Continuous velocity logs may be approximated by a series of zones in which the velocity is a linear function of the depth. The reflection response of a series of transition layers may be calculated from an iterative type formula, developed in this paper, which is well suited to digital computer use. This solution takes into account multiple reflections between layers. The reflection output for any input wave shape may be calculated. In this paper a Gram Charlier series pulse having a spectrum peaked at 40 cps is used throughout to facilitate comparison of results. The dependence of the reflection response of single and double layers on frequency and the reflections for the standard input pulse are illustrated. It is shown that 1. Symmetrical double transition layers give an appreciable reflection output even for a base thickness as low as 10 ft. 2. The upper layers of a multilayer group may influence considerably the reflection character from the lower layers.
In recent years, it has been found possible to record shear‐wave reflections and horizontally traveling shear waves using continuous signal methods. Thus paper traces the equipment development and field work performed during this research. The earliest work with a version of a swinging‐weight vibrator showed that shear‐wave reflections could be recorded. This fact provided the impetus to make modifications to equipment to meet difficulties caused by lack of energy and lack of frequency bandwidth. Examples are given which show the flexibility of the system in providing comparison between the horizontally traveling surface waves induced and recorded by the various combinations of vibrator sources and geophone types and their relative orientations. Frequency selection by the different modes is well illustrated. For most of the reflection examples, the average ratio of shear‐wave velocity to compressional‐wave velocity in the first few thousands of feet is near 0.5. Finally, to complete the early development, the version of the shear‐wave vibrator and recording system which was used for most of the additional work is described. In order to make comparison of P‐wave and SH‐wave reflection records easier, this system provided for a 2:1 compression of the shear‐wave time scale as well as a 2:1 ratio of frequency output between the P‐ and SH‐vibrator systems. A few examples of SH reflection profiles achieved with this system are presented.
The emphasis in this shear‐wave research was placed on determining the general quality of data which could be obtained in different areas and whether such quality was consistent with the main objective of getting information from the shear‐wave data which could not be obtained from the corresponding P‐wave data. Borehole data are presented to show that the SH source of vibrations generates a downward‐propagating, horizontally polarized shear wave. Shear velocities were determined for depth intervals of two to three hundred feet, but no absolute correlation between [Formula: see text] and lithology could be established. In the deeper sedimentary section, [Formula: see text] averages about one‐half; but in the low velocity, or weathering layer, the ratio may be as small as one sixth. All the reflection record problems which arise from wave propagation phenomena in the LVL are generally much worse for SH waves than for P waves because of the very small SH velocities in the LVL. Nevertheless, by using large source and receiver patterns and various processing techniques, interpretable SH reflection records were obtained in almost every test area. It has been possible to obtain a depth of penetration about equal to that of the corresponding P‐wave records, with some reservations. The relative quality to be obtained has proved unpredictable. Several examples of SH reflection sections are presented with the corresponding P reflection sections. Some of these field examples show definite differences between the corresponding P and SH reflection sections. Such differences represent new information which potentially can be useful to the exploration geophysicist.
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