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The source characteristics of southern California earthquakes with local magnitudes ML between 2 and 7 have been estimated from the gross spectral properties of the locally recorded S waves written on broad band torsion seismograph systems that have operated in California since 1932. The seismic moments M0 are consistent with the magnitude-moment relation obtained by M. Wyss and J. N. Brune from surface wave amplitudes, although a single straight line given by log M0 = 1.5 ML + 16.0 fits the data equally well. Source dimensions 2r vary from about 0.6 to 25 km, and stress drops Δσ lie between 0.3 and 200 bars. Neither parameter is a well-defined function of magnitude, although source size roughly increases with increasing ML. A theoretical relation between ML and source parameters is developed by using Brune's source model and the displacement response of the Wood-Anderson seismograph. The result is ML = log M0 − 32 log r − 17.8, where 3 < ML < 7, M0 is in dynes centimeters, and r is in kilometers. The ML may be accurately obtained by this equation, and the result is used to construct the following relations: log M0 = 2.0 ML + 14.2 − log Δσ, where Δσ is in bars, and log 2r = ⅔ ML + 2.9 − ⅔ log Δσ. Single-valued relations are not expected unless Δσ is constant. However, all available data are bracketed by these equations if stress drops vary over the range observed in this study. Radiated energies computed by spectrum integration agree with a theoretical result, log Es = 2.0 ML + 8.1, where Es is in ergs. Both are consistent with B. Gutenberg and C. F. Richter's energy-magnitude relation above ML = 4.5 but depart considerably from their result at lower magnitudes. The apparent stress parameter can provide source information that is independent of stress drop only if the high-frequency spectral falloff is a well-determined source property, which is unlikely for most of the data examined in this and other recent spectrum studies. Regional differences in source dimensions and stress drops within the southern California area are suggested by the spectral observations. However, the pattern is complex, and there are significant variations in these source parameters within any one region. Close-in seismic measurements are needed to substantiate the suggested regional differences, and determination of fault zone properties at depth is required to more fully understand the regional and local variations in seismic source parameters suggested by this study.

An estimate is made of the gamma -ray spectrum resulting from an extragalactic, evolving source model of cosmic ray origin in the absence of intergalactic gas. The experimental situation does not at present appear to allow definite rejection of this theory, since the calculated spectrum lies between the extreme observational limits. It is possible that such a theory can explain the cosmic ray spectrum, the isotropy of cosmic rays and the diffuse gamma -ray spectrum.

A quantitative analysis of the minimum CW CO2 laser power required for the drilling of thin stainless steel sheets in vacuum and in air is reported. These results are interpreted theoretically in terms of a simple cylindrical source model. A nomograph is given for the prediction of critical powers for CO2 laser drilling of other metals.

Vertical gradients of heat production were estimated from measurements on samples from eight boreholes in granitic rocks. Samples contained from 10 to 100 specimens, and the bore-hole depths range from 350 meters to 3 km. For holes less than 1 km deep the scatter of results is consistent with theoretical expectations based on known small-scale inhomogeneities. Gradient estimates from the deeper holes are not strongly influenced by such inhomogeneities, but their uncertainty cannot be evaluated statistically because of the possible effects of small perturbations of longer wavelength. The data suggest a general decrease in heat production with depth in the granitic rocks of a magnitude consistent with the exponential source model, although alternate models are not precluded. A 3-km hole in schist did not exhibit this trend, consistent with the view that upward concentration of sources occurred in the presence of a melted phase. As uncertainties in the numerical results are large and difficult to evaluate, many more analyses will be needed to establish vertical heat-production trends with confidence.

The static displacement field in an elastic half-space caused by a general, finite disturbance is derived in the form of an infinite series (multipole) expansion. The relationship between this theory and dislocation theory is discussed with the aid of examples. A multipole source model is derived for the strain-step field associated with the nuclear blast HANDLEY set off at the Nevada Test Site on March 26, 1970. The results suggest that there was significant fault movement associated with the detonation.

A method has been developed for considering the effect of the radiation pattern on the determination of the body-wave magnitude. The focal mechanism solutions of one intermediate and four deep-focus earthquakes analyzed in this study were determined from the P-wave first-motion directions and the S-wave polarization angles. All the mechanism solutions are well determined and conform to a double-couple source model. The results of magnitude computations from the data at different stations for each of these earthquakes are presented. The application of the method to the data of the five earthquakes studied by using the values of S. J. Duda (1969)2 reveals definite improvements in the determination of the magnitudes from the vertical component of P waves. The method does not, in general, improve the results for magnitudes determined from the horizontal components of S waves. The need for a more accurate chart for values as a function of depth and epicentral distance is emphasized. The results determined for the other earthquakes studied are given in a tabular appendix, which is available on microfiche along with the entire article. Order from the American Geophysical Union, Suite 435, 2100 Pennsylvania Ave., N.W., Washington, D.C. 20037. Document J70-002; $1.00. Payment must accompany order.

Expressions for surface displacements due to a fault in a multi-layered medium were derived in Part I of this paper. In Part II, numerical approach to calculate theoretical seismograms in the near field is prsented with some examples. Further extension of the problem for a two-dimensional moving fault will be studied in the forthcoming paper.

Analysis of radiated body waves from a set of South American deep earthquakes indicates the existence of a dominant period in the amplitude spectrum, as predicted by Archambeau's theory. Further, the dominant period is longer for S waves than P waves. The dominant period increases with magnitude; for P waves TmaxP varies from 1.5 to 30 sec as the magnitude ranges from 3.8 to 6.1. In terms of Archambeau's theory, these magnitudes indicate rupture zones with dimensions in the range 3 to 60 km. Such zones are consistent with estimates made on the assumption that the duration of high-frequency radiation is a measure of the size of the event. Radiated energy has been obtained by integrating over the arrival and correcting back to the source. A simple source model is proposed in which strain energy is released from a spherical volume as a result of slip across a thin molten disk. If the energy loss is that required to melt the disk, efficiency increases with magnitude. For a stress drop (assumed to be complete) of 3 bars, this model yields a relation between predominant period and radiated energy that agrees well with the experimental results for events with magnitudes less than 6. Larger events depart from this simple relation, radiating more energy per unit volume, possibly because they draw relatively more energy from greater depths where the strength is higher. The conclusions drawn here are somewhat different from those of previous studies of this region, and possible causes of these discrepancies are considered.

A source model is proposed to describe the behavior of an arc column in a crossflow. The drag force on the arc column is found to be D = qUm/cpTm^ where q = joule heating per unit length, C/oo = freestream velocity, cp = specific heat, and Too = freestream temperature. When the drag force is balanced by a Lorentz force arising from an externally imposed magnetic field, the source model yields a relationship between crossflow Mach number and magnetic field which is in good agreement with experimental data for M^ < 0.3.

Program IRREG is used to calculate dose rate and percentage depth doses at any number of selected points in a a patient irradiated by a single irregularly shaped beam. The primary and scatter components of the dose are computed separately and then added. Both are computed by a sector integration method; the scatter calculation uses scatter—air ratios; the primary calculation uses zero-area tissue—air ratios and an extended source model. A correction is made for surface curvature, but not for tissue heterogeneity. The program is designed to run on a commercial timesharing system.

The simple pressure source model of the sound radiated by a sonic jet is investigated analytically and experimentally. From the simple source model, the ratio of the frequency spectra of the radiated sound power and the jet pressure is derived for an assumed form of the jet‐pressure cross correlation. The spatial variation of the overall jet pressures, the frequency spectra of the jet pressures, the axial and radial cross correlations of the jet pressures, and the cross correlation between jet pressure and farfield sound pressure are measured for a cold jet. Some implications of the simple source model with regard to noise suppression are also discussed.