Ph.D.  Geosciences (Solid Earth Geophysics)
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ItemAn investigation of the relation between source characteristics and T phases in the north Pacific area([Honolulu], 1968)Earthquake body waves refracted into the ocean are called T waves. They propagate as acoustic waves in the deep ocean sound channel at frequencies near 10 Hz. Arrival times of T waves, as recorded on widely spaced hydrophones in the sound channel off Eniwetok, Midway, Wake and Oahu Islands in the northern Pacific, are used to locate the Tphase source area. Sources thus located are correlated with published earthquake epicenters. The amplitude, onset rate, duration, frequency content and number of peaks of Tphase signals differs with earthquake magnitude as well as epicentral location. A study of T phases from earthquake epicenters in a localized source area, the western Aleutian Islands, was undertaken to investigate the cause of variation in Tphase signals. The earthquakes studied occurred in a series of aftershocks following the 7 3/4 magnitude earthquake south of the Rat Islands in the Aleutian Islands on February 4, 1965. The aftershocks occurred in a zone, about 300 miles long and 150 miles wide, roughly parallel to the WNWESE trend of the Aleutian arc. Tphase signals were different for earthquakes on the Aleutian arc, and behind the arc, from earthquakes on the Aleutian insular slope and Aleutian Trench. The Tphase strength, for earthquakes of a given magnitude, was greater for earthquakes on the arc, least for earthquakes in the Trench and outer ridge, and intermediate for earthquakes on the insular slope. The onset rate of Tphase signals varied with earthquake magnitude, but in general was most rapid for epicenters on the Aleutian arc, intermediate for epicenters on the Aleutian slope and gradual for epicenters in the Trench and outer ridge. Decay rates varied with earthquake magnitude because of reverberation and topographic reflections. Onset and decay rates were symmetrical for earthquakes in the Trench and on the outer ridge. Earthquakes on the Aleutian arc produced multiple peaked T phases due to radiation of T waves from more than one slope in the epicentral area. Earthquakes far out on the Aleutian slope. bench, Trench and outer ridge sometimes produced multiple peaked T phases because of both reflections from the slope behind the epicenter and radiation of T waves from that slope as well as from the epicenter. The accuracy of source location. as compared with epicentral location using the arrival times of earthquake body waves, was best for earthquakes on the Aleutian arc and in the Trench, and poorest for slope and bench earthquakes. Source solutions for signals from underwater explosions at known locations in the area indicate a source location accuracy of ±10 miles. The accuracy of earthquake epicentral location by T phase is limited by the relatively broad signal peak of the T phase, and the fact that the point, or points, of radiation of the T phase is usually at an ocean bottom slope near the epicenter instead of at the epicenter itself.

ItemDevelopment of a new theory for determination of geopotential from the orbital motion of artificial satellites([Honolulu], 1967)A new theory has been developed to exploit the satellite data particularly the position vector and the relative velocity of a satellite in the problem of obtaining the terrestrial gravity field with special consideration to its localised anomalous features. The new theory makes use of the fact that the dynamical variable Hamiltonian, associated with the satellite motion is timeinvariant in the ideal case when all the perturbing forces are neglected. With this as a working premise, it is possible to take into account the effects of perturbing forces such as lunar attraction, air drag, radiation pressure and solar attraction. The ideal case ignoring all the perturbing forces, here called the 'simplified theory' and the more factual case allowing for the effect of the important perturbing forces, here called the 'extended theory' are both discussed in detail. The potential function of the earth appears additively in the Hamiltonian function and can be determined from observations of the position vector and the relative velocity of a satellite at a number of points along a small segment of the orbit. Minimally, there must be as many observations as there are unknown coefficients in the expansion of geopotential but an abundance of measurements is desirable for the application of the least squares method. In case the position vector and the relative velocity of a satellite are not available as directly observed quantities, the equations can be expressed in terms of the orbital elements of the satellite. The theory emphasizes the local features of the gravity field by allowing for the fact that a satellite gives information weighted primarily by conditions in its immediate proximity and thus provides expressions for describing the gravitational potential of regions immediately below its orbit. Theoretically, it appears possible to cover the surface of the earth by overlapping expressions of this type and hence to obtain an adequate description of the gravity field of the earth. The equations of condition obtained when the theory is developed to include the effects of lunar attraction and air drag, are shown to remain valid when all the important perturbations; i.e., lunar attraction, air drag, radiation pressure, solar attraction, etc., are taken into consideration. The method of setting up the equations of condition appears to have the advantage of eliminating the necessity of quantifying the perturbing factors, thus enabling us to avoid some of the poorer approximations involved in the process. The new theory appears to offer the possibility of exploiting the 'short wavelength sensing potentiality' of the low altitude satellites which cannot be used with advantage in the perturbation theory. If the geopotential coefficients can be determined to a fairly high degree of accuracy, the theory theoretically has the potential for determining the timevariant part of the earth's gravity field and may be used to give some idea as to the differential rotation of the core and mantle if the core has a radial asymmetry of mass distribution as one resulting from convection currents within the core. For purposes of comparison, a short review of the existing method to determine the geopotential using perturbation theory, is included as well as the results obtained by some other investigators in the field.