Reflection and transmission coefficients for transition layers

Summary Formulae are derived for the reflection and transmission coeficients of plane elastic waves for a transition layer. Haskell's technique and the so-called delta matrices[5, 7] are used for this purpose. No problems are encountered in deriving the reflections and transmission coefficients from Haskell's matrices[3]. However, in some cases Haskell's matrices do not guarantee the accuracy required. For this reason attention is mainly devoted to deriving the reflection and transmission coefficients from the delta matrices. In deriving the transmission coefficients use is made of the fact that some3×3 subdeterminants of the delta matrices are squares of the3×3 subdeterminants of Haskell's matrices.     

Expansion of a Plane Wave into Gaussian Beams

Magnetic susceptibility measurements on topsoils have often been used during the last few years to detect anthropogenic pollution. In most cases, a Bartington susceptibility meter for field measurements was used. However, up to now, no standard procedure has been developed for carrying out such investigations. The purpose of our study was to test the compatibility of different set-ups of instruments used for this purpose and the possible influences of subjective (human) factors. Field magnetic susceptibility measurements, carried out with four different Bartington MS2D instruments in strictly defined positions, are very consistent both for low and high values. The correlation coefficient between the magnetic susceptibility values recorded with different Bartington MS2D probes reached 97–98%. A test area was mapped independently by two groups, without any restrictions concerning the choice and distribution of the measured points, but respecting a few standard conditions (e.g., measuring at a distance from tree trunks; on the flattest place possible; recording between 10–30 values per point). The resulting susceptibility maps show the same general features in both cases, suggesting that the measuring strategy applied is suitable for topsoil magnetic screening. The methodology proposed can be used to map magnetic susceptibility on a larger scale—for example Europe—providing large sets of representative data and eliminating border-transition biases and human errors.     

Numerical modelling of seismic wave fields in models containing stacks of thin layers

Summary The possibilities of numerical modelling of high-frequency seismic wave fields in laterally varying layered structures containing stacks of thin layers are discussed. It is shown that the hybrid code based on the combination of the Gaussian beam summation method and of the matrix method (Thompson-Haskell, or other) may be very suitable for this purpose. The Guassian beam summation method is applied to thick smooth layers and the matrix method is locally applied to stacks of thin layers. Numerical examples for a simplified model of a transition layer between two halfspaces are shown. Certain interesting properties of waves reflected from a single interface and from a transition layer are discussed from the seismological point of view. Considerable attention is devoted to converted reflected waves.

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Effects of causal absorption on seismic body waves

Summary The effects of the causal absorption on seismic wave fields are discussed. Several computer programs for the evaluation of seismic wave fields have been modified to include the causal absorption. The programs are based mostly on matrix and ray methods. The main attention is paid to ray methods. A simple plane wave algorithm is described, which can be used along the ray to compute elementary seismograms in dissipative media. For a certain class of signals, commonly used in seismology, its application does not require any convolution or frequency-domain computations, and is only slightly slower than the evaluation of elementary seismograms in non-dissipative media. The derived algorithm even describes the velocity dispersion related to absorption and the decrease of the prevailing frequency of the signal well. Numerical examples are presented, both exact and approximate.