Velocity and attenuation in partially molten rocks

Interpretation of seismic velocity and attenuation in partially molten rocks has been limited, with few exceptions, to models that assume the melt to be distributed either as spheres or as thin films. However, other melt phase geometries, such as interconnected tubes along grain edges, might equally well account for seismic observations if there is a much larger fraction of melt. Seismic velocity and attenuation are estimated in rocks in which the melt phase has the tube geometry, and the results are compared with results expected for the more familiar film model under similar conditions. For a given melt fraction, tubes are found to give moduli intermediate between moduli for rigid spherical inclusions and compliant films. For example, in polycrystalline olivine at 20 kbar the model predicts a decrease in V/sub s/ of 10% and a decrease in V/sub p/ of 5% at 0.05 melt fraction, without considering inelastic relaxation. Shear attenuation appears to be dominated by viscous flow of melt between the tubes and/or films. For olivine the tube model predicts the increment of relaxation due to melt, ..delta mu../..mu.., to be 0.01 at 0.05 melt fraction. Relaxation of the bulk modulus is dominated by flow between melt pockets ofmore » different shape, heat flow, and solid-melt phase change. If melt is present, considerable bulk attenuation is expected, although the relaxation may be observable only at long periods, outside the seismic body wave band.« less

[1]  J. A. Tyburczy,et al.  Mechanical and thermodynamic constraints on fluid distribution in partial melts , 1979 .

[2]  D. Shimozuru.  On the Possibility of the Existence of the Molten Portion in the Upper Mantle of the Earth , 1963 .

[3]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[4]  J. Vaisnys.  Propagation of acoustic waves through a system undergoing phase transformations , 1968 .

[5]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[6]  Y. Fung.  Foundations of solid mechanics , 1965 .

[7]  J. Mackenzie,et al.  The Elastic Constants of a Solid containing Spherical Holes , 1950 .

[8]  佐藤 泰夫.  Velocity of Elastic Waves Propagated in Media with Small Holes. , 1952 .

[9]  Cyril Stanley Smith,et al.  SOME ELEMENTARY PRINCIPLES OF POLYCRYSTALLINE MICROSTRUCTURE , 1964 .

[10]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  J. Watt,et al.  The Elastic Properties of Composite Materials , 1976 .

[12]  Amos Nur,et al.  Melt squirt in the asthenosphere , 1975 .

[13]  T. Shankland.  Electrical conduction in rocks and minerals: Parameters for interpretation , 1975 .

[14]  Attenuation of elastic waves in granular mediums , 1965 .

[15]  F. Gaßmann.  Uber die Elastizitat poroser Medien. , 1961 .

[16]  Don L. Anderson,et al.  The Effect of Temperature and Partial Melting on Velocity and Attenuation in a Simple Binary System , 1968 .

[17]  D. C. Presnall,et al.  Changes in electrical conductivity of a synthetic basalt during melting , 1972 .

[18]  L. Walpole,et al.  On the overall elastic moduli of composite materials , 1969 .

[19]  Tai Te Wu,et al.  The effect of inclusion shape on the elastic moduli of a two-phase material* , 1966 .

[20]  D. Gough.  Electrical Conductivity under Western North America in Relation to Heat Flow, Seismology, and Structure , 1974 .

[21]  C. Zener.  Elasticity and anelasticity of metals , 1948 .

[22]  Maurice A. Biot,et al.  Generalized Theory of Acoustic Propagation in Porous Dissipative Media , 1962 .

[23]  M. N. Toksoz,et al.  Attenuation of seismic waves in dry and saturated rocks: II. Mechanisms , 1979 .

[24]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[25]  J. B. Walsh.  New analysis of attenuation in partially melted rock , 1969 .

[26]  J. Oldroyd.  The Effect of Small Viscous Inclusions on the Mechanical Properties of an Elastic Solid , 1956 .

[27]  F. Frank,et al.  Two-component Flow Model for Convection in the Earth's Upper Mantle , 1968, Nature.

[28]  Guriĭ Nikolaevich Savin,et al.  Stress concentration around holes , 1961 .

[29]  R. Gordon,et al.  Velocity and internal friction in partial melts , 1975 .

[30]  S. Solomon.  Seismic-wave attenuation and partial melting in the upper mantle of North America , 1972 .

[31]  S. Boucher.  On the Effective Moduli of Isotropic Two-Phase Elastic Composites , 1974 .

[32]  J. B. Walsh.  The effect of cracks on the compressibility of rock , 1965 .

[33]  H. Waff,et al.  Equilibrium fluid distribution in an ultramafic partial melt under hydrostatic stress conditions , 1979 .

[34]  Einar Kjartansson,et al.  Constant Q-wave propagation and attenuation , 1979 .

[35]  T. Shankland,et al.  Conductivity in fluid‐bearing rocks , 1974 .

[36]  H. Waff.  Theoretical considerations of electrical conductivity in a partially molten mantle and implications for geothermometry , 1974 .

[37]  D. Walker,et al.  A numerical treatment of melt/solid segregation: Size of the eucrite parent body and stability of the terrestrial low-velocity zone , 1978 .

[38]  D. L. Anderson,et al.  Physical mechanisms of seismic‐wave attenuation , 1970 .

[39]  J. Nicholls,et al.  High-temperature properties of silicate liquids: applications to the equilibration and ascent of basic magma , 1977, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[40]  C. Goetze.  A BRIEF SUMMARY OF OUR PRESENT DAY UNDERSTANDING OF THE EFFECT OF VOLATILES AND PARTIAL MELT ON THE MECHANICAL PROPERTIES OF THE UPPER MANTLE , 1977 .

[41]  Bernard Budiansky,et al.  Viscoelastic properties of fluid-saturated cracked solids , 1977 .

[42]  A. Nur.  Viscous phase in rocks and the low‐velocity zone , 1971 .

[43]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[44]  Bernard Budiansky,et al.  Seismic velocities in dry and saturated cracked solids , 1974 .

[45]  K. Winkler,et al.  Seismic Wave Attenuation in Rocks , 1979 .

[46]  J. B. Walsh.  Seismic wave attenuation in rock due to friction , 1966 .

[47]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[48]  D. L. Anderson,et al.  Partial melting and the low-velocity zone , 1970 .

[49]  T. Shankland,et al.  Partial melting and electrical conductivity anomalies in the upper mantle , 1977 .