In all seismic refraction surveys, the problem is to determine the constants in a system of equations of the type t i j = at+bj+Atj/w where at and bj are "time terms" which are characteristic of the shotpoint and seismograph station respectively, Agj is the distance between the shot point and the seismograph, t t j is the time of propagation of a refracted wave and w is the velocity of propagation of seismic waves in an underlying marker layer. I t is shown that the equations can be solved for interpenetrating networks of shot-points and seismographs provided that certain general conditions are satisfied. Factors which determine the uncertainties of the final solution are discussed, and methods of correcting for the effects of steeply dipping boundaries are included.

The planning, execution and preliminary results of a major Anglo-German explosion seismic project are presented in this, paper I of a series. This Lithospheric Seismic Profile in Britain (LISPB) was planned as a reversed 1000 km line between two major sea-shot points off Cape Wrath in Scotland and one in the English Channel; additional sea-shots and intermediate land-shots were fired to give reversed and overlapping crustal coverage (to 180400 km distance) along the line. In all, 29 shots were fired and 60 mobile magnetic tape stations recorded three-components of ground 'motion. The resulting 14 crustal and three long-range profiles have observations at intervals of typically 2-4 km. Recordings have been digitized and four examples of filtered, computer-plotted record sections are presented to illustrate data quality. In a preliminary analysis, phase correlations are discussed and some models presented; the latter especially are more relevant to future interpretations than to geological or tectonic problems. However, significant variations in crustal thickness and in the nature of the crust-mantle transition do seem to occur beneath the British Isles.

During large‐scale seismic surveys it is often impossible to arrange shot points and seismometers in a simple pattern, so that the data cannot be treated as simply as those of small‐scale prospecting arrays. It is shown that the problem of reducing seismic observations from m shot points and n seismometers (where there is no simple pattern of arranging these) is equivalent to solving (m+n) normal equations with (m+n) unknowns. These normal equations are linear, the matrix of their coefficients is symmetric. The problem of inverting that matrix is solved here by the calculus of “Cracovians,” mathematical entities similar to matrices. When all the shots have been observed at all the seismometers, the solution can even be given generally. Otherwise, a certain amount of computation is necessary. An example is given.

2. O rganization 124 6. Comparison with other studies 148 3. T reatment of results 127 7. N otes on apparatus and technique 149 4. T imes of travel 131 R eferences 151 Seismic waves produced by explosions near Soltau were observed at distances up to 50 km., and others from the Heligoland explosion from 50 to 1000 km. Special time signals and a high recording speed enabled the instant of a sharp onset to be determined to 0T sec. Short-range seismic data were used to eliminate some of the effect of rocks near the surface. The average velocity of the first arrivals was 4-4 km./sec. between 4 and 24 km. from the shot point, 5'95 km./sec. between 24 and 120 km., and 8T 8 km./sec. beyond 120 km. Significant local variations were found at the shorter distances. Alternative hypotheses covering the distribution of velocity in the upper layers gave estimates of 27-4 and 29*6 km. for the depth of the ultrabasic layer. Later arrivals proved difficult to identify, and a statistical method was used to estimate the signi ficance of travel-time curves drawn through selected groups of onsets. This test showed that was not significantly recorded, but a number of onsets at 7 or 8 sec. after Pn probably represented a wave travelling for most of its path in the ultrabasic layer and reflected at the critical angle between that layer and the surface. The test failed to decide whether the onsets close to the ex pected times of Pg should be treated as one or more phases. Confused motion persisted during the period when transverse waves were expected, but, with the possible exception of Sn, there was no significant concentration of observations about lines representing recognized phases. The thermal energy of the Heligoland explosion was T3 x 1020 ergs, and the energy in the seismic waves was of the order of 1017 ergs. The efficiency was therefore comparable with that of a surface explosion, and measurements of the crater confirmed that the rock which covered the charge could not have had much effect on the momentum entering the ground.

Fundamental requirements for refraction surveysIn commenting on the foregoing communication of Francis, it seems necessary to start with a fundamental statement of the requirements and possibilities of refraction surveys, and then to consider the practical techniques as special cases. The general requirements are as follows:(a) A clear boundary must exist such that materials below the boundary propagate seismic waves within a higher range of velocity than those above.(b) Waves from several sources, refracted through the materials below the boundary, should be recognized at several detectors.Given sufficiently dense coverage, it is possible to determine the two-dimensional distribution of propagation velocity for the materials immediately below the boundary, and all of the ' delay times ' which describe the transmission of the waves through the upper layer. Types of refraction surveyThe complete solution would require very dense coverage and, if all connections were to be used, an impracticably complex technique of interpretation. The following two techniques for reducing the total complexity are therefore used:(a) Linear profiles. In a reversed linear profile, wave fronts passing under the central section have most of their propagation paths in common with each other, and this enables the propagation velocities below the layer, and the delay times for transmission to the surface, to be determined separately (Hagedoorn 1959). When an abrupt change of structure occurs within the profile, delay times for a single station, looking along the profile in opposite directions, may be different. O'Brien (1968) allows for this difference in his interpretation of the Lake Superior experiment, and uses it to estimate the velocity in the upper layer.(b) The time-term approach. In this case the distribution of shots and detectors may be two-dimensional. The solution is derived on the assumption that the material below the boundary has a uniform propagation velocity, and that the delay time for any given survey point is the same for all the ray paths which begin and end at that point. This requires careful definition of the quantities involved.We start with the general refraction equation t i j = U , +~~+ A~~/ U~ 227