Surface wave tomography for azimuthal anisotropy in a strongly reduced parameter space

Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.     

Existence of transverse waves in anisotropic poroelastic media

Out of the four waves in an anisotropic poroelastic medium, two are termed as quasi-transverse waves. The prefix 'quasi' refers to their polarizations being nearly, but not exactly, perpendicular to direction of propagation. In this composite medium, unlike perfectly elastic medium, the propagation of a longitudinal wave along a phase direction may not be accompanied by transverse waves. The existence of a transverse wave in anisotropic poroelastic media is ensured by the two equations restricting the choice of elastic coefficients of porous aggregate as well as fluid–solid coupling. Necessary and sufficient conditions for the existence of transverse waves along the coordinate axes and in the coordinate planes for general anisotropy are discussed. The discussion is extended to the case of orthotropic materials and existence for few specific phase directions is also explored. The conditions for the transverse waves decided on the basis of their apparent polarizations, that is, particle motion being perpendicular to ray direction, are also discussed. For a particular numerical model, the existence of these apparent transverse waves is solved numerically for phase directions in coordinate planes. For general directions of phase propagation, the existence of these transverse waves is checked graphically for the chosen numerical model.     

Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling

The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.     

Synchronizing seismic networks with ambient noise

The technique of retrieving Green's functions by pairwise correlation of a random wavefield is used to estimate the stability of the timing system of a seismic network. The method is demonstrated with data from a network consisting of stations with four independent clocks and GPS-receivers. For a two years period, daily measurements of the timing error of each of the four systems are obtained. These measurements can be used to correct the timing of the data in periods without GPS reception. The accuracy of this method can exceed the precision of the internal station clocks already after a single day of uncorrected drift.     

Field experiment and numerical study on active vibration isolation by horizontal blocks in layered ground under vertical loading

In this paper, a series of field experiments were carried out to investigate the active vibration isolation for a surface foundation using horizontal wave impedance block (WIB) in a multilayered ground under vertical excitations. The velocity amplitude of ground vibration was measured and the root-mean-square (RMS) velocity is used to evaluate the vibration mitigation effect of the WIB. The influences of the size, the embedded depth and the shear modulus of the WIB on the vibration mitigation were also systematically examined under different loading conditions. The experimental results convincingly indicate that WIB is effective to reduce the ground vibration, especially at high excitation frequencies. The vibration mitigation effect of the WIB would be improved when its size and shear modulus increase or the embedded depth decreases. The results also showed that the WIB may amplify rather than reduce the ground vibration when its shear modulus is smaller or the embedded depth is larger than a threshold value. Meanwhile, an improved 3D semi-analytical boundary element method (BEM) combined with a thin layer method (TLM) was proposed to account for the rectangular shape of the used WIB and the laminated characteristics of the actual ground condition in analyzing the vibration mitigation of machine foundations. Comparisons between the field experiments and the numerical analyses were also made to validate the proposed BEM.