A seismic trace after application of suitable amplitude recovery may be treated as a stationary time‐series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto‐correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time‐domain pulse itself is then reconstituted under the assumption of minimum‐phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z‐transform, (C) a fast method based on inverting the least‐squares inverse of the wavelets, i.e. inverting the normal time‐domain deconvolution operator. Problems associated with these three methods are most acute when the z‐transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace‐to‐trace, from shot‐to‐shot, and from one shot‐point medium to another. There is reasonable agreement between the minimum‐phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge‐factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.

Recordings were made with three types of detector of the primary compressional (P) and shear (S) wave pulses generated by explosions in boreholes. Charge weights varied from 0.08 kg to 9.5 kg and detector distances varied from about 3 m to about 80 m. Scaling by the simple factor WI/s, where

List of symbols .

Model experiments on the head wave are described. Quantitative data are obtained for three different pairs of media: light lubricating oil on top of a saturated solution of calcium chloride, water on top of wax, and water on top of concrete. Within the limits of experimental error these data agree with the theoretical prediction that the head wave should decay with distance as [Formula: see text] (Heelan, 1953).

Richards (1961) and several others have shown that wide angle reflections may attain large amplitudes. This note extends the plane wave calculations of Richards to include the effect of the phase changes which occur at angles greater than critical. On seismic pulses this introduces a time lead of up to one half period and alters peak‐to‐peak amplitudes by up to 15‐20 %. It is pointed out that the plane wave reflection coefficient is not applicable at angles very close to critical where the true reflection coefficient is reduced by a factor depending on (R/λ) ¼ In ultrasonic experiments this factor reduced the reflection coefficient by between ½ and ⅓. Neither does the plane wave coefficient apply at grazing incidence, when it has to be reduced by a factor depending on (R/λ)1‐0. Graphs are given of the amplitudes of wide angle reflections and head waves for two cases and it is concluded that, except for shallow refractors and angles close to critical, the reflection is always significantly greater than the head wave.