CALCULATION OF DISPERSION CURVES AND AMPLITUDE‐DEPTH DISTRIBUTIONS OF LOVE CHANNEL WAVES IN HORIZONTALLY‐LAYERED MEDIA*

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Abstract
We present dispersion curves, and amplitude‐depth distributions of the fundamental and first higher mode of Love seam waves for two characteristic seam models. The first model consists of four layers, representing a coal seam underlain by a root clay of variable thickness. The second model consists of five layers, representing coal seams containing a dirt band with variable position and thickness. The simple three‐layer model is used for reference.It is shown that at higher frequencies, depending on the thickness of the root clay and the dirt band, the coal layers alone act as a wave guide, whereas at low frequencies all layers act together as a channel. Depending on the thickness, and position of the dirt band and the root clay, in the dispersion curves of the group velocity, secondary minima grow in addition to the absolute minima. Furthermore, the dispersion curves of the group velocity of the two modes can overlap. In all these cases, wave groups in addition to the Airy phase of the fundamental mode (propagating with minimum group velocity) occur on the seismograms recorded in in‐seam seismic surveys, thus impeding their interpretation. Hence, we suggest the estimation of the dispersion characteristics of Love seam waves in coal seams under investigation preceding actual field surveys.All numerical calculations were performed using a fast and stable phase recursion algorithm.