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Recent models of Earth structure suggest large horizontal gradients, especially in shear velocities. Some changes in existing methods are required to construct synthetics for broadband signals in many situations, especially when energy can reach the receiver by up-going as well as down-going paths. This can be accomplished by allowing locally dipping structure and making some modifications to generalized ray theory. Local ray parameters are expressed in terms of a global reference which allows a de Hoop contour to be constructed for each generalized ray with the usual application of the Cagniard-de Hoop technique. Several useful approximations of ray expansions and WKBJ theory are presented. Comparisons of the synthetics produced by these two basic techniques alone, or in combination with known solutions, demonstrates their reliability and limitations.
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