Introduction

Levin and Shah (1977) compute analytical traveltimes for internal multiples generated by a single-CMP seismic survey over a 2-D, two-layer, constant-velocity Earth. Their expression treats the specific case of a single reflection from the bottom of the second layer, preceded and followed by a number of bounces inside the first layer. To obtain the traveltimes, they use the method of images, computing successive images of the source through successive reflections towards the receivers, then computing an image of the receiver through the last reflector. The traveltime is obtained by dividing the distance between the two images to the wavespeed. This way they obtain an analytical traveltime along the pegleg ray that joins the given source and receiver positions only as a function of the respective positions, without the need to take the ray parameter into account.

We extend this procedure to an Earth model with an arbitrary number of layers and an arbitrary sequence of internal bounces between the respective layers. The Earth model is still 2-D, constant-velocity, and with linear interfaces defining constant-density layers. The computations are also done individually for each CMP. The ultimate goal of this study is to assist in the computation of amplitudes for pegleg multiples. This will be used in further studies to isolate the geologic settings in which pegleg multiples are strong enough to cause errors in the interpretation.