moduli in seismic exploration may stimulate interest in the use of shear‐wave reflection methods in the field.

scholarly journals Direct Measurements of Giant Star Effective Temperatures and Linear Radii: Calibration against Spectral Types and V − K Color

2021 ◽  
Vol 922 (2) ◽  
pp. 163
Author(s):  
Gerard T. van Belle ◽  
Kaspar von Braun ◽  
David R. Ciardi ◽  
Genady Pilyavsky ◽  
Ryan S. Buckingham ◽  
...  
Keyword(s):  
Effective Temperature ◽  
Spectral Energy Distribution ◽  
Angular Size ◽  
Spectral Energy ◽  
Distribution Fitting ◽  
Data Set ◽  
Giant Stars ◽  
Direct Measurements ◽  
Versus Color ◽  
Two Parameters

Abstract We calculate directly determined values for effective temperature (T eff) and radius (R) for 191 giant stars based upon high-resolution angular size measurements from optical interferometry at the Palomar Testbed Interferometer. Narrow- to wideband photometry data for the giants are used to establish bolometric fluxes and luminosities through spectral energy distribution fitting, which allows for homogeneously establishing an assessment of spectral type and dereddened V 0 − K 0 color; these two parameters are used as calibration indices for establishing trends in T eff and R. Spectral types range from G0III to M7.75III, V 0 − K 0 from 1.9 to 8.5. For the V 0 − K 0 = {1.9, 6.5} range, median T eff uncertainties in the fit of effective temperature versus color are found to be less than 50 K; over this range, T eff drops from 5050 to 3225 K. Linear sizes are found to be largely constant at 11 R ⊙ from G0III to K0III, increasing linearly with subtype to 50 R ⊙ at K5III, and then further increasing linearly to 150 R ⊙ by M8III. Three examples of the utility of this data set are presented: first, a fully empirical Hertzsprung–Russell diagram is constructed and examined against stellar evolution models; second, values for stellar mass are inferred based on measures of R and literature values for log g ; finally, an improved calibration of an angular size prediction tool, based upon V and K values for a star, is presented.

scholarly journals Correlation of Elastic Moduli and Serpentine Content in Ultramafic Rocks

2019 ◽  
Author(s):  
Aida Farough ◽  
Alexander Karrasch
Keyword(s):  
Physical Properties ◽  
Lower Crust ◽  
Elastic Moduli ◽  
Oceanic Lithosphere ◽  
Ultramafic Rocks ◽  
Seismic Velocities ◽  
Rock Composition ◽  
Metamorphic History ◽  
History Of ◽  
Thin Crust

Understanding the physical properties of ultramafic rocks is important for evaluating awide variety of petrologic models of the oceanic lithosphere, particularly upper mantle and lower crust. Hydration of oceanic peridotites results in increasing serpentine content, which affects lithospheric physical properties and the global bio/geochemical cycles of various elements. In understanding tectonic, magmatic and metamorphic history of the oceanic crust, interpreting seismic velocities, rock composition and elastic moduli are of fundamental importance. In this study we show that as serpentine content increases, density decreases linearly with a slope of 7.85. We also correlate increase in serpentine content with a linear decline in shear, bulk and Young’s moduli with slopes of 0.48, 0.77, 0.45 respectively. Our results show that increase in serpentine content of lower crust and forearc mantle could decrease elasticity of lithospehere and result in break-offs. Therefore tectonic processes at peridotite rich slow spreading ridges may be strongly affected by serpentine content, particularly serpentinization may be responsible for discontinuities in thin crust, and formation of weak fault zones.

scholarly journals Can the Mass Balance of a Glacier be Estimated from its Equilibrium-Line Altitude?

1984 ◽  
Vol 30 (106) ◽  
pp. 364-368 ◽  
Author(s):  
Roger J. Braithwaite
Keyword(s):  
Mass Balance ◽  
Linear Relationship ◽  
Sufficient Accuracy ◽  
Statistical Analyses ◽  
Equilibrium Line ◽  
Model Parameters ◽  
Equilibrium Line Altitude ◽  
Direct Measurements ◽  
Balanced Budget ◽  
Two Parameters

AbstractThe possibility of replacing or supplementing direct measurements of mass balance by estimates calculated from equilibrium-line altitude (ELA) measurements is investigated by statistical analyses of data from 31 glaciers. A linear relationship between mass balance and ELA in terms of two parameters, the effective balance gradient and the balanced-budget ELA, is tested. It is concluded that existing mass-balance series can be usefully extrapolated by using ELA data for additional years. However, accurate mass balance cannot be calculated for glaciers where no such measurements have been made because of the difficulties in prescribing the two model parameters with sufficient accuracy. For example, the effective balance gradient is of the order of 5 mm water/m so that errors of only a few decametres in the estimation of the balanced-budget ELA can have a great effect upon calculations of mass balance.

The temperature dependence of seismic waves in ice

1974 ◽  
Vol 13 (67) ◽  
pp. 144-147 ◽  
Author(s):  
Heinz Kohnen
Keyword(s):  
Temperature Dependence ◽  
Seismic Waves ◽  
Seismic Velocity ◽  
Seismic Velocities ◽  
Velocity Data

In this paper all available seismic velocity data from Greenland and Antarctica are used to determine the relation between seismic velocities and temperatures in the ice.

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