Source-mechanism from spectra of long-period seismic surface waves. 3. The Alaska earthquake of July 10, 1958

Source-mechanism is derived from amplitude and phase spectra of mantle Love and Rayleigh waves of the Alaska earthquake of July 10, 1958. The signals R_2, R_3, G_2, G_4, G_5 recorded on the Gilman 80–90 and the Press-Ewing 30–90 seismograph systems at Pasadena, California, are separated, digitized, filtered and Fourier-analyzed. An agreement between theory and observations is obtained for a unilateral fault of 300–350 km, which ruptured with a speed of 3-3.5 km/sec in the direction N40°W. Fault length is in good agreement with the extent of aftershock distribution in the month of July, 1958, and the time of rupture checks with the duration of an impressive T-phase recorded at Hawaii. The phases of the signals are corrected for propagation, instrumental shift and the source finiteness. Initial phases thus obtained agree on a mechanism of a right double-couple with a unit step-function in time

Velocities of mantle Love and Rayleigh waves over multiple paths

Phase velocities of Love waves from five major earthquakes are measured over six great circle paths in the period range of 50 to 400 seconds. For two of the great circle paths the phase velocities of Rayleigh waves are also obtained. The digitized seismograph traces are Fourier analyzed, and the phase spectra are used in determining the phase velocities. Where the great circle paths are close, the phase velocities over these paths are found to be in very good agreement with each other indicating that the measured velocities are accurate and reliable. Phase velocities of Love waves over paths that lie far from each other are different, and this difference is consistent and much greater than the experimental error. From this it is concluded that there are lateral variations in the structure of the earth's mantle. One interpretation of this variation is that the mantle under the continents is different from that under the oceans, since the path with the highest phase velocities is almost completely oceanic. This interpretation, however, is not unique and variations under the oceans and continents are also possible. Group velocities are computed from the phase velocities and are also directly measured from the seismograms. The group-velocity curve of Love waves has a plateau between periods of 100 and 300 seconds with a shallow minimum at about 290 seconds. The sources of error in both Fourier analysis and direct time domain methods of phase velocity measurement are discussed

Source mechanism from spectrums of long-period surface waves: 2. The Kamchatka earthquake of November 4, 1952

Fourier analysis of mantle Love and Rayleigh waves from the source of the Kamchatka earthquake of November 4, 1952, recorded on the Benioff linear strain seismograph at Pasadena, furnished further evidence in support of the moving-source theory. Amplitude and phase spectrums of G_1, G_2, G_3, G_4, R_2, and R_3 were processed to obtain information on the mechanism at the source. Both the directivity and the differential phase agree on a unilateral fault of 700 km which ruptured with a speed of 3 km/sec in the direction N 146° W. The fault length is in good agreement with the extent of aftershock distribution in the month of November 1952. The initial phases of Love and Rayleigh waves agree on a mechanism of a right orthogonal double couple with a time dependence which is close to the Heaviside step function

Determination of source parameters by amplitude equalization of seismic surface waves: 2. Release of tectonic strain by underground nuclear explosions and mechanisms of earthquakes

The radiation patterns of Love and Rayleigh waves from three nuclear explosions (Hardhat, Haymaker, and Shoal) are studied to determine the nature of the asymmetry of radiation and the mechanism of Love wave generation. From a comparative study of different explosions it is reasoned that the Love waves are generated at the source of the explosion. The source function, represented as the superimposition of an isotropic dilatational component due to the explosion and a multipolar component due to the release of tectonic strain energy, is consistent with the observed radiation patterns and the amplitude spectrums. The amount of seismic energy due to the strain release is computed. In some cases (Haymaker and Shoal) it is found that this energy may be due to the relaxation of the pre-stressed medium by the explosion-formed cavity. In the case of Hardhat it is concluded that the explosion must have triggered some other strain release mechanism, such as an earthquake. The amplitude equalization method is applied to surface waves from an earthquake to determine the source parameters. From only the amplitude spectrums and radiation patterns of Love and Rayleigh waves, the source functions, source depth, strike and dip of the fault plane, and the rake of displacement are determined for the July 20, 1964, Fallon earthquake

Towards an analysis of shear suspension flows using radial basis functions

In this paper, radial basis functions are utilised for numerical prediction of the bulk properties of particulate suspensions under simple shear conditions. The suspending fluid is Newtonian and the suspended particles are rigid. Results obtained are compared well with those based on finite elements in the literature

Integrating Mathematics and Educational Robotics: Simple Motion Planning

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics

Source-mechanism from spectra of long-period seismic surface-waves: 1. The Mongolian earthquake of December 4, 1957

The Pasadena seismograms of the Mongolian earthquake of December 4, 1957, were studied. Mantle Rayleigh waves R_3, R_4, R5, and R_6 were separated, digitized, filtered, and Fourier-analyzed. After the evaluation of the phase velocities and the absorption coefficients from amplitude ratios R_3/R_5 and R_4/R_6 the directivity was computed from the amplitude ratio of R_3/R_4. A fault of 560 km, with an azimuth of 100°, and a rupture velocity of 3.5 km/sec gave the best fit to the observed directivity. Auxiliary data from aftershock distribution, initial motions, air waves from the main shock, and geological surveys of the fault area seem to support these findings. The phase spectra of R_3 and R_4 were corrected for the propagation phase and the instrumental phase shift to obtain the initial phases at the source. A rough estimate of the depth of faulting is obtained on the basis of the calculated strain release and observed displacements at the fault