On a curious property of Bell numbers

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.Comment: 6 page

Modeling of residual spheres for subduction zone earthquakes: 1. Apparent slab penetration signatures in the NW Pacific caused by deep diffuse mantle anomalies

We have computed focal residual spheres for 145 subduction zone earthquakes along the northwest edge of the Pacific using regional and global mantle velocity models from tomographic inversions. The mantle models explain much of the observed residual sphere data and, to a certain extent, suggest the location of mantle velocity heterogeneities which are responsible for various residual sphere patterns. For most deep events considered, the fast slablike residual sphere anomalies are caused by diffuse heterogeneities, mainly of deep lower mantle and receiver mantle origin rather than by an extension of the slab. The region immediately below the deepest earthquakes, depths of 650–1500 km, has an effect usually smaller than or comparable to the effect of other regions of the mantle. Without a proper account of the teleseismic effect, attributing the long-wavelength anomalies of the residual sphere to near-source slab effects alone, or even primarily, is not valid. The fast bands in many observed residual spheres agree with seismicity trends. Once the deep mantle and receiver mantle effects are removed, these may give the approximate orientation, but not the depth extent, of near-source fast velocities. For most deep earthquakes under Japan the predominant fast band is subhorizontal rather than near vertical. This type feature would be overlooked in conventional residual sphere studies using only steeply diving rays and cosine weighting of the data

TIPS: Taking Inflation Premium Seriously

This paper asks the question of whether the newly available TIPS yields data can help us achieve a better understanding of the real term structure and the inflation expectations. The yield differential between TIPS and comparable nominal coupon securities is not a direct measure of inflation expectations, because it contains inflation risk premium, and because the TIPS yield may depart from the true "real yield," due to low investor demand especially in the early years. Without using data from the (indexed) real bond market, we cannot fully identify the real interest rate from the inflation risk premium, unless we assume that all information affecting the real term structure is reflected in the nominal bond prices. Even with this assumption, empirical identification of the real term structure is hard to achieve because of the poor measurement and the frequent revisions of the price series. We develop a flexible multifactor term-structure model to allow for suitable specifications of liquidity premium on TIPS, as well as complications caused by lagged indexation. We estimate the model by the Kalman filter using TIPS yields, nominal bond yields, realized inflation and survey data on interest rates and inflationTIPS, Inflation risk premium, term structure of interest rates

Source Mechanism and Rupture Directivity of the 18 May 2009 M_W 4.6 Inglewood, California, Earthquake

On 18 May 2009, an M_w 4.6 earthquake occurred beneath Inglewood, California, and was widely felt. Though source mechanism and its location suggest that the Newport–Inglewood fault (NIF) may be involved in generating the earthquake, rupture directivity must be modeled to establish the connection between the fault and the earthquake. We first invert for the event’s source mechanism and depth with the cut-and-paste method in the long-period band (>5 s). Because of the low velocity shallow sediments in the Los Angeles (LA) basin, we use two velocity models in the inversion for stations inside and outside the LA basin. However, little difference is observed in the resolved source mechanism (M_w 4.6, strike 246°/145°, dip 50°/77°, rake 17°/138°) and depth (7 to ~9 km), compared to an inversion using the standard southern Calfornia model. With the resolved source parameters, we calibrate the amplitude anomaly of the short-period (0.5–2 Hz) P waves with amplitude adjustment factors (AAF). These AAFs are used as corrections when retrieving source mechanisms of the smaller aftershocks using short-period P waves alone. Most of the aftershocks show similar source mechanisms as that of the mainshock, providing ideal empirical Green’s functions (EGFs) for studying its rupture process. We use a forward modeling approach to retrieve rupture directivity of the mainshock, consistent with movement on the NIF with rupture toward the southeast. Although we focus on P waves for analyzing rupture directivity, the resolved unilateral pattern is also confirmed with the azimuthal variation of the duration of SH waves observed in the basin. The high rupture velocity near the shear velocity and relatively low stress drop are consistent with the hypothesis of rupture on a mature fault

PSIDD (2): A Prototype Post-Scan Interactive Data Display System for Detailed Analysis of Ultrasonic Scans

This article presents the description of PSIDD(2), a post-scan interactive data display system for ultrasonic contact scan and single measurement analysis. PSIDD(2) was developed in conjunction with ASTM standards for ultrasonic velocity and attenuation coefficient contact measurements. This system has been upgraded from its original version PSIDD(1) and improvements are described in this article. PSIDD(2) implements a comparison mode where the display of time domain waveforms and ultrasonic properties versus frequency can be shown for up to five scan points on one plot. This allows the rapid contrasting of sample areas exhibiting different ultrasonic properties as initially indicated by the ultrasonic contact scan image. This improvement plus additional features to be described in the article greatly facilitate material microstructural appraisal

Earthquake Centroid Locations Using Calibration from Ambient Seismic Noise

Earthquakes occur in complex geology, making it difficult to determine their source parameters and locations because of uncertainty in path effects. We can avoid some of these problems by applying the cut-and-paste (CAP) method, which allows for timing shifts between phases, assuming a 1D model, and determines source parameters. If the travel times or lags of the phases due to path effects are known relative to a reference model, we can locate the events’ centroid with surface waves without knowledge of the 3D velocity structure. Here, we use ambient seismic noise for such a calibration. We cross correlate the seismic stations near the earthquake with stations 100–300 km away to obtain the 10–100-s surface wave Green’s functions. The new method is tested in southern California to locate the 2008 Chino Hills earthquake, which proves consistent with the epicenter location from P waves. It appears possible to use the location offset between the high-frequency P-wave onset relative to the centroid to provide a fast estimate of directivity

Hidden hotspot track beneath the eastern United States

Hotspot tracks are thought to be the surface expressions of tectonic plates moving over upwelling mantle plumes, and are characterized by volcanic activity that is age progressive. At present, most hotspot tracks are observed on oceanic or thin continental lithosphere. For old, thick continental lithosphere, such as the eastern United States, hotspot tracks are mainly inferred from sporadic diamondiferous kimberlites putatively sourced from the deep mantle. Here we use seismic waveforms initiated by the 2011 M_w 5.6 Virginia earthquake, recorded by the seismic observation network USArray, to analyse the structure of the continental lithosphere in the eastern United States. We identify an unexpected linear seismic anomaly in the lower lithosphere that has both a reduced P-wave velocity and high attenuation, and which we interpret as a hotspot track. The anomaly extends eastwards, from Missouri to Virginia, cross-cutting the New Madrid rift system, and then bends northwards. It has no clear relationship with the surface geology, but crosses a 75-million-year-old kimberlite in Kentucky. We use geodynamical modelling to show that an upwelling thermal mantle plume that interacts with the base of continental lithosphere can produce the observed seismic anomaly. We suggest that the hotspot track could be responsible for late Mesozoic reactivation of the New Madrid rift system and seismicity of the eastern United States