For non‐linear kinematic inversion of elastic anisotropy parameters and related investigations of the sensitivity of seismic data, the derivatives of the wavespeed (phase velocity and group velocity) with respect to the individual elastic moduli are required. This paper presents two analytic methods, called the eigenvalue and eigenvector methods, to compute the derivatives of the wavespeeds for wave propagation in a general anisotropic medium, which may be defined by up to 21 density‐normalized elastic moduli. The first method employs a simple and compact form of the eigenvalue (phase velocity) and a general form of the group velocity, and directly yields general expressions of the derivatives for the three wave modes (qP, qS1, qS2). The second method applies simple eigenvector solutions of the three wave modes and leads to other general forms of the derivatives. These analytic formulae show that the derivatives are, in general, functions of the 21 elastic moduli as well as the wave propagation direction, and they reflect the sensitivity of the wavespeeds to the individual elastic moduli. Meanwhile, we give results of numerical investigations with some examples for particular simplified forms of anisotropy. They show that the eigenvalue method is suitable for the qP‐, qS1‐ and qS2‐wave computations and mitigates the singularity problem for the two quasi‐shear waves. The eigenvector method is preferable to the eigenvalue method for the group velocity and the derivative of the phase velocity because it involves simpler expressions and independent computations, but for the derivative of the group velocity the derivative of the eigenvector is required. Both methods tackle the singularity problem and are applicable to any degree of seismic anisotropy for all three wave modes. 相似文献
Most pingos in the permafrost region of the high northern Tibetan Plateau form along active fault zones and many change position annually along the zones and thus appear to migrate. The fault zones conduct geothermal heat, which thins permafrost, and control cool to hot springs in the region. They maintain ground-water circulation through broken rock in an open system to supply water for pingo growth during the winter in overlying fluvial and lacustrian deposits. Springs remain after the pingos thaw in the summer. Fault movement, earthquakes and man's activities cause the water pathways supplying pingos to shift and consequently the pingos migrate.
The hazard posed to the new Golmud–Lhasa railway across the plateau by migrating pingos is restricted to active fault zones, but is serious, as these zones are common and generate large earthquakes. Pingos have damaged the highway and the oil pipeline adjacent to the railway since 2001. One caused tilting and breaking of a bridge pier and destroyed a highway bridge across the Chumaerhe fault. Another has already caused minor damage to a new railway bridge. Furthermore, the construction of a bridge pier in the North Wuli fault zone in July–August 2003 created a conduit for a new spring, which created a pingo during the following winter. Measures taken to drain the ground-water via a tunnel worked well and prevented damage before the railway tracks were laid. However, pier vibrations from subsequent train motion disrupted the drain and led to new springs, which may induce further pingo growth beneath the bridge.
The migrating pingos result from active fault movement promoting artesian ground-water circulation and changing water pathways under the seasonal temperature variations in the permafrost region. They pose a serious hazard to railway construction, which, in turn can further disturb the ground-water conduits and affect pingo migration. 相似文献