Peiliang Xu

Truncated singular value decomposition (TSVD) techniques have been widely used in inversion. The method of truncation determines the quality of a truncated SVD solution, but truncation has often been done arbitrarily. The first workable criterion for truncation was based on F-statistical testing, but has only rarely been used in geophysical inversion. Recently, the L-curve approach was proposed for the same purpose, and soon found many applications in interdisciplinary inverse problems. Up to th

The findings of this paper are summarized as follows: (1) We propose a sign-constrained robust estimation method, which can tolerate 50% of data contamination and meanwhile achieve high, least-squares-comparable efficiency. Since the objective function is identical with least squares, the method may also be called sign-constrained robust least squares. An iterative version of the method has been implemented and shown to be capable of resisting against more than 50% of contamination. As a by-prod

Determination of surface gravity anomalies from gradiometric observables poses one of the downward continuation problems in physical geodesy. The unstable characteristics of the problem have been well exposed on the base of spectral analysis. The purpose of this paper is to develop a new approach to obtaining the best resolutions of mean gravity anomalies in terms of mean square errors, biases and error variances from the point of view of biased estimation. The three algorithms of ridge regressi

The method of generalized cross-validation (GCV) has been widely used to determine the regularization parameter, because the criterion minimizes the average predicted residuals of measured data and depends solely on data. The data-driven advantage is valid only if the variance-covariance matrix of the data can be represented as the product of a given positive definite matrix and a scalar unknown noise variance. In practice, important geophysical inverse ill-posed problems have often been solved

Abtract Crustal deformation on land can now be measured and monitored routinely and precisely using space geodetic techniques. The same is not true of the seafloor, which covers about 70 percent of the earth surface, and is critical in terms of plate tectonics, submarine volcanism, and earthquake mechanisms of plate boundary types. We develop new data processing strategies for quantifying crustal deformation at the ocean floor: single- and double-difference methods. Theoretically, the single dif

Although real-valued linear models, whether or not of full rank, have been thoroughly investigated and are well documented, very little is known about statistical and probabilistic aspects of a mixed integer linear model, which arose from space geodesy and serves as the standard starting model for precise positioning using the global positioning system (GPS). Voronoi cells play a fundamental role in the least squares estimation of the integer unknowns of the model. In this paper, we first develo