Trigonometric Leveling Research Articles

Crustal movements along a collision boundary of plates (case of Eastern Taiwan)

Abstract 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.

Deformations associated with the El Asnam earthquake of October 10, 1980 (Algeria)

The resurvey of both a geodetic network and a levelling net was carried out in June 1981, 8 months after the M s = 7.3 El Asnam earthquake of 10 October 1980. Previous seismological and neotectonic studies indicate that this event results from a north-east-trending overthrust complex fault of about 40-km length, which shows at least three principal segments with slightly different directions. Vertical movements, evaluated by means of a trigonometric levelling method show an uplift of the thrust fault of about 5 m and a depression of the southeastern edge of about 1 m. These movements are progressively attenuated away from the fault trace (see fig. 1). Horizontal movements have been evaluated by a classical first-order triangulation method. (see fig. 2 and table 1). The resulting mean strain tensors, calculated for different triangles of the geodetic network, indicate a shortening of about 2.50 m which is consistent with the SE-NW direction of compression determined from neotectonic evaluations and focal mechanisms (see fig. 3). Dislocation models are used to explain and discuss the observed deformations in the light of the seismological data and the observed ground breakages. Five segments are required to explain both horizontal and vertical deformations. The magnitude of vertical displacement (about 6 m) at the junction between the southwest and the central segments of the fault argues for the breaking of this area during the main shock and for a slip vector of about 8 m, at least in the central segment. In such circumstances where the first field observations show that a strong coseismic movement has taken place, the best methodology to be used seems to be: • - to resurvey as quickly as possible the widest acceptable zone of the old existing geodetic network, without special attention paid to the precision of these measurements. • - to set up as soon as possible a small aperture geodetic network of high accuracy in order to monitor the possible postseismic readjustments. For vertical movements, trigonometric leveling using reciprocal zenith measurements with two high-precision theodolites and EDM appears to be far the best solution. It is much quicker than classical leveling and it can afford the same precision if necessary. In our case, the precision was not critical, so that long ranges (up to 1500 m) between stations were used when necessary.

Application of Stationary Geodimeter to Study the Velocity of the Kozel’skiy Glacier Movement, Kamchatka, U.S.S.R. (Abstract)

Kozel’skiy glacier is located in lat. 53.1°N., 50 km from the Pacific Ocean, and has a southern exposure. It flows from the saddle between Avachinskiy and Kozel’skiy volcanoes. Its highest point is at an altitude of 1850 m a.s.l. The glacier tongue descends to an altitude of 900 m a.s.l. At present, this is the best-studied glacier in Kamchatka.In May and June 1981, for the purpose of organizing routine monitoring of the movement of Kozel’skiy glacier, systematic geodimeter measurements were made at the “Mishennaya” Observatory. A model 8 geodimeter (AGA, Sweden) was used for measuring straight-line distances. The source of radiation was a He–Ne laser beam with a power of 5 MW and a wavelength of 0.6328 m. In Kamchatka this geodimeter can measure distances of 60 km and in some cases 90 km. If a special (diurnal) procedure of measurements is used, one can attain an accuracy of 1 × 10−6 of the length of the line D. Sixteen prism-angle reflectors were installed on the glacier.The entire firn area of the glacier could be seen well from the top of Mount Mishennaya. Two profiles consisting of six points on the glacier surface were constructed. A bench mark on the ancient lava flow of Kozel’skiy volcano was taken as static in elevation and was used to control the accuracy of the measurements. The points on the glacier were established by 2 m poles with a diameter of 1.5 cm. Reflectors were installed on tripods and were centred with the help of an optical plumb bob. The points for measurement of the movement velocity were located at a distance of more than 26 km from the instrument. Studies were carried out during periods of stationary images (without inversions), generally early in the morning and late in the evening.Two-sided trigonometrical levelling was carried out simultaneously. Zenith distances were measured four times by a Teo-010A theodolite. Meteorological conditions were determined at 1.5–2 h near the reflectors and at the observatory during the whole cycle of measurements. The processing of the results of distance measurements was done according to the procedure published in Lobachev. The elevation of points over the observatory was determined from the measured zenith distances.The error in distance measurements was ± 0.04 m and in elevation ± 0.8 m (an increase in accuracy up to 0.2 m is possible). The displacement of points of velocity changed from 0.3 to 2.37 m over the whole period of observation. This corresponds to a glacier velocity from 1 to 6 m/d. Thus, a cycle of geodimeter measurements may be carried out once a week, providing an accuracy of distance measurements of ± 4 cm. Routine measurements of the velocities of glacier movement, using geodimeters, may be organized subject to reliable long-term attachment of reflectors to the surface of the glacier.Experience of the studies made indicated good opportunities for application of a stationary geodimeter to the investigation of glacier movement. The data obtained agree with previous measurements made by the usual geodetic methods.

Application of Stationary Geodimeter to Study the Velocity of the Kozel’skiy Glacier Movement, Kamchatka, U.S.S.R. (Abstract)

Kozel’skiy glacier is located in lat. 53.1°N., 50 km from the Pacific Ocean, and has a southern exposure. It flows from the saddle between Avachinskiy and Kozel’skiy volcanoes. Its highest point is at an altitude of 1850 m a.s.l. The glacier tongue descends to an altitude of 900 m a.s.l. At present, this is the best-studied glacier in Kamchatka. In May and June 1981, for the purpose of organizing routine monitoring of the movement of Kozel’skiy glacier, systematic geodimeter measurements were made at the “Mishennaya” Observatory. A model 8 geodimeter (AGA, Sweden) was used for measuring straight-line distances. The source of radiation was a He–Ne laser beam with a power of 5 MW and a wavelength of 0.6328 m. In Kamchatka this geodimeter can measure distances of 60 km and in some cases 90 km. If a special (diurnal) procedure of measurements is used, one can attain an accuracy of 1 × 10−6 of the length of the line D. Sixteen prism-angle reflectors were installed on the glacier. The entire firn area of the glacier could be seen well from the top of Mount Mishennaya. Two profiles consisting of six points on the glacier surface were constructed. A bench mark on the ancient lava flow of Kozel’skiy volcano was taken as static in elevation and was used to control the accuracy of the measurements. The points on the glacier were established by 2 m poles with a diameter of 1.5 cm. Reflectors were installed on tripods and were centred with the help of an optical plumb bob. The points for measurement of the movement velocity were located at a distance of more than 26 km from the instrument. Studies were carried out during periods of stationary images (without inversions), generally early in the morning and late in the evening. Two-sided trigonometrical levelling was carried out simultaneously. Zenith distances were measured four times by a Teo-010A theodolite. Meteorological conditions were determined at 1.5–2 h near the reflectors and at the observatory during the whole cycle of measurements. The processing of the results of distance measurements was done according to the procedure published in Lobachev. The elevation of points over the observatory was determined from the measured zenith distances. The error in distance measurements was ± 0.04 m and in elevation ± 0.8 m (an increase in accuracy up to 0.2 m is possible). The displacement of points of velocity changed from 0.3 to 2.37 m over the whole period of observation. This corresponds to a glacier velocity from 1 to 6 m/d. Thus, a cycle of geodimeter measurements may be carried out once a week, providing an accuracy of distance measurements of ± 4 cm. Routine measurements of the velocities of glacier movement, using geodimeters, may be organized subject to reliable long-term attachment of reflectors to the surface of the glacier. Experience of the studies made indicated good opportunities for application of a stationary geodimeter to the investigation of glacier movement. The data obtained agree with previous measurements made by the usual geodetic methods.

Triaxial positioning from an unoccupied baseline

Abstract This paper examines the use of trilateration and trigonometric levelling for determining triaxial co-ordinates of occupied and observed points, by measurement to baseline stations. The purpose of the study was to determine the feasibility of using an off-site baseline as a means of providing on-site control on areas such as surface mines which require repeated quantity surveys and on which survey control is liable to destruction. Two study areas of 1.7 and 16.1 hectares were used. Base positional data was obtained by traverse and differential levelling over a 6 or 7 station test network. On each test site two survey stations were selected as the termini of a baseline. The remaining stations in each network were occupied and slope distance and zenith angle observation to the baseline stations were used to compute the horizontal position of the point occupied. On study area one, mean horizontal positional errors averaged 0.018 m and 0.020 m in y and x respectively. The mean horizontal positional er...

SMALL TRILATERATION NETS IN THREE DIMENSIONS

Trilateration nets measured with short range equipment are normally adjusted in a horizontal plane thus giving only the horizontal control. Vertical control is done separately and usually by trigonometric levelling. By arranging the field measurements in such a way that the measured distances form a chain of tetrahedrons, one can combine both controls in one computation. The condition is that every point must be intersected by at least three distances. Measured distances in addition to this minimum of three will be redundant and will lead to an adjustment. The adjustment can be performed by either the method of variation of coordinates or the method of condition equations. The latter method was used in this paper.

SMALL TRILATERATION NETS IN THREE DIMENSIONS

Trilateration nets measured with short range equipment are normally adjusted in a horizontal plane thus giving only the horizontal control. Vertical control is done separately and usually by trigonometric levelling. By arranging the field measurements in such a way that the measured distances form a chain of tetrahedrons, one can combine both controls in one computation. The condition is that every point must be intersected by at least three distances. Measured distances in addition to this minimum of three will be redundant and will lead to an adjustment. The adjustment can be performed by either the method of variation of coordinates or the method of condition equations. The latter method was used in this paper.

AN EMPIRICAL METHOD FOR REFRACTION MODELLING IN TRIGONOMETRICAL HEIGHTING

The monitoring of vertical displacements of engineering structures is largely carried out by spirit levelling. Sometimes spirit levelling may turn out to be not only slow and laborious, but also impractical. This is when trigonometrical levelling is considered. The Earth's curvature and atmospheric refraction effects are substantially eliminated by using simultaneous reciprocal levelling. However, there are situations when neither spirit levelling nor reciprocal trigonometrical levelling are appropriate. Targets on near vertical high dam walls can be observed from a number of control stations in a one-way trigonometrical mode, with no possibility of reciprocal observations. The same applies to tall buildings, chimneys and other inaccessible structures. Test observations made by using one-second theodolites and applying well known standard textbook models have consistently demonstrated that one-way trigonometrical levelling leads to accuracies ranging from 10 to 100 mm-per-kilometre, well below the requirements for monitoring the vertical displacements of structures.

Strain effects near Palmdale associated with the San Fernando earthquake (1971)

Abstract Field data from the southeast Palmdale network in California are the basis for a practical strain analysis, with triangulation data available for the year 1938 and 1958 and trilateration data at 1- year intervals from 1971 to date. A uniform, although small, strain accumulation over the last forty years appears to be evident from this data set. A possible soceismic strain jump of 2 μ strain in both shearing strain components, related to the 1971 San Fernando earthquake, may be postulated in the observations. However, it was already pointed out previously, that this coseismic strain jump needs further qualifications due to the corrupting influence of uncertainties in the network height differences. This particular situation arises because triangular data have to be compared with trilateration data for the computation of the coseismic strain changes. To clarify this situation, the height differences of the southeast Palmdale network were determined by trigonometric levelling in spring 1981. The effect of this new height data on the interpretation of the coseismic strain change is discussed in detail. A comparison of this result with strain model calculations is presented.

An attempt to determine areas with homogeneous vertical soil movement

An algorithm is given for determining vertical soil movements from all available height determinations. The interpretation of the results will attempt to delimit tectonic plates and to give homogeneous vertical movements (tilts) for each tectonic plate. All available levelling data and trigonometric height determinations are divided into partial nets. All simultaneous observations of possible ratios of motion are put together into one partial net. These partial nets are adjusted in the common, free, static pattern by the well-known solutions of an adjustment of observation equations. The precision of the partial nets may be investigated for geometric levelling as well as for trigonometric levelling without disturbance by real movements. By bringing the partial nets together, a general system for the vertical point movements is formulated. The observations of this followup adjustment are the adjusted heights of the partial nets. The covariance matrices of the partial nets give the stochastic model for the general system. The first stage of calculating the general system is to adopt a static velocity model for the bench marks. A highly sensitive global test will reject the model if it is not justified by the observation precision. The strict form of a deformation analysis will filter out all bench marks which indeed are stable. The next stage will be to adopt a linear velocity model for the unstable points. Again, a deformation analysis will give those points which move linearily. The third stage will give all points which move accordingly to a quadratic velocity model. All moving parameters are given with their covariance matrix. The remaining bench marks have to be taken as disturbed in their height. The local distribution of the disturbed bench marks will indicate possible boundaries of tectonic plates. Within one plate a tilt should be recognizable.

Deformations associated with the El Asnam earthquake of 10 October 1980: Geodetic determination of vertical and horizontal movements

abstractThe resurvey of both a geodetic network and a leveling net was carried out in June 1981 8 months after the MS = 7.3 El Asnam earthquake of 10 October 1980. Previous seismological and neotectonic studies (Ouyed et al., 1981; Yielding et al., 1981) indicate that this event results from a northeast-trending overthrust complex fault of about 40-km length, which shows at least three principal segments with slightly different directions. Vertical movements, evaluated by means of a trigonometric leveling method, show an uplift of the northwestern side of the thrust fault of about 5 m and a depression of the southeastern edge of about 1 m. These movements are progressively attenuated away from the fault trace. Horizontal movements have been evaluated by a classical first-order triangulation method. The resulting mean strain tensors, calculated for different triangles of the geodetic network, indicate a shortening of about 2.50 m which is consistent with the SE-NW direction of compression determined from neotectonic evaluations and focal mechanisms. Dislocation models are used to explain and discuss the observed deformations in light of the seismological data and observed ground breakages. Five segments are required to explain both horizontal and vertical deformations. The magnitude of vertical displacements (about 6 m) at the junction between the southwest and the central segments of the fault argues for the breaking of this area during the main shock and for a slip vector of about 8 m, at least in the central segment.

COMPUTATION OF LOCAL ANOMALIES OF THE VERTICAL's DEFLECTION IN GEODETIC NETWORKS

This report presents a comparison between spirit and trigonometric levelling methods used to provide altimetric control in seismic areas.In particular we examine a method used for estimating local anomalies of the vertical's deflection and their influence on the estimate of the height differences measured by trigonometric techniques. The application of this method to the results of various surveys made in the Ancona geodetic network is presented.

COMPUTATION OF LOCAL ANOMALIES OF THE VERTICAL's DEFLECTION IN GEODETIC NETWORKS

AbstractThis report presents a comparison between spirit and trigonometric levelling methods used to provide altimetric control in seismic areas.In particular we examine a method used for estimating local anomalies of the vertical's deflection and their influence on the estimate of the height differences measured by trigonometric techniques. The application of this method to the results of various surveys made in the Ancona geodetic network is presented.

Height Triangulation with Modern Engineering Theodolites

Results from tests for the accuracy of the self positioning of the automatic vertical index built into the Kern DKM 2A theodolite are quoted. The advantage to be derived from theodolites with automatic vertical index are discussed. Height control established with reciprocal rays, auxiliary point and by traversing is analysed. Trigonometric levelling and spirit levelling are compared.

Evaluation of refraction by geodetic measurements

The merits of two refraction methods are discussed with the result that the line refraction method is appropriate for elaboration of trigonometric leveling traverses whereas the station refraction method is comparatively more convenient for trigonometric and three-dimensional networks of a larger extent especially those designed in high mountain regions.

An Accurate Method of Airborne Trigonometric Leveling

A description is given of a method used in survey operations in Northern Ontario for accurate one-way trigonometric leveling from ground stations to a hovering helicopter. Results indicate a standard error of 0.5 feet in height difference determination over lines 6 to 10 miles in length. The method depends on the application of a modified form of Snell’s Law utilizing dry-bulb temperature and pressure measurements made along the line of sight.

Measuring Building Movement by Precise Survey

The current project is an application of the methods of intersection and trigonometric leveling to the measurement of absolute building movements in the three coordinate directions. The horizontal positions of five targets permanently attached to a reinforced concrete frame building column were determined by intersection from three observation piers of known position. Then angles were turned to a precision of 2.2 sec with a Wild T3 theodolite. The precision of the horizontal coordinates determined for the building targets is believed to be 0.001ft. The angles for the trigonometric leveling were also turned to a precision of 2.2 sec with the Wild T3 theodolite. The vertical coordinates determined for the building targets is believed to be 0.0017 ft.

Trigonometric levelling and spatial triangulation in mountain regions

Trigonometric levelling and spatial triangulation in mountain regions

Surveyor vs. Refraction

Abstract While the accuracy of instruments and techniques in surveying is constantly being improved, the atmosphere through which we observe remains unchanged. In order to determine the adequacy of present methods of dealing with the bending of light rays, causes of refraction are analysed and data are assembled on the amount of bending and its variation, based on observed temperature gradients. The effects of this bending, both in magnitude and variation, are discussed in relation to trigonometric heighting, levelling, photogrammetry, triangulation, and high precision traversing, and the relevance to geodimeter and tellurometer observations is also noted.

Curvature correction in electronic distance measurement

The usual methods for curvature correction, which consist of a geometric and a velocity component, are based on standard atmospheric conditions and thus take no account of variable refraction. A formula has been developed expressing the correction as a function of atmospheric refraction: K=(1-k_2 S2/(24 R2) whereS is the measured distance, R is the radius of the earth, and k is the coefficient of refraction. This formula leads to a practical procedure employing trigonometric levelling in the determination of curvature correction for long-range geodimeter measurements.