Trigonometric Leveling Research Articles

Elevation determination of nunataks in the Grove Mountains

A majority of the exposed nunataks located in the Grove Mountains of the Antarctic interior haveyet to have had their elevations measured. The elevations of Mason Peak and Wilson Ridge were precisely determined by the Grove Team of the 26th CHINARE in 2010, with Mason Peak turning out to be the highest of theGrove Mountains. Considering that both Mason Peak and Wilson Ridge are difficult to climb because of theircragginess, we first selected three control points on the ice surface near Mason Peak and positioned them withGPS. Thus, accurate elevations of Mason Peak and Wilson Ridge could be calculated from three directions usingforward intersection and trigonometric leveling of a high-precision theodolite at the chosen control points. Theresults provide basic geodetic information that can be referred to as high-precision control points for surveyingand mapping in this part of Antarctica. This paper elaborates on the process of measurement and computation ofthe mountains summit elevations, and also analyzes the details of the principal elements influencing the accuracyof trigonometric leveling, the determination of refraction coefficients k, and observations of structure and distance.

Height Determination of Qomolangma Feng (MT. Everest) in 2005

Since the 1960s China has carried out several geodetic campaigns for measuring the height of Qomolangma Feng-Mt. Everest independently or in cooperation with foreign countries. Large scale geodetic field work and data processing have been done in the campaigns, dealing with positioning, height determination, gravimetry, astronomical measurement and atmospheric reflection observation etc. Some survey tasks were done in order to improve the accuracy and reliability for the height determination of Mt. Everest. These tasks include setting up of a survey target on the summit of Mt. Everest (MES) in the 1975, 1992 and 2005 campaigns, joint use of GPS, laser ranging and trigonometric levelling in the 1992 and 2005 campaigns, exploration of the thickness of the ice-snow layer on the summit and refinement of the local gravity field including the geoid in the northern slope area with new surface ground gravity data, DTM and astro-gravity levelling or GPS levelling results in the campaigns mentioned. It is the first time in China that the thickness of the ice-snow layer on the summit was measured by ground penetrating radar integrated with GPS in the 2005 campaign. The orthometric heights of the snow surface and rock surface of the summit were determined as 8847.93m and 8844.43m respectively in the 2005 campaign. The rate of decrease of the snow summit of Mt. Everest between 1992 and 2005 was 1.8cm/a.

Precise height determination using simultaneous-reciprocal trigonometric levelling

Precise levelling method has been used for the determination of precise height for many years. The application of this technique is difficult, time consuming and expensive especially in rough terrains. These difficulties have forced researchers to examine alternative methods of height determination.As a result of modern technological developments for high-tech instruments, research of the precision trigonometric levelling has been required once again. In this study, simultaneous-reciprocal trigonometric levelling (SRTL) method is applied with different sight distances in order to determine optimum sight distances using a sample test network in Selcuk University Campus, Konya, Turkey. The results are compared with precise geometric levelling in terms of precision, cost and feasibility. SRTL method for sight distance S=200m resulted with the standard deviations of ±1.86 mm / √ km and with the production speed of 4 km/day.

Theoretical and Numerical Aspects of the Geodetic Method for Determining the Atmospheric Refraction Coefficient Using Simultaneous and Mutual Zenith Observations

The estimation of the atmospheric refraction coefficient by conducting simultaneous and mutual zenith observations is a well-known geodetic procedure. The respective mathematical model is based on certain assumptions regarding the actual path followed by the optical ray while propagating in the atmosphere (spherical symmetric model). Starting from this model an approximate solution can be derived, which is generally accepted in the literature on the subject. The present paper examines the mathematical model of this geodetic technique in a rigorous manner, which results in an exact solution for the computation of the atmospheric refraction coefficient or equivalent for the zenith angle correction that is due to the effect of the atmospheric refraction. As the direct computation of the exact solution is rather complicated, an iterative way of computing the same quantity is derived, which can be realized easily on any pocket calculator. In order to assess the derived formulas we investigate the applicability of the exact, the convergence rate of the iterative and the errors introduced by the approximate formulas, by conducting a representative series of synthetic numerical experiments. The overall discussion aims to provide a helpful insight into the geometric and theoretical features of this traditional geodetic method. To practitioners that attempt to apply the standard correction formulas to zenith observations in order to compensate the effect of atmospheric refraction in the frame of typical surveying applications, such as trigonometric leveling, the paper also points out possible numerical errors introduced by the traditional approximate formulas.

DETERMINAÇÃO DE DESNÍVEIS DE PRECISÃO COM NIVELAMENTO TRIGONOMÉTRICO UTILIZANDO ESTAÇÃO TOTAL

The advances of the microelectronics applied to the instruments used in Topography and Geodesy have led to the development of precise, light and easy handling equipments, as the Total Stations, which have enormously facilitated the field work. With such characteristics, an issue raises: the achievement of the precise difference in elevation when using the method of trigonometric leveling with total station. A research was carried out in order to find out the accuracy in the determination of elevation difference by trigonometric leveling using total stations classified by the Associacao Brasileira de Normas Tecnicas (ABNT) as of low, medium and high precision - in comparison with the elevation difference obtained by the method of the differential leveling established in accordance with the Especificacoes e Normas Gerais para Levantamentos Geodesicos do Instituto Brasileiro de Geografia e Estatistica (IBGE). The results present the expected accuracy and depend on the precision of the total station.

UMA ABORDAGEM GEODÉSICA DE TÉCNICAS ÓPTICAS DE MEDIÇÃO TRIDIMENSIONAL PARA DETERMINAÇÃO E TRANSPORTE DE ALTURAS EM ÁREAS DE RISCO

This work deals with methods of applied geodesics related to threedimensional measurement optic techniques applied to determine vertical movements and transport of heights through modern geodesic instrumentation. It considers the importance and necessity for the study of geodesic methods of three-dimensional positioning, by polar measurement systems based on theodolites. It considers the current demands for industrial applications resulting from the need for greater geometrical precision in the construction industry and in the operation of machines and efficiency in the control of operational and environmental risks, conventional geodesic measurement methods need to be automated to be able to be employed. Such is the case, for example, of the requirements for an increase in speed and precision as well as a reduction of measurement costs that are associated to quality control. The acquisition of vertical movement as well as the transport of heights can be carried out by using the geometric levelling method as well as through transference of theodolitic height. By the polar method, grid line method and procedures derived from trigonometric levelling. For angular measurements of directions and distances, based on advance intersection and polar measurement, they are potentially useful-principally in restricted surroundings or in no conventional monitoring applications - pointing and video theodolites, electronic tacheometry and video tacheometry. In a general way, these systems are based on theodolites, as the hybrid measurement system, which have manual functioning (manual system) or are adapted to motors (motorized systems) for completely automatic functioning. The importance of pre-analysis and field observations are worth emphasizing, in three-dimensional geodesic network as reference to precise positioning of the objects under study, so that they can be studied and analysed as much for vertical movement as height transport. Thus searching for more appropriate solutions for stability of buildings and therefore a reduction in construction risks.

Determination of Northeast Asia's Highest Peak (Mt. Jade) by Direct Levelling

This paper demonstrates the results and problems in determining the height of Mt. Jade by direct levelling. Mt Jade is the highest peak in northeast Asia. GPS levelling and trigonometricl levelling were also made to validate the result of direct levelling. For GPS levelling a new geoid model is constructed using Taiwan's latest gravity database and elevation model. The accuracy of the geoid model ranges from cm in coastal plains to dm in high mountains. Helmert deflections of the vertical derived from this geoid model improve the accuracy of trigonometric levelling. Gravity data at benchmarks were collected to compute orthometric corrections for the heights from direct levelling. The Poincaré-Prey reduction and the modified Mader reduction of mean gravity yield orthometric corrections that differ by up to dm near Mt. Jade. The Helmert orthometric height of Mt. Jade determined in this work is 3951.798 m, with a 72-mm commission error. The problem of using a rigorous orthometric height is discussed.

Precise Height Determination Using Leap-Frog Trigonometric Leveling

Precise leveling has been used for the determination of accurate heights for many years. The application of this technique is difficult, time consuming, and expensive, especially in rough terrain. These difficulties have forced researchers to examine alternative methods of height determination. As a result of modern high-tech instrument developments, research has again been focused on precision trigonometric leveling. In this study, a leap-frog trigonometric leveling (LFTL) is applied with different sight distances on a sample test network at the Selcuk University Campus in Konya, Turkey, in order to determine the optimum sight distances. The results were compared with precise geometric leveling in terms of precision, cost, and feasibility. Leap-frog trigonometric leveling for the sight distance S=150 m resulted in a standard deviation of ±1.87 mm∕km and with a production speed of 5.6 km∕day .

Progress in technology for the 2005 height determination of Qomolangma Feng (Mt. Everest)

In 2005 China carried out a new geodetic campaign for the height determination of Qomolangma Feng——Mt. Everest (QF in short). The technical progresses in geodesy for the 2005 campaign are presented in the paper. GPS positioning was the key technique in the campaign. After summarizing the experiences and lessons of the GPS positioning on the QF summit in the previous QF height determination campaigns, some measures were taken to raise the accuracy and reliability of the height determination with GPS techniques. In order to raise the accuracy of the height determination of the QF summit with classical geodetic techniques, laser ranging was used together with the trigo-nometric levelling in the 2005 campaign. It is the first time in China the thickness of the ice-snow layer on the QF summit was measured by ground penetrating radar integrated with GPS. The local gravity field and geoid in the QF area was improved on the basis of earth gravity field model integrated with new ground gravity data, DTM data and GPS leveling data in the QF area. In the 2005 campaign the normal height and orthometric height (height above sea level) of the snow surface of the QF summit were obtained as 8846.67 m and 8847.93 m respectively. The orthometric height of the rock surface of the QF summit is 8844.43 m，and the thickness of the ice-snow layer on the QF summit is 3.50 m.

Determination of Geoid Heights by GPS and Precise Trigonometric Levelling

Determination of Geoid Heights by GPS and Precise Trigonometric Levelling

Determination of Geoid Heights by GPS and Precise Trigonometric Levelling

Most commonly used method for the determination of geoid is the evaluation of GPS (Global Positioning System) and levelling measurements together. Despite the fact that geometric levelling (GL) is in general easy and practicable, it is a measurement method that is hard and uneconomic to apply particularly in mountainous, hilly and rugged areas. This study aims the use of precise trigonometric levelling (PTL) method instead of GL for the determination of precise geoid heights. The method has been probed into in consideration of the accuracy, practicability, measurement and evaluation criteria, and has been compared with GL measurement results. In addition, geoid profiles that have been determined both (GPS_GL) and (GPS_PTL) measurements have been compared with TG-99A (Turkish Geoid-1999A) and IGNA (Istanbul GPS Network) geoid models to explore their consistency.

Research on precise trigonometric leveling in place of first order leveling

Through the analysis of the principle, error sources and precision of trigonometric leveling, this paper points out the key problems about first order leveling replaced by trigonometric leveling; and for the first time puts forward that, in some given conditions, it is not only feasible but also valuable to replace first order leveling by precise trigonometric leveling, and proves it by experimentation as well. The content and conclusion of this paper have consulting significance and practicable value for our setting down relational criterion and production practice.

Functional Models and New Stochastic Model in Combined Leveling Nets

The aim of this study is to improve functional models and to form a new stochastic model that takes into account both different measurement methods and important sources of errors affecting the accuracy of the measurements in a combined leveling net measured by different instruments and measurements methods. In this study, three functional models are explained. In addition, four well-known stochastic models and a new stochastic model are presented. Two types of unknowns are used in the least-squares adjustment of functional models. One of them is the scale factor, and the other is the parameter of refraction and deviation of the plumb line. Four criteria are explained to examine the functional old and new stochastic models. The first criterion is whether or not the adjustment gives reasonable results. The other criteria are the functional model test, stochastic model test, homogeneity, and mean accuracy test. To achieve the objectives stated earlier, a leveling net located in and around Istanbul, Turkey, is used, consisting of 81 benchmarks and 76 lines. Five lines are measured using both reciprocal trigonometric leveling and valley crossing leveling. The rest are measured by the precise leveling method. The net is adjusted using the free adjustment approach along with stochastic models, which are known and suggested.

Refraction in leveling and method for its determination - theoretical basis

The curvature of the trajectories of propagation of optical rays in the atmosphere (refraction) is one of the basic effects which causes systematic errors in the height determination by leveling and moreover which is very difficult to take into account. In spite of quite intensive investigations during many years, it remained a problem that could not obtain practical solution. Using the methodological principles of the theory of similarity and modeling, the author succeeded in obtaining a basically new solution of the task. This solution enabled the development of a technological method to determine refraction in high precision and trigonometric leveling. The application of the method needs negligible surplus measurements.

A Modified Theodolite Instrument: Conceptual Work

Abstract A proposed modified theodolite instrument is presented. The instrument concept, sequence of operation of measurements, and design plans are reported. The proposed instrument has a potential similar to metric photogrammetry in computing 3-D coordinates without physically touching the target point. A sliding graduated rod (arm) has been introduced to connect the upper and lower parts, each of which has a separate vertical vernier. The rod supports the theodolite head that can be extended upward an arbitrary distance, thus effectively providing a second position for the head. Appropriate angular measurements, together with the length of the extension (the rod) can be used to calculate the inaccessible distances. The instrument relies on simple trigonometric functions to measure the height of objects and the horizontal and slope distances, and to perform trigonometric leveling. Accuracy potential of the instrument has been presented based on the law of propagation of random error. The flow of operations for different measurement cases has been mathematically demonstrated. The instrument is anticipated to bypass the cost-effectiveness and technological bottlenecks between plane surveying and photogrammetric systems.

Recent crustal movements of the travale geothermal area measured by classical geodetic control network

In order to support and integrate an existing precise levelling control network, in the Travale geothermal area (Tuscany, Italy), a geodetic network was set up in 1973 to monitor the ground displacements occurring as natural neotectonic activity and induced by steam production in the geothermal field. This network consists of 7 benchmarks located across the main distensive fault system at the SW boundary of a regional graben-shaped tectonic feature that trends in Apenninic direction. The area is also affected by intensive geothermal exploitation. The net was measured several times with different types of geodetic methods: geometric and trigonometric levelling, distances and GPS. In the years 1988, 1990 and 1991 the distances were measured with the Mekometer ME 5000. The use of this very high precision distance meter allows to evidence a constant displacement trend also within a short period of measures.

Validating and improving elevation data of a satellite-image map of Filchner,Ronne Ice Shelf, Antarctica, with Results from ERS-1

A satellite-image map with surface-elevation contours of Filchner Ronne Ice Shelf has been published previously as a topographic map. The image map was constructed from a mosaic of 69 Landsat Multispectral Scanner (MSS) images and NOAA AVHRR data. The standard deviation in position in the central part of the mosaic is ±125m. Topographic-glaciologic features were taken from Landsat scenes and represent the best coastline of this region. Surface elevations have been calculated from airborne and ground measurements of either ice thickness (by assuming hydrostatic equilibrium) or barometric pressure. Accuracies vary from ±2 to ±7 m, Oversnow trigonometric levelling in the northeastern part of the ice shelf, tied to sea level at the ice front, has given accuracies of ± 1m. Accuracies reduce to about ±20 m in the grounded ice areas,ERS-I radar-altimeter data over the ice shelf have been processed to give ellipsoidal heights elevation above the ellipsoid), Geoidal reductions have been used to convert these to orthometric heights (elevation above sea level). No tidal corrections have been applied. The overall accuracy of the radar-altimeter-derived elevations is estimated to be better than ±5m. There are noticeable differences from the topographic map in the central part where the radar data indicate a lower surface. However, the maps agree to within the stated error figures.

Validating and improving elevation data of a satellite-image map of Filchner,Ronne Ice Shelf, Antarctica, with Results from ERS-1

A satellite-image map with surface-elevation contours of Filchner Ronne Ice Shelf has been published previously as a topographic map. The image map was constructed from a mosaic of 69 Landsat Multispectral Scanner (MSS) images and NOAA AVHRR data. The standard deviation in position in the central part of the mosaic is ±125m. Topographic-glaciologic features were taken from Landsat scenes and represent the best coastline of this region. Surface elevations have been calculated from airborne and ground measurements of either ice thickness (by assuming hydrostatic equilibrium) or barometric pressure. Accuracies vary from ±2 to ±7 m, Oversnow trigonometric levelling in the northeastern part of the ice shelf, tied to sea level at the ice front, has given accuracies of ± 1m. Accuracies reduce to about ±20 m in the grounded ice areas, ERS-I radar-altimeter data over the ice shelf have been processed to give ellipsoidal heights elevation above the ellipsoid), Geoidal reductions have been used to convert these to orthometric heights (elevation above sea level). No tidal corrections have been applied. The overall accuracy of the radar-altimeter-derived elevations is estimated to be better than ±5m. There are noticeable differences from the topographic map in the central part where the radar data indicate a lower surface. However, the maps agree to within the stated error figures.

A method of precise trigonometric leveling for deformation surveys

A method of precise trigonometric leveling, for application in deformation survey networks that are periodically observed, is described. The advantages over precise spirit leveling are outlined and the special observational and analysis procedures required in the method are given. The method is then applied to the Barrier Dam Deformation Survey Network and a comparison is made with precise spirit leveling results. The results indicate that vertical movements of 5 millimeters over lines of observation of 500 meters can be detected.

Crustal movement along a collision boundary of plates (case of eastern Taiwan)

Recent crustal movements in eastern Taiwan were investigated based on geodetic and seismological data as a case study of the tectonics along a colliding plate boundary. Secular horizontal strain along the Longitudinal Valley, a probable arc-continent collision boundary between the Philippine Sea and Eurasion plates, is compressive with a large rate of 2 microstrains/year, and the maximum compression axis trends in NW-SE direction. This means that nearly two-thirds of the convergence rate between the two plates is consumed in the narrow zone along the valley and confirms the view that the valley is the plate boundary between the two. The amount of uplift in the Central Range, deduced from trigonometric leveling, reaches more than one meter during the past 60 years. Such active orogeny is caused by the high strain rate in this area. Horizontal displacement of the Coastal Range, a leading edge of the Philippine Sea plate, has a left-lateral component, suggesting that the boundary is a region of oblique collision and the range moves toward the north, producing subduction of the Philippine Sea plate off the Coast of northeastern Taiwan. An extensional strain pattern is found northeastern Taiwan near Hualien, in northern Taiwan near Ilan, and in southeastern Taiwan south Taitung. In northeastern Taiwan, the direction of the maximum extension axis is nearly parallel to the isodipth contours of deep-focus earthquakes that occurred under the southern part of the Ryukyu Trench. From a model calculation using a finite-element method, this pattern of strain is interpreted as an edge effect of the collision-subduction junction in northeastern Taiwan. The direction of the maximum extension in northern Taiwan forms high angles with the direction of the tectonic line near Ilan stretching from the Okinawa Trough. This fact is harmonious with the view that the Okinawa Trough is spreading. Extensional strain observed in southeastern Taiwan may be related to the eastward subduction since the area is situated on a transition zone, from collision to subduction.