Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

Distribution of vertical crustal movement rates in the Tohoku district, Japan, predicted by least-squares collocation

Least-squares prediction using an empirically deduced local covariance function was performed to investigate the temporal change in the rates of vertical crustal movements in the Tohoku district, Japan. Levelling data covering an area of approximately 450 × 275 km² observed between 1966 and 1995 were used and the results shown in the form of contour maps. Firstly we derived a covariance function of the rates of vertical crustal movement with a Gaussian form function. We used this function to estimate the spatial distribution of the rates of vertical crustal movements. By the present method, a steady tilt of the Tohoku district to the east, toward the Japan Trench and an areal uplift in the southwestern part were well reproduced. Moreover, a significant temporal change in vertical movement rates is clearly seen. Received: 15 July 1996      

Application and comparison of two symptom-based eutrophication-assessment methods in Jiaozhou Bay,China

Increasing numbers of approaches to assess eutrophication, such as estuarine trophic status, the Oslo-Paris Commission Common Procedure, and the Water Framework Directive, focus on the symptoms of eutrophication. In China, however, nutrient index methods dominate the assessment of coastal waters. In this study, an integrated method that includes both water quality and ecological response was compared with the Northwest Pacifi c Action Plan (NOWPAP) Common Procedure. Observation data from Jiaozhou Bay, Shandong, China, were used in a comparison of the two methods in a trophic status study. Overall, both clearly revealed a high level of nutrient enrichment in the bay, indicated by high nutrient concentrations. Though the two methods diff ered in their methodological design in the assessment of the ecological eff ects of nutrient enrichment, they have acquired similar results: the integrated method suggested that the status was good, and the NOWPAP Common Procedure suggested that the status was low (indicating that the bay had no serious eutrophication problem). The introduction of fi lter feeders (shellfi sh aquaculture) into the bay on a reasonable scale may have been eff ective in mitigating eutrophic conditions, and perhaps explains the low ecological impacts there. Our results will be useful to ecosystem-based eutrophication management in the bay and in similar areas.     

逐步逼近曲化平方法研究

位场资料的常规处理解释方法是建立在平面数据理论之上的,然而实际的位场数据大多为曲面数据,若把曲面数据当成平面数据进行处理,必然导致很大的误差,因此有必要进行“曲化平”处理. 曲化平目前存在的主要问题是计算精度低、计算量大,因此,研究快速、精度高且适合大数据量处理的曲化平方法具有重要的价值. 本文在已有的泰勒级数曲化平方法基础上提出了逐步逼近技术和平均平面技术,使得曲面位场资料处理的精度得到了很大提高. 最后通过理论模型和实际资料的处理验证了该方法的应用效果.     

Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet

We develop a new approach for the spectral analysis of the superconducting gravimeter data to search for the spheroidal oscillation ₁S₁ of the Earth solid inner core. The new method, which we call least-squares (LS) self-coherency analysis, is based on the product of the least-squares spectra of segments of the time series under consideration. The statistical foundation of this method is presented in the new least-squares product spectrum theorem that establishes rigorously confidence levels for detecting significant peaks. We apply this approach along with a number of other innovative ideas to a 6-year long gravity series collected at the Canadian Superconducting Gravimeter Installation (CSGI) in Cantley, Canada, by splitting it into 72 statistically independent monthly records. Each monthly record is analysed spectrally and all monthly LS spectra are multiplied to construct the self-coherency spectrum of the 6-year gravity series. The self-coherency spectrum is then used to detect significant peaks in the band 3-7 h at various significant levels with the aim to identify a triplet of periods associated with the rotational/ellipsoidal splitting of ₁S₁ (Slichter triplet). From all the Slichter periods predicted by various researchers so far, Smylie's triplet appears to be the most supported one, albeit very weakly, both, before and after the atmospheric pressure effect is removed from the series. Using the viscous splitting law [Smylie, D.E., 1992. The inner core translational triplet and the density near Earth's center. Science 255, 1678-1682] as guide, we can also see one interesting and statistically significant triplet with periods A = {4.261 h, 4.516 h, 4.872 h}, which changes slightly to A′ = {4.269 h, 4.516 h, 4.889 h} after the atmospheric pressure correction is applied to the gravity series.     

Mapping and initial dilution estimation of an ocean outfall plume using an autonomous underwater vehicle

A monitoring mission to study the shape and estimate initial dilution of the S. Jacinto outfall plume using an autonomous underwater vehicle (AUV) was performed on July 30, 2002. In order to reduce the uncertainty about plume location and to concentrate the vehicle mission only in the hydrodynamic mixing zone, outputs of a near-field prediction model, based on effective real-time in situ measurements of current speed and direction and density stratification, were opportunistically used to specify in real time the mission transects. The surface characteristics of the outfall plume were found to be influenced strongly by the relatively weak stratification and low current velocities. Dilution was estimated using a temperature–salinity (TS-) diagram with initial mixing lines between wastewater and ambient waters. Effluent dilutions were at least 30:1 in this study. In order to efficiently map the plume dispersion we applied the least-squares collocation method technique. Our results demonstrate that AUVs can provide high-quality measurements of physical properties of effluent plumes in a quite effective manner and valuable considerations about the initial mixing processes under real oceanic conditions can be further investigated.     

New analytical and numerical approaches for geopotential modeling

 The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential coefficients _n,m . In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal harmonic series is developed for the geopotential and then its coefficients _n,m ^e are transformed to the unknown _n,m . The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From two sets of _n,m (n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068) by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to apply the LS technique for evaluating geopotential coefficients. Received: 12 December 2000 / Accepted: 21 June 2001     

大连双井测汞震例分析

根据大连双井测汞震例，用最小二乘法原理，就汞测量预测地震进行了定理化研究，给出适宜本地区的经验预测公式，取得初步研究成果。     

A study on the combination of satellite, airborne, and terrestrial gravity data

Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.     

The ‘Stained Glass Procedure’, a new method to compare classification performance of images acquired with different pixel sizes

Objective comparison of classification performance of earth observation images, acquired at different spatial resolutions (e.g. NOAA-AVHRR, IRS-MOS, IRS-WiFS, Landsat-TM, IRS-LISS), is complicated because both class definition and training site selection are hampered by the inherent scale differences. This paper presents a new, generic method to compare the information content of such a set of images, the “Stained Glass Procedure”. It overcomes the stated problems by computing the scale-dependent, internal spectral variation in an image and by using this as an indicator for land cover information. The Stained Glass Procedure creates segments in the images and calculates the internal spectral variation in a high-spatial-resolution image for each segment. For each image from the set the average variance, weighted to area, is calculated. The Stained Glass Procedure can be used to predict the performance of sensors that are not available, yet, or to roughly determine the optimal spatial resolution for the classification of a specific area.The procedure was applied to images with pixel sizes ranging from 23 to 1100 m. Classification detail of Envisat-MERIS (300 m pixel size), not included in the image set, could be predicted accurately using the Stained Glass Procedure.The Stained Glass Procedure applies one procedure to all images, without any subjective decision during the analysis, thus offering a method to compare images with different pixel sizes in terms of classification detail that is truly objective.