“Spectral model ω2” and non-linear inner structure of the magnitude scale for body waves

1975 ◽  
Vol 19 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Ludmil Christoskov ◽  
J. Vaněk
1956 ◽  
Vol 46 (2) ◽  
pp. 105-145 ◽  
Author(s):  
B. Gutenberg ◽  
C. F. Richter

Abstract This supersedes Paper 1 (Gutenberg and Richter, 1942). Additional data are presented. Revisions involving intensity and acceleration are minor. The equation log a = I/3 − 1/2 is retained. The magnitude-energy relation is revised as follows: (20) log ⁡ E = 9.4 + 2.14 M − 0.054 M 2 A numerical equivalent, for M from 1 to 8.6, is (21) log ⁡ E = 9.1 + 1.75 M + log ⁡ ( 9 − M ) Equation (20) is based on (7) log ⁡ ( A 0 / T 0 ) = − 0.76 + 0.91 M − 0.027 M 2 applying at an assumed point epicenter. Eq. (7) is derived empirically from readings of torsion seismometers and USCGS accelerographs. Amplitudes at the USCGS locations have been divided by an average factor of 2 1/2 to compensate for difference in ground; previously this correction was neglected, and log E was overestimated by 0.8. The terms M2 are due partly to the response of the torsion seismometers as affected by increase of ground period with M, partly to the use of surface waves to determine M. If MS results from surface waves, MB from body waves, approximately (27) M S − M B = 0.4 ( M S − 7 ) It appears that MB corresponds more closely to the magnitude scale determined for local earthquakes. A complete revision of the magnitude scale, with appropriate tables and charts, is in preparation. This will probably be based on A/T rather than amplitudes.


1997 ◽  
Vol 163 ◽  
pp. 575-579
Author(s):  
P. E. Hardee ◽  
J. M. Stone ◽  
J. Xu

AbstractResults of a spatial stability analysis and of numerical simulations of a “slab” jet in which optically thin radiative cooling is dynamically important are presented. Two different cooling curves are used. Unstable Kelvin-Helmholtz modes are significantly different from the adiabatic limit, and the form of the cooling function strongly affects the results. The numerical simulations are in excellent agreement with the linear stability analysis. In the non-linear regime growth of the surface wave at low frequencies results in sinusoidal oscillation which can disrupt the jet, while non-linear body waves produce low amplitude wiggles within the jet that can result in shocks within the jet. In cooling jets, these shocks can produce dense knots and filaments of cooling gas within the jet, and weak shock “spurs” in the ambient gas. Acceleration of ambient gas can be produced by these “spurs”, or by rapid entrainment if the jet is disrupted. For parameters typical of protostellar jets perturbations with a period of < 100 yrs should excite body waves which produce internal shocks and small amplitude wiggles. The lack of large amplitude wiggles in most observed systems is consistent with the suggestion that jets arise from the inner regions (r < 1 AU) of accretion disks.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


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