Mathematical Questions in Seismology

Seismologists, like mathematicians, are accustomed to dividing their subject into a pure and an applied branch. The desirability of such division is underlined by the manner in which non-seismologists frequently approach the subject. I t is too often taken for granted that, because an earthquake is a motion of the ground, seismology must be chiefly concerned with the detailed analysis of that motion for its own sake. Such analysis is important in the engineering section of applied seismology; but it is unrepresentative of seismology as a whole, which deals largely with more remote problems: the causative mechanism of earthquakes, the distribution of their origins geographically and in depth, or the structure and physical condition of the interior of the earth. Engineering applications are out of bounds for the present speaker. Briefly, they refer to the design of earthquake-resistant (not "earthquake-proof") structures. The problems differ from those of most structural engineering in being dynamical, not statical; buildings, bridges, and other structures must be designed with reference to their behavior when in violent vibratory motion. Further, horizontal forces must be considered more explicitly than is done in ordinary design, where the chief load forces, due to gravity, are vertical. Problems of principle are few; but the mechanical characteristics of large structures are only less complex than the motion of the ground in an earthquake. To arrive at solvable propositions it is usually necessary to idealize both sets of data to a degree which seriously limits the practical applicability. Consequently, progress has depended heavily on empirical investigation of the behavior of models on a shaking-table. A very vocal offshoot of seismology is its application to geophysical prospecting—the investigation of subsurface structures by recording, with specially designed seismometers, the artificial earthquakes produced when explosives are detonated. Numerous books and periodicals deal with the problems of "geophysics"—which, in the vocabulary of the profession, means geophysical prospecting; a rather unwarranted restriction of the meaning of a necessary term, long in use with its proper significance as the physics of the earth. These problems present little of individual interest to the mathematician,