Phase velocity

About: Phase velocity is a research topic. Over the lifetime, 11730 publications have been published within this topic receiving 252368 citations. The topic is also known as: phase speed.

S40RTS: A degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements

Abstract: We have developed model S40RTS of shear-velocity variation in Earth's mantle using a new collection of Rayleigh wave phase velocity, teleseismic body-wave traveltime and normal-mode splitting function measurements. This data set is an order of magnitude larger than used for S20RTS and includes new data types. The data are related to shear-velocity perturbations from the (anisotropic) PREM model via kernel functions and ray paths that are computed using PREM. Contributions to phase delays and traveltimes from the heterogeneous crust are estimated using model CRUST2.0. We calculate crustal traveltimes from long-period synthetic waveforms rather than using ray theory. Shear-velocity perturbations are parametrized by spherical harmonics up to degree 40 and by 21 vertical spline functions for a total of 35 301 degrees of freedom. S40RTS is characterised by 8000 resolved unknowns. Since we compute the exact inverse, it is straightforward to determine models associated with fewer or more unknowns by adjusting the model damping. S40RTS shares many characteristics with S20RTS because it is based on the same data types and similar modelling procedures. However, S40RTS shows more clearly than S20RTS the abrupt change in the pattern of shear-velocity heterogeneity across the 660-km phase transition and it presents a more complex patern of shear-velocity heterogeneity in the lower mantle. Utilities to visualise S40RTS and software to analyse the resolution of S40RTS (or models for different damping parameters) are made available.

Constant Q-wave propagation and attenuation

Abstract: A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. The wave propagation is completely specified by two parameters, e.g., Q and c0, a phase velocity at an arbitrary reference frequency ω0. A simple exact derivation leads to an expression for the phase velocity c as a function of frequency: c/c0 = (ω/ω0)γ, where γ = (1/π) tan−1 (1/Q). Scaling relationships for pulse propagation are derived and it is shown that for a material with a given value of Q, the risetime or the width of the pulse is exactly proportional to travel time. The travel time for a pulse resulting from a delta function source at x = 0 is proportional to xβ, where β = 1/(1 - γ). On the basis of this relation it is suggested that the velocity dispersion associated with anelasticity may be less ambiguously observed in the time domain than in the frequency domain. A steepest descent approximation derived by Strick gives a good time domain representation for the impulse response. The scaling relations are applied to field observations from the Pierre shale formation in Colorado, published by Ricker, who interpreted his data in terms of a Voigt solid with Q inversely proportional to frequency, and McDonal et al., who interpreted their data in terms of nonlinear friction. The constant Q theory fits both sets of data.

Longshore currents generated by obliquely incident sea waves: 1

Abstract: By using known results on the radiation stress associated with gravity waves, the total lateral thrust exerted by incoming waves on the beach and in the nearshore zone is rigorously shown to equal (E0/4) sin 2θ0 per unit distance parallel to the coastline, where E0 denotes the energy density of the waves in deep water and θ0 denotes the waves' angle of incidence. The local stress exerted on the surf zone in steady conditions is shown to be given by (D/c) sin θ per unit area, where D is the local rate of energy dissipation and c is the phase velocity. These relations are independent of the manner of the energy dissipation, but, because breaker height is related to local depth in shallow water, it is argued that ordinarily most of the dissipation is due to wave breaking, not to bottom friction. Under these conditions the local mean longshore stress in the surf zone will be given by (5/4)ρumax2 s sin θ, where ρ is the density, umax is the maximum orbital velocity in the waves, s is the local beach slope, and θ is the angle of incidence. It is further shown that, if the friction coefficient C on the bottom is assumed constant and if horizontal mixing is neglected, the mean longshore component of velocity is given by (5π/8)(s/C) umax sin θ. This value is proportional to the longshore component of the orbital velocity. When the horizontal mixing is taken into account, the longshore currents observed in field observations and laboratory experiments are consistent with a friction coefficient of about 0.010.

Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis: I - Phase velocity maps

Abstract: SUMMARY Empirical Green’s functions (EGFs) between pairs of seismographs can be estimated from the time derivative of the long-time cross-correlation of ambient seismic noise. These EGFs reveal velocity dispersion at relatively short periods, which can be used to resolve structures in the crust and uppermost mantle better than with traditional surface-wave tomography. We combine Rayleigh-wave dispersion estimates from EGFs and from traditional two-station (TS) analysis into a new approach to surface-wave array tomography with data from dense receiver arrays. We illustrate the methodology with continuous broad-band recordings from a temporary seismographic network on the southeastern part of the Tibetan plateau, in Sichuan and Yunnan provinces, SW China. The EGFs are robust under temporal changes in regional seismicity and the use of either ambient noise (approximated by records without signal from events with magnitude mb ≥ 5 or 4) or surface wave coda produces similar results. The EGFs do not strongly depend on the presence of large earthquakes, but they are not reciprocal for stations aligned in the N‐S direction. This directionality reflects the paucity of seismicity to the north of the array. Using a far-field representation of the surface-wave Green’s function and an image transformation technique, we infer from the EGFs the Rayleigh-wave phase velocity dispersion in the period band from 10‐30 s. A classical TS approach is used to determine Rayleigh-wave phase velocity dispersion between 20‐120 s. Together, they constrain phase velocity variations for T = 10‐120 s, which can be used to study the structure from the crust to the upper mantle. Beneath SE Tibet, short and intermediate period (10‐80 s) phase velocities are prominently low, suggesting that the crust and upper mantle beneath SE Tibet is characterized by slow shear wave propagation.

The critical layer for internal gravity waves in a shear flow

Abstract: Internal gravity waves of small amplitude propagate in a Boussinesq inviscid, adiabatic liquid in which the mean horizontal velocity U(z) depends on height z only. If the Richardson number R is everywhere larger than 1/4, the waves are attenuated by a factor as they pass through a critical level at which U is equal to the horizontal phase speed, and momentum is transferred to the mean flow there. This effect is considered in relation to lee waves in the airflow over a mountain, and in relation to transient localized disturbances. It is significant in considering the propagation of gravity waves from the troposphere to the ionosphere, and possibly in transferring horizontal momentum into the deep ocean without substantial mixing.