Imaging of refracted waves by convolution

Summary Refraction seismology has a long history in obtaining estimates of subsurface structures. Among the many methods developed for the refracted waves the reciprocal method is the most popular. However, the application of the reciprocal and most other methods depends initially on picking the first arrival times. In this paper, we discuss a method for imaging refraction interfaces by using a convolutional method that does not require picking first break times. This avoids both the time-consuming first break picking and the possibility of erroneous picks. We use the analogy of convolution to the summation of time delays and correlation to differences of time delays. Therefore, the reciprocal method can be performed as a convolution of the initial arrival portion of the forward and reverse profile traces and a correlation of the travel time between forward and reverse source positions. With the elimination of picking, the proposed method may be more productive than graphical procedures. However, convolutions produce more ringing than the original records, so it is necessary to apply some data processing procedures before using the proposed method. We present the theoretical background of the convolutional method and its application to synthetic and field data.