Theory of Errors and Least Squares Adjustment
Huaan Fan
ISBN 91-7170-200-8 Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics 100 44 Stockholm Sweden August 2010
Theory of Errors and Least Squares Adjustment
Huaan Fan, PhD Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics Teknikringen 72, 100 44 Stockholm, Sweden Phone: +46 8 7907340 Fax: +46 8 7907343 E-mail: hfan@kth.se URL: http://www.infra.kth.se/impgg
With 22 illustrations and 49 numerical examples
ISBN 91-7170-200-8 Copyright c 1997 by Huaan Fan All Rights Reserved Geodesy Report No. 2015 TRITA-GEOFOTO 1997:21 Printed by Universitetsservice AB, Drottning Kristinas väg 53 B, Stockholm October 1997, August 1998, August
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The author wishes to acknowledge all the help and encouragement from his colleagues and students. Special thanks go to TeknL George Stoimenov for proof-reading the manuscript and Mr Hossein Nahavandchi for helping draw some of the …gures. Of particular bene…t have been my students in the classes MK-92, TL-93, TL-94 and TL-95, who have worked through the raw materials as the compendium evolved. To all of them, I express my sincere thanks !
Stockholm, August 1997.
Huaan Fan
Contents
1 Fundamentals of Theory of Errors 1.1 Standard Errors and Weights . . . . . . . . . . . . . . . 1.1.1 Standard Errors . . . . . . . . . . . . . . . . . . 1.1.2 Weights and Unit-Weight Standard Error . . . . 1.1.3 Variance-Covariance Matrix and Cofactor Matrix 1.2 Error Propagation . . . . . . . . . . . . . . . . . . . . . 1.2.1 Error Propagation in Linear Functions . . . . . . 1.2.2 Error Propagation in Non-Linear Functions . . . 1.2.3 Propagation of Weights . . . . . . . . . . . . . . 1.2.4 Propagation of Cofactor Matrices . . . . . . . . . 1.3 Error Ellipse and Error Ellipsoid . . . . . . . . . . . . . 1.3.1 Point Errors . . . . . . . . . . . . . . . . . . . . . 1.3.2 Error Curve and Error Ellipse . . . . . . . . . . . 1.3.3 Probability inside Error Ellipses . . . . . . . . . 1.3.4 Error Ellipsoid . . . . . . . . . . . . . . . . . . . 1.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . 1.4.1 Probability
11. The horizontal distance in Figure 5 is measured in km from 77° W eastward to 71° W, covering a total length of about 550 km. The average maximum depth of the nearly horizontal eastern portion of the profile is about 4400 m. Compare this vertical cross-section with Figure 1. Figure 5 most closely resembles the [(left)(middle)(right)] portion of Figure 1.
This lab uses earthquake data to construct profiles of two convergent boundaries: the Tonga Trench and the Peru-Chile Trench. Where two tectonic plates converge, if one or both of the plates is an oceanic lithosphere, a subduction zone will form. When crust is formed at a mid-ocean ridge, it is hot and buoyant meaning it has a low density. As it spreads away from the ridge and cools and contracts, or becomes denser, it is able to sink into the hotter underlying mantle. When two oceanic plates collide, the younger of the two plates, because it is less dense will ride over the edge of the older plate. The density of the
There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to seasons on the Earth. Each of these sections has its own simulator(s). The background material necessary to utilize these tools is contained in each section.
There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to seasons on the Earth. Each of these sections has its own simulator(s). The background material necessary to utilize these tools is contained in each section.
Determine the relative age each of the geologic structures shown in the geologic cross section below (Figure 9.17) from youngest to oldest; then answer the questions below. As before, a wiggly line running across the geologic cross section indicates an unconformity and a fault is indicated with a bold straight line.
Questions and charts are from Geoscience Laboratory, 5th ed. (p. 155–167), by T. Freeman, 2009, New York, NY: John Wiley & Sons. Reprinted with permission.
The study is carried out in Bicentennial Park to investigate and analyse the local area and expand on the understanding of geological and climatic concepts that can be identified through careful analysis of the area.
Questions and charts are from Geoscience Laboratory, 5th ed. (p. 133-150), by T. Freeman, 2009, New York, NY: John Wiley & Sons. Reprinted with permission.
Complete this week’s lab by filling in your responses to the questions from Geoscience Laboratory. Select answers are provided for you in red font to assist you with your lab work. Although you are only required to respond to the questions in this worksheet, you are encouraged to answer others from the text on your own.
Lutgens, F. K. & Tarbuck, E. J. (2011). Foundations of earth science (6th ed.). Upper Saddle River, NJ: Prentice
Questions and charts are from Geoscience Laboratory, 5th ed. (p. 133-150), by T. Freeman, 2009, New York, NY: John Wiley & Sons. Reprinted with permission.
What is interesting about this paper is the author’s purpose. It seems as though he is attempting to raise awareness and support geophysics. However, all the points he brings up to discuss he quickly refutes with dangers. This confuses the reader as the article is more intimidating rather than informational. The overwhelming sense of danger associated with each
At the nearby valley wall, there is a distribution of rock lithology including mostly Limestone. The roundness of the samples is all angular, with a mean size of 8.325 cm in diameter. However, the stream bank has more clastic rock samples which have a rounder shape and a smaller mean size of 7.975 cm. These contrasting sections are between alluvium and colluvium data where the alluvium
In this heart you will find the beating pulse of fierce volcanoes, just waiting to be revealed. Taking us back millions of years to Earth’s origins. Make no mistake, this Island may be a jewel, but it is one gem not to mess with. The beauty is
There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to seasons on the Earth. Each of these sections has its own simulator(s). The background material necessary to utilize these tools is contained in each section.