On the Tutte-Krushkal-Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte-Krushkal-Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte-Krushkal-Renardy polynomial..Comment: Minor revision according to a reviewer comments. To appear in the Journal of Combinatorial Theory, Series

Time functions appropriate for nuclear explosions

The source-time function of megaton class nuclear explosions has been determined by modeling teleseismic short- and long-period body waves with synthetic seismograms. A simple analytic expression for the time function was used to closely match observations from both Novaya Zemlya and the U.S. test site at Amchitka. It was found that the time functions of all the events have a substantial overshoot. It was also found that, although the durations of the time functions did appear to depend on yield, the effect was very difficult to observe even in short-period records. All synthetics were computed by assuming a simple point source in a layered elastic half-space. It was not necessary to appeal to any nonlinear processes in the source region to explain the observations. Numerical calculations are presented to show that tectonic release triggered by earthquakes does not have a substantial effect on the P waves unless the long-period level of the tectonic event is as large or larger than the long-period level of the explosion. The pS wave, on the other hand, is shown to be very sensitive to even a moderate amount of tectonic release

Time functions appropriate for deep earthquakes

The seismic signatures of isolated body phases from many deep-focus earthquakes were analyzed in the time domain. Most shocks were found to be multiple events when examined in detail. The time history derived from P waves for single events predict synthetic S-wave shapes that match the observations, indicating compatibility with shear dislocation theory. Several other features of source functions in the time domain have been brought to light

Preliminary observations from the use of US-Soviet Joint Seismic Program data to model upper mantle triplications beneath Asia

New short-period waveform data from the US-Soviet Joint Seismic Program (JSP) make possible investigations of Asian upper mantle structure. the goal of this paper is to explore the potential use of the newly available JSP data to gain a qualitative view of upper mantle structure beneath Asia, and to facilitate more detailed future detailed future upper mantle studies. In a reconnaissance approach, waveform upper mantle studies. In a reconnaissance approach, waveform predictions from upper mantle P-wave velocity models of previous studies are compared to the JSP data to investigate regional differences in the central Asian upper mantle. Data coverage brackets the upper mantle triplications with excellent multi-source-to-stations sections. the abundance of data for controlled source-receiver geometries and the impulsive nature of the arrivals enable us to stack seismograms to improve signal-to-noise ratio. Arrivals from the 400 and 670 km discontinuities are apparent in the data and are compared to predictions of the mantle models. the principal result is that, for the regions studied, paths through cratonic regions of Asia are compatible with shield-type models, while paths through highly deformed regions of Asia are compatible with models derived for tectonically active regions, suggesting large lateral variations beneath the Eurasian continent. Use of the JSP data in a comparative approach is fast and simple, and proves effective in obtaining a first-order understanding of the Asian upper mantle. This result also presents the potential for qualitative studies elsewhere with digital portable stations

Source-Indexed Migration Velocity Analysis with Global Passive Data

The reverse-time migration of global seismic data generated by free-surface multiples is regularly used to constrain the crustal structure, but its accuracy is to a large extent determined by the accuracy of the 3-D background velocity model used for wave propagation. To this improve the velocity model and hence the accuracy of the migrated image, we wish to apply the technique of migration velocity analysis (MVA) to global passive data. Applications of MVA in the active setting typically focus on o ffset- or angle-gather annihilation, a process that takes advantage of data redundancy to form an extended image, and then applies an annihilation operator to determine the success of image formation. Due to the nature of regional-scale passive seismic arrays, it is unlikely that the data in most of these studies will be su cient to form an extended image volume for use in annihilation-based MVA. In order to make use of the sparse and irregular array design of these arrays, we turn towards a shot-pro le moveout scheme for migration velocity analysis introduced by Xie and Yang (2008). In the place of extended image annihilation, we determine the success of the migration velocity model by using a weighted image correlation power norm. We compare pairs of images formed by migrating each teleseismic source by image cross-correlation in the depth direction. We look for a suitable background model by penalizing the amount of correlation power away from zero depth shift. The total weighted correlation power between source-pro le images is then used as the error function and optimized via conjugate gradient. We present the method and a proof-of-concept with 2-D synthetic data

A Robotic Training System for Studies of Post-SCI Stand Rehabilitation

This paper describes a robotic training system designed to rehabilitate the standing ability of mice after spinal cord injury(SCI). The system is composed of a 6 Degree-of-Freedom (DOF) parallel mechanism, an active weight support system, and other measuring equipments which can monitor the response of the mouse. Preliminary experiments showed that the mouse could generate a certain degree of weight-support stand response during the training

Time Domain Regional Discriminants

The time and frequency domains are equivalent displays of seismic trace, information, though some qualities of the signal are more easily observed in one domain than the other. The relative frequency excitation of Lg, for instance, is most easily viewed in the frequency domain, but such waveform qualities as the sequence in which pulses arrive in the wave train or the sharpness of pulse onset are most easily studied in the time domain (Murphy and Bennett, 1982, Blandford, 1981). Because of the tremendous complexity of high frequency regional data, most attempts at using it for discrimination purposes have involved analysis of the frequency content of the various arrivals either through transforming selected windows or through multiple bandpass filtering. We report here on our initial attempts to explore the alternative and to discriminate events using those waveform characteristics most easily observed in the time domain. A second advantage of time domain analysis approaches is that they permit a deeper insight into the physical processes creating a seismic signal's character. For this reason, they can be more e3silv used to evaluate the transportabilty of a discriminant to varying geophysical and tectonic regimes. This is an especially important feature in the development of regional discriminants. The most prominent and successful spectral regional discriminants have been empirically developed. This means that they must be redeveloped and reverified in each new area. As we shall show in the following, through rigorous time domain analysis such features as regional depth phases can be identified and used to discriminate. Discriminants based on such simple physical features as source depth should be transportable anywhere. In work recently completed under the treaty verification program, we have proved that such time domain discriminants do exist. In analyzing a test discrimination data set from the western U. S., we have discovered that the onset of P_n is always very similar for explosions and that few earthquakes have this unique waveform character. This information can be constructed into a simple discrimination scheme by testing the correlation of observed P_n waveform onsets with average waveforms observed from explosions. High correlations indicate explosions and low correlations earthquakes. We have also discovered that the regional phase P_g is actually composed of a sequence of sub-arrivals which correspond to successively higher orders of reverberation in the crust. In realistic crust models, the depth phases play an important role in the waveshapes of these sub-arrivals. By selecting an appropriate frequency band to analyze, we have been able to accurately model this type of data from explosions in the western United States. Over the very relevant regional distance ranges of 200 to 600 km, it appears that a discrimination procedure very similar to the one which is known to work for P_n will also be effective for P_g. We are investigating whether similar discriminants can be constructed based on the phases S_n and S_g in areas where those phases are prominent arrivals

Time Domain Regional Discriminants

The time and frequency domains are equivalent displays of seismic trace, information, though some qualities of the signal are more easily observed in one domain than the other. The relative frequency excitation of Lg, for instance, is most easily viewed in the frequency domain, but such waveform qualities as the sequence in which pulses arrive in the wave train or the sharpness of pulse onset are most easily studied in the time domain (Murphy and Bennett, 1982, Blandford, 1981). Because of the tremendous complexity of high frequency regional data, most attempts at using it for discrimination purposes have involved analysis of the frequency content of the various arrivals either through transforming selected windows or through multiple bandpass filtering. We report here on our initial attempts to explore the alternative and to discriminate events using those waveform characteristics most easily observed in the time domain. A second advantage of time domain analysis approaches is that they permit a deeper insight into the physical processes creating a seismic signal's character. For this reason, they can be more e3silv used to evaluate the transportabilty of a discriminant to varying geophysical and tectonic regimes. This is an especially important feature in the development of regional discriminants. The most prominent and successful spectral regional discriminants have been empirically developed. This means that they must be redeveloped and reverified in each new area. As we shall show in the following, through rigorous time domain analysis such features as regional depth phases can be identified and used to discriminate. Discriminants based on such simple physical features as source depth should be transportable anywhere. In work recently completed under the treaty verification program, we have proved that such time domain discriminants do exist. In analyzing a test discrimination data set from the western U. S., we have discovered that the onset of P_n is always very similar for explosions and that few earthquakes have this unique waveform character. This information can be constructed into a simple discrimination scheme by testing the correlation of observed P_n waveform onsets with average waveforms observed from explosions. High correlations indicate explosions and low correlations earthquakes. We have also discovered that the regional phase P_g is actually composed of a sequence of sub-arrivals which correspond to successively higher orders of reverberation in the crust. In realistic crust models, the depth phases play an important role in the waveshapes of these sub-arrivals. By selecting an appropriate frequency band to analyze, we have been able to accurately model this type of data from explosions in the western United States. Over the very relevant regional distance ranges of 200 to 600 km, it appears that a discrimination procedure very similar to the one which is known to work for P_n will also be effective for P_g. We are investigating whether similar discriminants can be constructed based on the phases S_n and S_g in areas where those phases are prominent arrivals