Peeling linear inversion of upper mantle velocity structure with receiver functions

A peeling linear inversion method is presented to study the upper mantle （from Moho to 800 km depth） velocity structures with receiver functions. The influences of the crustal and upper mantle velocity ratio error on the inversion results are analyzed, and three valid measures are taken for its reduction. This method is tested with the IASP91 and the PREM models, and the upper mantle structures beneath the stations GTA, LZH, and AXX in northwestern China are then inverted. The results indicate that this inversion method is feasible to quantify upper mantle discontinuities, besides the discontinuities between 3hM （hM denotes the depth of Moho） and 5hM due to the interference of multiples from Moho. Smoothing is used to overcome possible false discontinuities from the multiples and ensure the stability of the inversion results, but the detailed information on the depth range between 3hM and 5hM is sacrificed.

Estimation on site-amplification from different methods using strong motion data obtained in Tangshan, China

A seismic observation array for strong motions was deployed to estimate seismic source, propagation path and local site effects in Tangshan, China. We compared site response from the S-wave inversion and those from other techniques, such as traditional direct spectral ratios of S waves and receiver-function of S waves. From the inversion, we found that S-wave quality factor, i.e. Qs-value, is approximately satisfied with the relation of Qs=67f1.1 in the range of frequency from 0.5 Hz to 32 Hz and that the source spectra follow the ω-2 model of seismic source for low frequencies less than about 12 Hz. From the comparison of site responses estimated by the different methods for each soil site, we found that all the methods can extract the same predominant peaks from the responses, the amplifications from direct S-wave spectral ratios are well correlated with those from the S-wave inversion within a factor of 2 to 3, while the correlation between the amplifications from S-wave receiver-function and those from the S-wave inversion is not good, especially for high frequencies more than 8 Hz.

Estimating the Retrievability of Temperature Profiles from Satellite Infrared Measurements

A method is developed to assess retrievability, namely the retrieval potential for atmospheric temperature profiles, from satellite infrared measurements in clear-sky conditions. This technique is based upon generalized linear inverse theory and empirical orthogonal function analysis. Utilizing the NCEP global temperature reanalysis data in January and July from 1999 to 2003, the retrievabilities obtained with the Atmospheric Infrared Sounder （AIRS） and the High Resolution Infrared Radiation Sounder/3 （HIRS/3） sounding channel data are derived respectively for each standard pressure level on a global scale. As an incidental result of this study, the optimum truncation number in the method of generalized linear inverse is deduced too. The results show that the retrievabilities of temperature obtained with the two datasets are similar in spatial distribution and seasonal change characteristics. As for the vertical distribution, the retrievabilities are low in the upper and lower atmosphere, and high between 400 hPa and 850 hPa. For the geographical distribution, the retrievabilities are low in the low-latitude oceanic regions and in some regions in Antarctica, and relatively high in mid-high latitudes and continental regions. Compared with the HIRS/3 data, the retrievability obtained with the AIRS data can be improved by an amount between 0.15 and 0.40.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

A spectrometer for measuring particle size distributions in the range of 3 nm to 10 μm

A spectrometer combining electrical mobility sizing and aerodynamic sizing was developed to measure aerosol size distributions in the range of 3 nm to 10 μm. It includes three instruments which cover different size ranges （a nano scanning mobility particle sizer （NSMPS, 3 - 60 nm）, a regular scanning mobility particle sizer （RSMPS, 40 - 700nm）, and an aerodynamic particle sizer （APS, 550nm- 10 μm））. High voltage and sheath flow of the NSMPS and RSMPS were supplied using two home-built control boxes. A LabVIEW program was developed for spectrometer automatic operation. A linear inversion method was applied to correct particle multiple charging effects and to integrate data from the three instruments into a wide-range size distribution. Experi- ments were conducted to compare distributions in the overlap size ranges measured by three instruments. Good agreement between the NSMPS and RSMPS was achieved after correcting for the difference in counting efficiencies of the two particle counters. Aerodynamic size distribu- tions reported by the APS were converted to mobility size distributions by applying an effective density method. Distributions measured by the RSMPS and APS were consistent in the overlap size range of 550 - 700 nm. A full spectrum in the size range of 3nm to 10~tm was demonstrated by measuring aerosol generated using a mixture of different sized polystyrene latex spheres.

A STOCHASTIC ALGORITHM FOR FAULT INVERSE PROBLEMS IN ELASTIC HALF SPACE WITH PROOF OF CONVERGENCE

A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in[11].We show in this paper how it can be used to solve the fault inverse problem,where a planar fault in elastic half-space and a slip on that fault have to be reconstructed from noisy surface displacement measurements.With the parameter giving the plane containing the fault denoted by m and the regularization parameter for the linear part of the inverse problem denoted by C,both modeled as random variables,we derive a formula for the posterior marginal of m.Modeling C as a random variable allows to sweep through a wide range of possible values which was shown to be superior to selecting a fixed value[11].We prove that this posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.Simply put,our proof only assumes that the regularized discrete error functional for processing measurements relates to an order 1 quadrature rule and that the union of the finite-dimensional spaces for discretizing slips is dense.Our proof relies on trace class operator theory to show that an adequate sequence of determinants is uniformly bounded.We also explain how our proof can be extended to a whole class of inverse problems,as long as some basic requirements are met.Finally,we show numerical simulations that illustrate the numerical convergence of our algorithm.