Non-linear inversion using general measures of data misfit and model structure

We investigate the use of general, non- l ₂ measures of data misfit and model structure in the solution of the non-linear inverse problem. Of particular interest are robust measures of data misfit, and measures of model structure which enable piecewise-constant models to be constructed. General measures can be incorporated into traditional linearized, iterative solutions to the non-linear problem through the use of an iteratively reweighted least-squares (IRLS) algorithm. We show how such an algorithm can be used to solve the linear inverse problem when general measures of misfit and structure are considered. The magnetic stripe example of Parker (1994 ) is used as an illustration. This example also emphasizes the benefits of using a robust measure of misfit when outliers are present in the data. We then show how the IRLS algorithm can be used within a linearized, iterative solution to the non-linear problem. The relevant procedure contains two iterative loops which can be combined in a number of ways. We present two possibilities. The first involves a line search to determine the most appropriate value of the trade-off parameter and the complete solution, via the IRLS algorithm, of the linearized inverse problem for each value of the trade-off parameter. In the second approach, a schedule of prescribed values for the trade-off parameter is used and the iterations required by the IRLS algorithm are combined with those for the linearized, iterative inversion procedure. These two variations are then applied to the 1-D inversion of both synthetic and field time-domain electromagnetic data.     

A TEST OF THREE FITTING CRITERIA FOR MULTIRESPONSE NON-LINEAR MODELING

This work evaluates objective functions for multiresponse non-linear modeling using computersimulations.Tests are performed under a variety of signal-to-noise ratios and noise variance-covariancestructures.The standard error of prediction for the model parameters,computed from 50 trials,is usedfor performance comparisons.The full rank and rank-deficient problems are considered.For the fullrank problem one model was investigated,a first-order two-step consecutive reaction model,and twoobjective functions were considered,the total sum of squares and the determinant criterion.Nodistinction could be made between the two objective functions for this model.For the rank-deficient case two models were investigated,a first-order two-step consecutive reactionas in the full rank case,and a pH titration model described by the Henderson-Hasselbalch equation.Three objective functions were investigated for the rank-deficient case,the total sum of squares,aweighted total sum of squares and the determinant criterion.The total sum of squares was found toperform poorly under all conditions tested compared to the weighted total sum of squares and thedeterminant criterion.The determinant criterion was found to perform much better than the other twocriteria when the data have a combination of a low signal-to-noise ratio and high variance-covariancenoise structure.     

A model for the Am (Km) planetary geomagnetic activity index and application to prediction

We studied the existence of dynamical stochastic relations in the evolution of the am index. A first analysis of the autocorrelation functions showed evidence of several seasonalities. We first used linear (ARMA) models, and it was found that these do not account for the whole internal dynamics of the data series. We then used various non-linear models to provide a better fit to reality. The forecast performances of the non-linear models are not significantly different from those of the linear model. We give a tentative explanation for the failure of the non-linear predictions. Finally, ARCH models were used in order to take into account the fact that the confidence interval for the predicted value depends on past observations.     

洋山港海域潮动力特征及其对工程的响应

距上海陆域外约32 km的洋山港是以小洋山岛链为基础建造的中国首个离岸式深水港口, 其港区陆域是通过封堵北岛链三个主要汊道并抛填成陆而成。大规模的封堵陆连工程改变了该海域的地形边界条件, 海域潮动力特征也随之响应。通过对洋山港海域堵汊陆连工程前后潮位及潮流实测资料的分析研究, 发现洋山港海域的潮动力特征主要表现在:海域潮波倍潮及复合潮增幅随工程的进行而增大, 潮动力表现出明显的非线性特征;海域中部发生壅水;海域潮波向驻波性质变异并于憩流时段引发环状流场。