Ambient noise surface wave inversion using OBS data from the north Atlantic, north of the Gloria fault.

<p>The Gloria fault is a strike-slip oceanic plate boundary fault, which has remained poorly studied due mostly to its remote location in the north Atlantic Ocean. The fault has hosted some of the largest strike-slip earthquakes in the oceanic domain, notably the 1941 M8.3 and the 1975 M8.1 earthquakes, and generating tsunamis is the surrounding areas.</p><p>The seismic data used for this study was recorded by 12 broadband ocean bottom seismometers (OBSs) located about 100 km north of the Gloria fault during a 10-month experiment. The dataset has been used before to image crustal and mantle discontinuities using receiver function analysis and to infer the S-wave velocity structure of the oceanic lithosphere north of the Gloria fault from P-wave polarization. These studies indicate a slight crustal thickening towards the Gloria fault, as well as an increase in uppermost mantle S-wave velocities towards the fault.</p><p>In this study, we use ambient noise surface wave tomography to find the velocity structure beneath the OBS deployment. First, we present a 1D shear-velocity model obtained from inversion of the average fundamental mode Rayleigh and Love wave group and phase velocities. In addition, the hydrophone is also used to better constrain the inversion at shallow depths, because the hydrophone shows a clear fundamental mode without interference of the first higher mode. Because of the short interstation distances of the array, it is not possible to extract the dispersion curves at periods longer than ~16 s. To compute the Vs inversions, we used the code SURF96 (Herrmann and Ammon, 2004) and consider a water layer in the initial model for Rayleigh waves, because these waves are affected by the water layer. Our results show an upper mantle low-velocity zone, which may be related to serpentinization due to the proximity of the Gloria Fault. Finally, we present the lateral variations of group and phase velocities, as a function of period obtained using FMST (Rawlinson and Sambridge, 2005), which show strong contrast velocity anomalies at the center of the array at short periods (shallow depths).</p><p>The authors acknowledge support from the Portuguese FCT – Fundação para a Ciência e a Tecnologia, I.P., within the scope of project UTAP-EXPL/EAC/0056/2017 and with the FCT grant PD/BD/135069/2017 - IDL.</p>

Rayleigh wave velocity maps beneath the Caucasus from the Caucasus seismic network (CNET)

Ambient noise surface wave tomography is a widely used method for determining the velocity structure of the upper layers of the Earth. It is based on the fact that the cross-correlation function (CCF) of noise at two stations, averaged over a long time interval, determines the Green's function of the surface wave. This allows us to estimate the group and phase velocities of surface waves on the paths between stations. The method was applied to the records of the vertical components of 67 seismic stations of the Caucasian network CNET network, which were obtained during 2018. The cross-correlation functions for all interstation paths were calculated. The dispersion curves of group and phase Rayleigh velocities for periods from 5 to 30 s were obtained by means of frequency-time analysis. The lateral distribution of the velocities was received for periods from 7 to 22 s, which correlate with velocity structure at depths of 5-25 km. The group and phase velocity maps for Rayleigh wave for periods 7, 10, 12, 14, 17, 22 s are presented.

Waveguided modes in a planar structure «graphene – thin semiconductor film – graphene»

We investigated optical-range waveguide modes propagating in a semiconductor film sandwiched between two graphene plates. The mode characteristics were shown to depend on the chemical potential of graphene and the film thickness. Based on the numerical analysis, we obtained dispersion relations for the first waveguide modes, frequency dependences of their group and phase velocities, and the distribution of the energy flux density in the structure. We discovered the presence of spectral bands characterized by small phase and negative group velocities of the waveguide modes. The possibility of tuning the waveguide mode by changing the chemical potential of graphene and the thickness of the semiconductor film was established.

May Rayleigh waves propagate with group- and phase-velocities of opposite sign in the valley of Mexico City?

Con base a la fórmula que determina la velocidad de grupo de las ondas sísmicas y utilizando resultados previamente publicados por los autores, se discute en forma teórica la ocurrencia de velocidades de grupo negativas de ondas de Rayleigh en modelos simplificados de la cuenca del Valle de México.

Do dipole sonic logs measure group or phase velocity (revisited)?

We have revisited the debate about whether flexural waves from dipole sonic tools and standard processing algorithms measure group or phase velocities in anisotropic formations. We observe that much of the confusion arises from a failure to understand the different meanings of group and phase velocities. Using a transversely isotropic medium with a vertical axis of symmetry that exhibits a triplication in its S-wave group slowness surface, we generate synthetic flexural sonic waveforms corresponding to boreholes at angles of 0°–90° with respect to the anisotropy symmetry axis in 1° increments. We processed these synthetic data using standard time- and frequency-domain semblance methods. The results conclusively demonstrate that dipole sonic logs measure the group slowness for the group angle corresponding to the angle between the borehole and the anisotropic symmetry axis. In addition, data that we have evaluated suggest that current tool geometries and semblance processing may not always be sensitive enough to resolve all branches of the group slowness triplication surface.

THE MODIFIED WHITHAM MODULATION THEORY FOR THE NONLINEAR KLEIN-GORDON-FOCK EQUATION WITH THE SIMPLEST RATIONAL FUNCTION AS ITS POTENTIAL

It is well-known that one can construct approximate solution of the nonlinear KleinGordon-Fock equation (NKGF) by means of the Whitham modulation theory (Whitham, 1977). In this work in the framework of the modified Whitham modulation theory presented at (Alekseeva, Rassadin, 2018) and (Kostromina et al., 2017) for NKGF with potential U(x) = (x–1/x)2 its asymptotic solution v(x, t) has been found. Due to isochronism of onedimensional movement of classical particle with unit mass in this potential amplitude a(x, t) of asymptotical solution obeys the linear transfer equation ∂a/∂t + V∂a/∂x = 0 with velocity V belonging to the interval –1<V<1. Peculiarity of the constructed solution is absence of gradient catastrophe therefore it is convenient for investigation of the next terms of asymptotic expansion of the NKGF solution with considered potential (Maslov, Omel’yanov, 1981). Product of Whitham-analogs of group and phase velocities of wave from constructed asymptotic solution of NKGF is equal to unit. This is the same value as for the linear Klein-Gordon-Fock equation. The mean square <v2(x, t)> of asymptotic solution of NKGF has been calculated under assumption that its initial phase shift is random value with stable distribution of probabilities. The obtained asymptotic solution due to its simplicity and informativity can be used by lecturers to illustrate abilities of the Whitham modulation theory.

Group versus Phase Velocity of Shear Waves in Soft Tissues

Across the varieties of waves that have been studied in physics, it is well established that group velocities can be significantly greater than or less than phase velocities measured within comparable frequency bands, depending on the particular mechanisms involved. The distinction between group and phase velocities is important in elastography, because diagnoses are made based on shear wave speed estimations from a variety of techniques. We review the general definitions of group and phase velocity and examine their specific relations within an important general class of rheological models. For the class of tissues and materials exhibiting power law dispersion, group velocity is significantly greater than phase velocity, and simple expressions are shown to interrelate the commonly measured parameters. Examples are given from phantoms and tissues.