# Seismic imaging: Description of the method

This method is based on the calculation of the variation of delay times generated by changes in the near-surface layer. We have simplified the analysis by assuming that all the variations are due to thickness variations in the near-surface layer. We have used a single, average velocity for sound propagation in the near-surface layer and a second, average velocity for sound propagation in the bedrock. Our refraction calculation requires several steps:

1. The associated first-break geometry is sorted in common-receiver records.
2. We choose first breaks that correspond to the second refracted layer. All offset data less than 120 ft are removed.
3. An average offset and first-break time is computed for each receiver. To be sure that trigger inaccuracies are filtered, only receivers with 16-fold or higher are used.
4. A time shift is applied to remove the offset effect: t0 = t - (a / 8500 ft/s or 2590 m/s) where t0 is the time at the zero distance offset, t is the average first break time, a is the average offset and 8500 ft/s or 2590 m/s (P-wave) is an estimated bedrock velocity propagation of sound generally observed on the data set.
5. Depth is calculated by using an average low-velocity (soil) of 1500 ft/s or 450 m/s (P-wave) and the equation: h = ½ * 1500 ft/s * t0 where h is the depth at the receiver location.

An example of first breaks from a series of shot records is shown in Figure 4, upper graph. Our refraction calculation, represented in the lower graph, estimates the depth of unconsolidated sediment overlying the bedrock. The shape of the lower curve matches that of the first breaks in the upper display. For example, a trough in the center of Figure 4 correlates with a delay in the head waves.

A comparison with existing borehole data shows that this method adequately estimates bedrock depth within an error of a few feet. However, the method does not account for lateral changes in the near-surface materials. Stream sediments, for instance, often exhibit relatively low propagation velocities compared to other shallow materials. Our analysis typically indicates thicker materials in stream valleys, but some of this apparent thickening may be a result of lower propagation velocities. Considering this observation, the depth to the top of bedrock may be over-estimated in stream valleys and other places where thicker soil layers may be present.