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.

Generalized linear joint PP-PS inversion based on two constraints

Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We propose a joint PP-PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion.A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data,the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion,low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness,and a fast algorithm is used to solve the objective function while minimizing the computational load.The proposed method has superior antinoising properties and well reproduces real data.

Noise filtering of full-gravity gradient tensor data

In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.

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.

Separation method for multi-source blended seismic data

Multi-source seismic technology is an efficient seismic acquisition method that requires a group of blended seismic data to be separated into single-source seismic data for subsequent processing. The separation of blended seismic data is a linear inverse problem. According to the relationship between the shooting number and the simultaneous source number of the acquisition system, this separation of blended seismic data is divided into an easily determined or overdetermined linear inverse problem and an underdetermined linear inverse problem that is difficult to solve. For the latter, this paper presents an optimization method that imposes the sparsity constraint on wavefields to construct the object function of inversion, and the problem is solved by using the iterative thresholding method. For the most extremely underdetermined separation problem with single-shooting and multiple sources, this paper presents a method of pseudo-deblending with random noise filtering. In this method, approximate common shot gathers are received through the pseudo-deblending process, and the random noises that appear when the approximate common shot gathers are sorted into common receiver gathers are eliminated through filtering methods. The separation methods proposed in this paper are applied to three types of numerical simulation data, including pure data without noise, data with random noise, and data with linear regular noise to obtain satisfactory results. The noise suppression effects of these methods are sufficient, particularly with single-shooting blended seismic data, which verifies the effectiveness of the proposed methods.

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.