Travel-time curves for a simple sea floor model |
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| Authors: | R A Stephen |
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| Institution: | (1) Woods Hole Oceanographic Institution, 02543 Woods Hole, Massachusetts, USA |
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| Abstract: | This paper reviews a simple technique for interpreting the velocity structure of upper oceanic crust from travel-time data of sonobuoy and ocean bottom receiver refraction experiments. The technique does not involve sophisticated digital processing or synthetic seismogram analysis. Interpretations can be carried out with a pencil, paper and slide rule.Travel-time inversion procedures based on the  -p transformation require the assumption of the shallowmost velocity. In some cases, however, such as oceanic crustal studies, the shallowmost velocity is one tf the critical parameters for which one wishes to invert. An inversion method for the shallowmost velocity is discussed which assumes a constant velocity gradient. The time, range and ray parameter of a point on the travel-time curve are sufficient to obtain the velocity at the top of the gradient zone and the gradient. The method can be used to interpolate the velocity-depth function into regions from which no seismic energy is returned as a first arrival. Once an estimate of the upper crustal velocity is obtained the traditional -p procedures can be applied.The model considered consists of a homogeneous layer over a layer in which velocity increases linearly with depth. For such a geometry there are three classes of behaviour of the travel-time curve based on the number of cusps: zero, one or two. The number of cusps depends on the uppermost velocity in the crust, the velocity gradient of the upper crust and the depth of the sources and receivers. It has not been previously recognized that two cusps in the travel time curve may be observed for this simple model. Since estimating the ray parameter from first arrival times is less ambiguous when there are no cusps, understanding the relations involved with the three classes aids in the design of experiments. It is reasonable to apply the model to shallow sea floor structure because of the high quality of marine refraction data which has recently been obtained. |
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