Determination of direction from instruments.—When speaking about earthquakes it was shown, as the result of many observations, that the same earthquake in the space of a few seconds, although it may sometimes have only one direction of motion, very often has many directions of motion. In certain cases, therefore, our records, if we assume the most permanent motions to be normal ones, give definite and valuable results. In other cases it is necessary to carefully analyse the records, comparing those taken at one station with those taken at another.
One remarkable fact which has been pointed out in reference to artificial earthquakes produced by exploding charges of gunpowder or dynamite, and also with regard to certain earthquakes, is that the greatest motion of the ground is inwards, towards the point from which the disturbance originated. Should this prove the rule, it gives a means of determining, not only the direction of earthquake, but the side from which it came.
Determination of earthquake origins by time observations.—The times at which an earthquake was felt at a number of stations are among the most important observations which can be made for the determination of an earthquake origin. The methods of making time observations, and the difficulties which have to be overcome, have already been described. When determining the direction from which a shock has originated, or determining the origin of the shock by means of time observations, it has been usual to assume that the velocity of propagation of the shock has been uniform from the origin. The errors involved in this assumption appear to as follows:—
1. We know from observations on artificial earthquakes that the velocity of propagation is greater between stations near to the origin of the shock than it is between more remote stations; and also the velocity of propagation varies with the initial force which produced the disturbance. If our points of observation are sufficiently close together as compared with their distance from the origin of the disturbance, it is probable that errors of this description are small and will not make material differences in the general results.
2. We have reasons for believing that the transit velocity of an earthquake is dependent on the nature of the rocks through which it is propagated. Errors which arise from causes of this description will, however, be practically eliminated if our observation points are situated on an area sufficiently large, so that the distribution of the causes tending to alter the velocity of a shock balance each other. It must be remarked, that causes of this description may also produce an alteration in the direction of our shock.
Other errors which may sometimes enter into our results, when determining the origin of shocks by means of observations on velocities, are the assumptions that the disturbance has travelled along the surface from the epicentrum and not in a direct line from the centrum. Again, it is assumed that the origin is a point, whereas it may possibly be a cavity or a fissure. Lastly, if we desire extreme accuracy, we must make due allowance for the sphericity of the earth and the differences of elevation of the observing stations.
I. The method of straight lines.—Given a number of pairs of points a0, a1, b0, b1, c0, c1, &c., at each of which the shock was felt simultaneously, to determine the origin.
Theoretically if we bisect the line which joins a0 and a1 by a line at right angles to a0, a1, and similarly bisect the lines b0, b1, c0, c1, all these bisecting lines a0, a1, b0, b1, c0, c1, &c., ought to intersect in a point, which point will be the epicentrum or the point above the origin.
This method will fail, first, if a0, a1, b0, b0, c0, c1 form a continuous straight line, or if they form a series of parallel lines.
Hopkins gives a method based on a principle similar to the one which is here employed—namely, given that a shock arrives simultaneously at three points to determine, the centre. In this case, the relative positions of the three points, where the time of arrival was simultaneous, must be accurately known, and these three points must not lie in a straight line, or the method will fail. For practical application the problem must be restricted to the case of three points which do not lie nearly in the same straight line.