Outlier detection algorithms and their performance in GOCE gravity field processing

The satellite missions CHAMP, GRACE, and GOCE mark the beginning of a new era in gravity field determination and modeling. They provide unique models of the global stationary gravity field and its variation in time. Due to inevitable measurement errors, sophisticated pre-processing steps have to be applied before further use of the satellite measurements. In the framework of the GOCE mission, this includes outlier detection, absolute calibration and validation of the SGG (satellite gravity gradiometry) measurements, and removal of temporal effects. In general, outliers are defined as observations that appear to be inconsistent with the remainder of the data set. One goal is to evaluate the effect of additive, innovative and bulk outliers on the estimates of the spherical harmonic coefficients. It can be shown that even a small number of undetected outliers (<0.2 of all data points) can have an adverse effect on the coefficient estimates. Consequently, concepts for the identification and removal of outliers have to be developed. Novel outlier detection algorithms are derived and statistical methods are presented that may be used for this purpose. The methods aim at high outlier identification rates as well as small failure rates. A combined algorithm, based on wavelets and a statistical method, shows best performance with an identification rate of about 99%. To further reduce the influence of undetected outliers, an outlier detection algorithm is implemented inside the gravity field solver (the Quick-Look Gravity Field Analysis tool was used). This results in spherical harmonic coefficient estimates that are of similar quality to those obtained without outliers in the input data.     

A parametric study on the impact of satellite attitude errors on GOCE gravity field recovery

In the recent design of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, the gravity gradients are defined in the gradiometer reference frame (GRF), which deviates from the actual flight direction (local orbit reference frame, LORF) by up to 3–4°. The main objective of this paper is to investigate the effect of uncertainties in the knowledge of the gradiometer orientation due to attitude reconstitution errors on the gravity field solution. In the framework of several numerical simulations, which are based on a realistic mission configuration, different scenarios are investigated, to provide the accuracy requirements of the orientation information. It turns out that orientation errors have to be seriously considered, because they may represent a significant error component of the gravity field solution. While in a realistic mission scenario (colored gradiometer noise) the gravity field solutions are quite insensitive to small orientation biases, random noise applied to the attitude information can have a considerable impact on the accuracy of the resolved gravity field models.     

GGM02 – An improved Earth gravity field model from GRACE

A new generation of Earth gravity field models called GGM02 are derived using approximately 14 months of data spanning from April 2002 to December 2003 from the Gravity Recovery And Climate Experiment (GRACE). Relative to the preceding generation, GGM01, there have been improvements to the data products, the gravity estimation methods and the background models. Based on the calibrated covariances, GGM02 (both the GRACE-only model GGM02S and the combination model GGM02C) represents an improvement greater than a factor of two over the previous GGM01 models. Error estimates indicate a cumulative error less than 1 cm geoid height to spherical harmonic degree 70, which can be said to have met the GRACE minimum mission goals. Electronic Supplementary Material Supplementary material is available in the online version of this article at     

Spaceborne gravitational field determination by means of locally supported wavelets

In space-borne gravitational field determination, two challenges are inherent. First, the continuation of the data down to the surface of the Earth is an ill-posed problem, requiring therefore regularization techniques. Second huge data sets result requiring efficient numerical methods. In this paper, we show how locally supported wavelets on the sphere can be developed by means of a spherical version of the so-called up function. By construction, the corresponding scaling functions and wavelets are infinitely smooth, so that they can be used for regularization purposes. In particular, we show how the ill-posed pseudo-differential equations coming from satellite missions can be regularized by efficient numerical schemes using locally supported wavelets. These methods seem in particular to be interesting for regional gravity field modelling.     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF

Multiple tuned mass dampers (MTMD) consisting of many tuned mass dampers (TMDs) with a uniform distribution of natural frequencies are taken into consideration for attenuating undesirable vibration of a structure under the ground acceleration. A study is conducted to search for the preferable MTMD which performs better and is easily manufactured from the five available models (i.e. MTMD‐1 – MTMD‐5), which comprise various combinations of the stiffness, mass, damping coefficient and damping ratio in the MTMD. The major objective of the present study then is to evaluate and compare the control performance of these five models. The structure is represented by its mode‐generalized system in the specific vibration mode being controlled by adopting the mode reduced‐order approach. The optimum parameters of the MTMD‐1 – MTMD‐5 are investigated to reveal the influence of the important parameters on their effectiveness and robustness using a numerical searching technique. The parameters include the frequency spacing, average damping ratio, tuning frequency ratio, mass ratio and total number. The criteria selected for the optimum searching are the minimization of the maximum value of the displacement dynamic magnification factor (DDMF) and that of the acceleration dynamic magnification factor (ADMF) of the structure with the MTMD‐1 – MTMD‐5 (i.e. Min.Max.DDMF and Min.Max.ADMF). It is demonstrated that the optimum MTMD‐1 and MTMD‐4 yield approximately the same control performance, and offer higher effectiveness and robustness than the optimum MTMD‐2, MTMD‐3, and MTMD‐5 in reducing the displacement and acceleration responses of structures. It is further demonstrated that for both the best effectiveness and robustness and the simplest manufacturing, it is preferable to select the optimum MTMD‐1. Copyright © 2002 John Wiley & Sons, Ltd.     

1987年8月2日江西省寻乌MS5.5级地震的震害与烈度分布

从寻乌5.5级地震的地震地质构造背景，宏观震害考察结果。结合近场强地面运动观测中几次较大地震的加速度峰值。分析宏观烈度分布特征。认为烈度分布特征除了受构造控制外，还与地形，地基土质条件有关，极震区长轴方向显示鸡笼嶂-寻乌-八尺北西向断裂是寻乌地震的主要发震断层，发震构造受控于华南块体构造应力场，发震区处于北北东向河源-邵武断裂中段和东西向断裂交汇部位。     

Evaluation of the seismic hazard of Lebanon

This paper presents the results of a study undertaken todetermine the seismic hazard of Lebanon. The seismic hazard evaluation wasconducted using probabilistic methods of hazard analysis. Potential sourcesof seismic activities that affect Lebanon were identified and the earthquakerecurrence relationships of these sources were developed from instrumentalseismology data, historical records, and earlier studies undertaken toevaluate the seismic hazard of neighboring countries. The sensitivityof the results to different assumptions regarding the seismic sources in theLebanese segment and choice of the attenuation relationship wasevaluated. Maps of peak ground acceleration contours, based on 10percent of probability of exceedance in 50 years and 100 years time spans,were developed.