Altimetry–gravimetry problems with free vertical datum

 The definition and connection of vertical datums in geodetic height networks is a fundamental problem in geodesy. Today, the standard approach to solve it is based on the joint processing of terrestrial and satellite geodetic data. It is generalized to cases where the coverage with terrestrial data may change from region to region, typically across coastlines. The principal difficulty is that such problems, so-called altimetry–gravimetry boundary-value problems (AGPs), do not admit analytical solutions such as Stokes' integral. A numerical solution strategy for the free-datum problem is presented. Analysis of AGPs in spherical and constant radius approximation shows that two of them are mathematically well-posed problems, while the classical AGP-I may be ill posed in special situations. Received: 2 December 1998 / Accepted: 30 November 1999     

A non-iterative and non-singular perturbation solution for transforming Cartesian to geodetic coordinates

The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km the second-order expansions yields ~mm satellite geodetic height errors and ~10⁻¹² rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate the effectiveness of the new algorithm.     

Geodetic methods for detecting volcanic unrest: a theoretical approach

In this paper we study the application of different geodetic techniques to volcanic activity monitoring, using theoretical analysis. This methodology is very useful for obtaining an idea of the most appropriate (and efficient) monitoring method, mainly when there are no records of geodetic changes previous to volcanic activity. The analysis takes into account the crustal structure of the area, its geology, and its known volcanic activity to estimate the deformation and gravity changes that might precede eruptions. The deformation model used includes the existing gravity field and vertical changes in the crustal properties. Both factors can have a considerable effect on computed deformation and gravity changes. Topography should be considered when there is a steep slope (greater than 10°). The case study of Teide stratovolcano (Tenerife, Canary Islands), for which no deformation or gravity changes are available, is used as a test. To avoid considering topography, we worked at the lowest level of Las Cañadas and examined a smaller area than the whole caldera or island. Therefore, the results are only a first approach to the most adequate geodetic monitoring system. The methodology can also be applied to active areas where volcanic risk is not associated with a stratovolcano but instead with monogenetic scattered centers, especially when sites must be chosen in terms of detection efficiency or existing facilities. The Canary Islands provide a good example of this type of active volcanic areas, and we apply our model to the island of Lanzarote to evaluate the efficiency of the monitoring system installed at the existing geodynamic station. On this island topography is not important. The results of our study show clearly that the most appropriate geodetic volcano monitoring system is not the same for all different volcanic zones and types, and the particular properties of each volcano/zone must be taken into account when designing each system.     

关于改善和更新国家大地测量基准的思考

大地测量基准是地理信息系统和测图的基础框架,其建立,维护,改善和更新是国家测绘行政主管部门的重要职责。大地测量基准中的重力基准和坐本身由于自然和人为原因,破损严重,因此顺应科技进步,国家建设和社会发展的需要。     

中国及邻近地区地磁正常场及其长期变化的计算

本文根据国际地磁参考场系数,计算了中国地区1945～1990年代2~0×2~0网格地磁正常场值,并绘出了相应的正常场等值线图和等变线图,对其变化规律进行了分析.     

Geodetic measurement of the local elastic response to the changing mass of water in Lago Laja, Chile

A geodetic station (ANTC) built in bedrock in southern Chile is undergoing non-steady vertical motion within a range of nearly 50 mm. These fluctuations are dominated by the earth’s local elastic response to the changing weight of water in a reservoir located about 20 km away. There is also an annual periodic component of motion that is attributed to global and regional patterns of loading, as well as a steady tectonic signal. The local loading response constrains the average elastic structure of the area, and implies a stiffness that falls near the lower end of the range observed in rock samples.     

Alternatives to current GPS-RTK services and some implications for CORS infrastructure and operations

The justification for the establishment of CORS networks was initially in support of geodesy and other geoscientific applications at the global and regional level. However, increasingly GPS CORS network operators have sought ways of making their network infrastructure the basis of a profitable business. This has arisen with the introduction of real-time centimeter-level accuracy services, carrier phase-based modes of operation generally referred to as GPS-RTK (real-time kinematic). One approach is to try to recruit a core group of users who are prepared to pay for the GPS-RTK services. But this is only feasible if the number of users, and the fees that are charged, are sufficient to generate a reasonable return-on-investment (ROI). This ROI (or at the very least “cost-recovery”) is important for many network operators in order that they may provide for the maintenance and upgrade of the CORS infrastructure. On the other hand, there are those who advocate that there is no need to recoup CORS investment, that the installed GPS receivers should be seen as public infrastructure in a similar manner to roads, bridges, etc. This paper discusses some new business and operational models for GPS-RTK services. These include models for the establishment and operation of CORS infrastructure, service provision, business cases, and options for value-added services beyond the standard GPS-RTK service. One concept is based on a “client–server” model. Currently GPS-RTK service providers have no control over the quality of the results computed by users. This makes it difficult for them to justify charging for their services. What if instead of broadcasting RTK corrections and placing the onus of obtaining a final solution on the user and his equipment, the user’s coordinates are determined by the service provider? Putting the computational effort on the server side will justify more easily the charging of users for a value-added product: an accurate and quality assured coordinate in the local reference frame. This paper describes the client–server concept as well as possible business models that may underpin such a service model. These models include some derived from mobile telephony and service/hospitality businesses. Furthermore, with the projected proliferation of independent, competitive GPS-RTK services, the concept of a GPS data or service “broker” is worth exploring.     

三维有限单元反演的数学方法

以三维节理单元为基础,讨论了利用三维双节点节理单元模型反演地形变资料的理论基础及方法的应用,推导了具体应用的有限元公式及反演的数学公式,并编制了相应的计算程序。最后,通过模型实例的实际计算,研究了方法的可行性。      

Evaluation of earthquake potential along the Northern Anatolian Fault Zone in the Marmara Sea using comparisons of GPS strain and seismotectonic parameters

Seismotectonic parameters including the Gutenberg-Richter b-value and multifractal dimensions D₂ and D₁₅ of seismicity patterns (both spatial and temporal) were compared to GPS-derived maximum shear and dilatation strains measured in the Marmara Sea region of western Turkey along the Northern Anatolian Fault Zone (NAFZ). Comparisons of seismotectonic parameters and GPS-derived maximum shear and dilatation strain along the NAFZ in the vicinity of the 1999 M7.4 Izmit earthquake reveal a positive correlation (r = 0.5, p = 0.05) between average dilatation and the Gutenberg-Richter b-value. Significant negative correlation (r = − 0.56, p = 0.03 and r = − 0.56, p = 0.02) was also observed between the spatial fractal dimension D₂ and GPS-derived maximum geodetic and shear strain. This relationship suggests that, as maximum geodetic and shear strains increase, seismicity becomes increasingly clustered.Anomalous interrelationships are observed in the Marmara Sea region prior to the Izmit event along a bend in the NAFZ near the eastern end of the Marmara Sea known as the Northern Boundary Fault (NBF). An asperity is located near the northwest end of the NBF. Along the 50-km length of the NBF, GPS strains become slightly compressive. The correlation between b-value and GPS-derived dilatation suggests that regions in compression have increased probability of larger magnitude rupture. The NBF appears to serve as an impediment to the transfer of strain from east to west along the NAFZ. Recurrence times for large earthquakes along the NBF are larger than in surrounding areas. Temporal clustering of seismicity in the vicinity of the NBF may represent foreshocks of an impending rupture.     

Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley’s Method

By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.