Time-domain observation and synthesis of split spheroidal and torsional free oscillations of the 1960 chilean earthquake: Preliminary results

The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred and fifty hours of the Isabella, California, strain record are narrow band filtered about the central frequency of each split multiplet to isolate the complex wave form resulting from the interference of the different singlets. We compute synthetic seismograms using our previous theoretical results, which show the dependence of the amplitude and phase of the singlets on source location, depth, mechanism, and the position of the receiver. By comparing these synthetics to the filtered record, we conclusively demonstrate the splitting of modes whose splitting had not been definitely resolved: torsional modes (_0T_3, _0T_4) and spheroidal modes (_0S_4, _0S_5). The splitting of _0S_2 and _0S_3 is reconfirmed. We obtain good agreement between the synthetics and the filtered data for a source mechanism (previously determined from long-period surface waves) of thrust motion on a shallow dipping fault

Normal modes of a laterally heterogeneous body: A one-dimensional example

Various methods, including first- and second-order perturbation theory and variational methods have been proposed for calculating the normal modes of a laterally heterogeneous earth. In this paper, we test all three of these methods for a simple one-dimensional example for which the exact solution is available: an initially homogeneous “string” in which the density and stiffness are increased in one half and decreased in the other by equal amounts. It is found that first-order perturbation theory (as commonly applied in seismology) yields only the eigenvalues and eigenfunctions for a string with the average elastic properties; second-order perturbation theory is worse, because the eigenfunction is assumed to be the original eigenfunction plus small correction terms, but actually may be almost completely different. The variational method (Rayleigh-Ritz), using the unperturbed modes as trial functions, succeeds in giving correct eigenvalues and eigenfunctions even for modes of high-order number. For the example problem only the variational solution correctly yields the transient solution for excitation by a point force, including correct amplitudes for waves reflected by and transmitted through the discontinuity. Our result suggests but does not demonstrate, that the variational method may be the most appropriate method for finding the normal modes of a laterally heterogeneous earth model, particularly if the transient solution is desired

Attenuation measurements of split normal modes for the 1960 Chilean and 1964 Alaskan earthquakes

Measurements of attenuation for the Earth's longest period modes can be significantly biased by the effects of frequency splitting. Using our previously developed methods of time domain synthesis of split normal modes, we measure Q without such a bias. We also conduct numerical experiments to confirm the errors in Q measurements which result from neglecting the effects of splitting. In contrast to frequency domain this time domain technique allows us to reject data below the ambient noise level for each mode. The Q's of the longest period spheroidal (_0S_(2–0)S_5) and torsional (_0T_(3–0)T_4) modes are determined using long (500 hr) records from the Chilean and Alaskan earthquakes

Split free oscillation amplitudes for the 1960 Chilean and 1964 Alaskan earthquakes

Splitting of the Earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The strong peaks in the observed spectrum of each split multiplet correspond to singlets with much higher amplitudes than the others. Using theoretical results we have derived elsewhere (Stein and Geller, 1977a), we are able to predict this pattern. We show that the source mechanisms inferred for these earthquakes from surface waves are consistent with the observed pattern of relative spectral amplitudes of the split modes. However other mechanisms, such as a slow isotropic volume change, are also consistent with the split-mode amplitudes and are excluded only by additional data

The Fiscal Impact of the U. S. Military Assistance Program, 1967-1976

The study of U.S. arms transfers and their impact on the fiscal decisions of aid recipients has been the subject of various interpretations and competing explanations. Absent in this literature has been a systematic testing of propositions derived from a general theory of aid impacts. A larger and somewhat related body of research has examined the political (Chaudhuri 1972; Hughes 1967; Gutteridge 1967) and general economic effects of domestic military spending (Deger and Smith 1983; Smith 1977, 1980; Benoit 1978; Kennedy 1974; Whynes 1979). These studies, however, have not examined the fiscal impact of foreign military assistance. To date only a few researchers have studied this issue in any systematic fashion (McGuire 1979, 1982; Wolf 1971). In this study we seek to fill this gap by applying grant economics theory (Pigou 1932; Oates 1972) to study the fiscal impact of U.S. military arms transfers on foreign nations. Drawing on the domestic aid literature (Oates 1972; Gramlich 1972), we identify a set of propositions concerning the expenditure decisions of domestic aid recipients, and test these propositions against the fiscal behavior of Military Assistance Program (MAP) recipients between 1967-1976. In addition to the substantive import of this question and its bearing on the implementation of U.S. foreign policy, this research provides a unique opportunity to test the applicability of domestic aid theory to the study of foreign aid policy

Robotic-Assisted Laparoscopic Management of Ureteral Endometriosis

This report describes 2 cases of ureteral obstruction secondary to endometriosis managed with robotic-assisted laparoscopic partial ureterectomy and ureteroneocystostomy