Scattering ofP andS waves by a spherically symmetric inclusion

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of thePS scattering is generally much stronger than theSP scattering. When averaged over all scattering angles, the mean intensity of thePS converted waves is2V _p ² /V _s ⁴ times the mean intensity of theSP converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.     

Two mantle sources, two plumbing systems: tholeiitic and alkaline magmatism of the Maymecha River basin, Siberian flood volcanic province

Rocks of two distinctly different magma series are found in a ∼4000-m-thick sequence of lavas and tuffs in the Maymecha River basin which is part of the Siberian flood-volcanic province. The tholeiites are typical low-Ti continental flood basalts with remarkably restricted, petrologically evolved compositions. They have basaltic MgO contents, moderate concentrations of incompatible trace elements, moderate fractionation of incompatible from compatible elements, distinct negative Ta(Nb) anomalies, and _Nd values of 0 to +2. The primary magmas were derived from a relatively shallow mantle source, and evolved in large crustal magma chambers where they acquired their relatively uniform compositions and became contaminated with continental crust. An alkaline series, in contrast, contains a wide range of rock types, from meymechite and picrite to trachytes, with a wide range of compositions (MgO from 0.7 to 38 wt%, SiO₂ from 40 to 69 wt%, Ce from 14 to 320 ppm), high concentrations of incompatible elements and extreme fractionation of incompatible from compatible elements (Al₂O₃/TiO₂∼1; Sm/Yb up to 11). These rocks lack Ta(Nb) anomalies and have a broad range of _Nd values, from −2 to +5. The parental magmas are believed to have formed by low-degree melting at extreme mantle depths (>200 km). They bypassed the large crustal magma chambers and ascended rapidly to the surface, a consequence, perhaps, of high volatile contents in the primary magmas. The tholeiitic series dominates the lower part of the sequence and the alkaline series the upper part; at the interface, the two types are interlayered. The succession thus provides evidence of a radical change in the site of mantle melting, and the simultaneous operation of two very different crustal plumbing systems, during the evolution of this flood-volcanic province. Received: 6 January 1998 / Accepted: 29 June 1998     

Laboratory measurements of guided‐wave propagation within a fluid‐saturated fracture

A fluid‐saturated flat channel between solids, such as a fracture, is known to support guided waves—sometimes called Krauklis waves. At low frequencies, Krauklis waves can have very low velocity and large attenuation and are very dispersive. Because they propagate primarily within the fluid channel formed by a fracture, Krauklis waves can potentially be used for geological fracture characterization in the field. Using an analogue fracture consisting of a pair of flat slender plates with a mediating fluid layer—a trilayer model—we conducted laboratory measurements of the velocity and attenuation of Krauklis waves. Unlike previous experiments using ultrasonic waves, these experiments used frequencies well below 1 kHz, resulting in extremely low velocity and large attenuation of the waves. The mechanical compliance of the fracture was varied by modifying the stiffness of the fluid seal of the physical fracture model, and proppant (fracture‐filling high‐permeability sand) was also introduced into the fracture to examine its impact on wave propagation. A theoretical frequency equation for the trilayer model was derived using the poroelastic linear‐slip interface model, and its solutions were compared to the experimental results.