The LSDARC method of seismic refraction analysis: principles, practical considerations and advantages

The LSDARC (least‐squares difference and reciprocal combination) method of seismic refraction analysis is an adaptation of the reciprocal method that optimizes resolution of refractor depths and lateral variations in refractor wavespeed, and provides direct estimates of errors. Both time depths and differences between time depths are calculated separately to allow determination of more complete and accurate adjusted time depths, and therefore optimal estimates of refractor depth. The most efficient way of estimating refractor wavespeed is not to use the ‘velocity function’, but to subtract the time‐depth terms from the measured times to project the sources and receivers on to the refractor surface. A least‐squares procedure is then used to calculate corrections to the times for each shot gather and apply them to make all times appear to be produced by a single shot placed on the refractor surface at one end of the profile. Refractor wavespeeds are estimated from these corrected times using variable distance windows that can be adjusted to get a preferred trade‐off between variance in wavespeed and window length. An alternative and simpler method of wavespeed determination involves using first‐break times to prepare slowness profiles in opposite directions, with a model for refraction across a dipping interface, to compute true refractor wavespeeds. However, although the alternative method will generally resolve significant variations in wavespeed, the estimated errors are larger than when time depths are used. The methodology is valuable for engineering‐scale refraction surveys in which economic considerations prevent dense spatial sampling of the ground. The main features of the method are illustrated using short refraction profiles undertaken during student field schools.