I show that the implementation of the Kirchhoff summation migration technique is equivalent to the generation of a synthetic focused array. The focused array theory, which is well developed in underwater acoustics, is used to deal with the factors limiting lateral resolution achieved when carrying out point diffractor imaging by Kirchhoff summation. Lateral resolution of a focused array, defined as the horizontal distance between two identical point diffractors which are just resolvable, is obtained from the width of the array response at the 0.35 amplitude points. The focused array theory approach should help in obtaining more insights into the practical aspects of Kirchhoff summation imaging technique, namely, choice of aperture and spatial sampling interval and the influence of velocity errors and seismic frequency. Examples given show how the lateral resolution can be improved by either increasing the array aperture or by using higher seismic frequency. I use the concept of the depth of focus to demonstrate the deterioration in the lateral resolution caused by migration velocity errors. Finally, I illustrate how imaging noise is generated when using a large spatial sampling interval.

It is well recognized that in order to realize the full potential of the Vibroseis technique, one needs to ensure accurate phase locking and a meaningful cross‐correlation. To achieve these two important objectives we require an accurate estimate of the compressional stress wave radiated by the vibrator into the ground. In this paper a simple method (subject of a patent application) is developed for predicting the compressional stress waves radiated by a vertical vibrator. The main feature of the proposed method is that it involves the field measurement of the acceleration of the reaction mass and the baseplate, respectively. The method is illustrated by computing the compressional stress waves generated by a typical vertical vibrator radiating into ice, chalk, sand, and mud. It is shown that for a seismic vibrator radiating into hard ground the pressure of the downgoing P‐wave is 180° out of phase with the baseplate velocity. It is also shown that when the driving force of the seismic vibrator has a flat amplitude spectrum, the amplitude spectrum of the downgoing P‐wave falls off by 6 dB/octave towards low frequencies.

The pattern of oscillation of a Piezon-Master 400 ultrasonic file driven by a piezoelectric transducer was studied in air and on water. In addition, the displacement amplitudes of the files were measured. The findings were compared with those observed with the Cavi-Endo unit reported in another study (Ahmad 1969). It was observed that the file vibrated such that a standing wave was formed on the file and it exhibited points of maximum deflection (antinode) and points of minimum deflection (node) with the largest deflection occurring at the apical end. This pattern of oscillation was similar to that exhibited by the Cavi-Endo file which employed a magnetostrictive transducer. However, the displacement amplitudes were very much higher than those exhibited by the Cavi-Endo. It is considered that the 120 degrees angle of the file holder inherent in the Piezon-Master 400 unit and the more effective power transmission with the piezoelectric transducer may have contributed to the large amplitudes.

A theoretical model is developed for predicting three important parameters of the pressure pulse radiated by an air‐gun, namely the rise time, the amplitude of the initial pulse, and the period of the bubble pulse. A knowledge of these three parameters is essential for the efficient design of air‐guns arrays. The prediction of the amplitude of the initial pulse is based on the assumption that the initial pulse is radiated by a spherical source with surface area equal to that of the air‐gun ports and not by a spherical source with initial volume equal to that of the air‐gun chamber, as has been assumed previously. A simple equation is obtained for predicting the period of the bubble pulsation, taking into account the effect of the air‐gun body, boundaries such as the sea‐surface and seabed and the presence of a number of identical air‐guns placed at the same depth and fired simultaneously.

It is shown that the threshold of rectified diffusion according to the Hsieh and Plesset solution is in fact frequency dependent when the inertial terms in the equation of motion of the bubble are not neglected. A comparison is made between the threshold calculated from the modified Hsieh and Plesset solution and that obtained by Eller and Flynn, using numerically computed radius-time curves.