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

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

Two Models of Health Sciences Center Leadership During Turbulent Times

Leadership and change in health sciences centers are explored through contrasting two models of leadership: commonly practiced leadership and what has been referred to as “good enough leadership” (GEL). Several common cases or scenarios are presented through the lens of each model, with the conclusion that good enough leadership is more functional, creative, and healing than more widespread conventional models

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 Fallacy of Selecting the Right Person for the Job

Recruiting senior level higher education executives is more challenging than the customary and presumably rational approach of forming a search committee, running an advertisement or hiring a search firm, interviewing candidates, and making a selection. This article discusses many of the organizational dynamics that suggest logic and rationality often are lacking in recruiting for these important positions. The inevitable presence of conflicting interpersonal and intergroup dynamics that may not be discussable in any meaningful way compromises recruiting outcomes. Hiring the best person for the position may well not occur

Run Afoul: Sodomy, Masculinity, and the Body in the Georgian Royal Navy

This dissertation explores the homoerotic and the “social production” of sodomy within British naval culture and shipboard society from 1690 to 1840. It is based on the first comprehensive analysis of extant manuscript legal records; official and private correspondence; and the periodical press and other printed sources. The dissertation reconstructs the place of homosociality and homoeroticism within this institution crucial to national and imperial needs and aims. Formal repression of sodomy was far more common than has been appreciated. In particular, there were many more courts martial for homoerotic crimes than previous scholarship has recognized. At the same time, however, I show that naval life was built on homosocial relations that institutionalized homoerotic possibility, and that naval society permitted a great deal of erotic contact between seafarers. Most “sodomy” ran little or no risk of punishment. The navy followed the early modern judicial practice of rare but spectacular punishments into the mid-nineteenth century, even as judicial practice on land transitioned to heavy policing and frequent yet relatively milder punishment. I argue that sodomy was socially-produced in very particular circumstances in this culture. Those offenses the navy did prosecute were abuses of authority in which higher-ranking men used status and power to obtain sexual contact with lower-ranking men and boys. Prosecution only became common in periods of unsettled shipboard social relations, when shifting conceptions of masculinity and sexuality changed the limits of acceptable behavior and led officers to police gendered and sexual activity strictly. This analysis produces a much richer and more complex view of same-sex relations within face-to-face Georgian communities than has previously been possible. In particular, it shows that the plebeian men of the “lower deck”—the working-class men who filled the navy’s muster rolls and provided most of the muscle power and much of the knowledge on which vessels depended—knew a great deal about same-sex relations and were fully integrated into broader British cultural discourses about the men who engaged in them. Previous literature has argued that sodomy was largely unspeakable, but this dissertation shows that there were multiple sites in this culture where extensive discussions of sodomy were conducted: from the lower deck of warships, to the upper reaches of the Admiralty, to the newspapers covering naval affairs for readers back on land. Even accused and convicted men had spaces in which to engage discursively, to shape and dispute discourses around sodomy. All of these areas were essential to the social production of sodomy in the Royal Navy of the long eighteenth century

I. Seismological study of the Ninetyeast and Chagos-Laccadive Ridges, Indian Ocean. II. Models for asymmetric and oblique spreading at midocean ridges. III. Attenuation studies using split normal modes.

Part I of this work is a study of the seismicity of the Ninetyeast and Chagos-Laccadive Ridges in the Indian Ocean. These two features, in the interior of the oceanic plate, both show unusual seismicity. The mechanisms of these earthquakes were studied using body and surface Waves. This analysis shows that the Ninetyeast Ridge is still an active zone of deformation within the plate, along which substantial relative motion is taking place. The Chagos-Laccadive Ridge, though far less active, shows unusual seismicity in its southern portion. The seismicity on both ridges differs substantially from any previously discussed in the ocean basins. Both features should still be regarded as active today, though they do not fit into the classic ridge-transform-trench classifications. Part II of this work is a study of the mechanics of oblique and asymmetric seafloor spreading. It proposes that asymmetric seafloor spreading occurs as a consequence of the relative motion between ridges and slow moving mantle material below. A mechanical model of asymmetric spreading predicts that the trailing flank of a ridge migrating with respect to the mantle spreads fastest. These predictions are tested against published data and found to be in good agreement in most places. Oblique spreading is said to occur at midocean ridges which spread slowly (half rate less than 3 cm/yr), while the spreading is perpendicular at faster spreading ridges. This relation is explored using the ratio of the power dissipated at ridges to that on transform faults to determine the most energetically favorable ridge-transform geometry. The angle of oblique spreading (θ) is approximately related to the spreading rate by sin θ ˜ V^(−1), in good agreement with observations. Part III of this Work is a study of the attenuation of the longest period normal modes of the earth. The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean and the 1964 Alaskan earthquakes by analysis in the time domain. Synthetic seismograms are computed using 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, the Qs of the longest period spheroidal (_0^S_2-_0^S_5) and torsional (_0^T_3, _0^T_4) modes can be estimated. In addition, the Q of the fundamental radial mode _O^S_O is measured

Simultaneously Load Balancing for Every p-norm, With Reassignments

This paper investigates the task of load balancing where the objective function is to minimize the p-norm of loads, for pgeq 1, in both static and incremental settings. We consider two closely related load balancing problems. In the bipartite matching problem we are given a bipartite graph G=(Ccup S, E) and the goal is to assign each client cin C to a server sin S so that the p-norm of assignment loads on S is minimized. In the graph orientation problem the goal is to orient (direct) the edges of a given undirected graph while minimizing the p-norm of the out-degrees. The graph orientation problem is a special case of the bipartite matching problem, but less complex, which leads to simpler algorithms. For the graph orientation problem we show that the celebrated Chiba-Nishizeki peeling algorithm provides a simple linear time load balancing scheme whose output is an orientation that is 2-competitive, in a p-norm sense, for all pgeq 1. For the bipartite matching problem we first provide an offline algorithm that computes an optimal assignment. We then extend this solution to the online bipartite matching problem with reassignments, where vertices from C arrive in an online fashion together with their corresponding edges, and we are allowed to reassign an amortized O(1) vertices from C each time a new vertex arrives. In this online scenario we show how to maintain a single assignment that is 8-competitive, in a p-norm sense, for all pgeq 1