A new scheme for fast calculation of seismic traveltimes and ray paths in heterogeneous media

IntroductionBoth traveltimes and ray paths are vital information for seismic theoretical research and practice such as stack migration, traveltime inverse, calculation of covering time and so on (Xu, et al,1992). At present, they are obtained usually by either ray shooting (Liu, el al, 1986) or finite difference solution of the eikonal equation (Vidale, 1988; Zhang, et al, 1996). The ray shootingmethod can be understood and programmed easily. However, it is difficult for the method to treatc…     

Estimation of the rocks statistical parameters from traveltime measurements

In this paper the method for estimating the statistical parameters of the medium from traveltime measurements of refracted waves is applied to study the statistical characteristics of crystalline rocks at the Multifunctional Station Faido (Gotthard Base Tunnel, Switzerland). The method is based on the geometrical optics (GO) approximation. A covariance function for traveltime fluctuations has been obtained by considering quasihomogeneous fluctuations of sound velocity in a plain-stratified medium. Strongly anisometric (having unequal dimensions in different directions) random inhomogeneities were embedded in this medium. To estimate the statistical parameters around the tunnel, the traveltime fluctuations are calculated. It is assumed that each observation of traveltime-distance relation for a given shot-receiver group corresponds to a particular realization of a medium statistical ensemble. By calculating the variance and the zero cross intervals of the first derivative of traveltime fluctuations, the standard deviation of the velocity fluctuations and the characteristic horizontal scale of the inhomogeneities are estimated. Although the method allows to obtain the characteristic lengths of the inhomogeneities in vertical as well as in horizontal direction, the limited offset of the field data made it only possible to measure the latter. The estimated horizontal characteristic scale is about 13 m, which is reasonably close to the direct geological measurements in the studied region, where quartz lenses are dominant among the inhomogeneities. The standard deviation of the velocity is estimated as 4.5%, which might be caused by the fractured structure around the tunnel and also by the fault zone near the study area.     

Short scale heterogeneity in the lowermost mantle: insights from PcP-P and ScS-S data

We compare lateral variations at the base of the mantle as inferred from a global dataset of PcP-P travel time residuals, measured on broadband records, and existing P and S tomographic velocity models, as well as ScS-S travel time data in some selected regions. In many regions, the PcP-P dataset implies short scale lateral variations that are not resolved by global tomographic models, except under eastern Eurasia, where data and models describe a broad region of fast velocity anomalies across which variations appear to be of thermal origin. In other regions, such as central America and southeastern Africa, correlated short scale lateral variations (several hundred kilometers) are observed in PcP and ScS, implying large but not excessive values for the ratio R=∂ ln V_s/∂ ln V_p (∼2.5). On the other hand, in at least two instances, in the heart of the African Plume and on the edge of the Pacific Plume, variations in P and S velocities appear to be incompatible, implying strong lateral gradients across compositionally different domains, possibly also involving topography on the core-mantle boundary. One should be cautious in estimating R at the base of the mantle from global datasets, as different smoothing and sampling of P and S datasets may result in strong biases and meaningless results.