Toolbox for Analysis of Flexural Isostasy (TAFI)—A MATLAB Toolbox for Modeling Flexural Deformation of the Lithosphere GEOSPHERE; V
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Fitting Gravimetric Geoid Models to Vertical Deflections
Journal of Geodesy (submitted) 1 Fitting gravimetric geoid models to vertical deflections 2 3 W.E. Featherstone ( ) 4 Western Australian Centre for Geodesy & The Institute for Geoscience Research, 5 Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia 6 Tel: +61 8 9266-2734; Fax: +61 8 9266-2703; Email: [email protected] 7 8 D.D. Lichti 9 Department of Geomatics Engineering & The Centre for Bioengineering Research and 10 Education, Schulich School of Engineering, The University of Calgary, 11 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada 12 Tel: +1 403 210-9495; Fax: +1 403 284 1980; Email: [email protected] 13 14 Abstract . Regional gravimetric geoid and quasigeoid models are now commonly fitted 15 to GPS-levelling data, which simultaneously absorbs levelling, GPS and quasi/geoid 16 errors due to their inseparability. We propose that independent vertical deflections are 17 used instead, which are not affected by this inseparability problem. The formulation is 18 set out for geoid slopes and changes in slopes. Application to 1080 astrogeodetic 19 deflections over Australia for the AUSGeoid98 model shows that it is feasible, but the 20 poor quality of the historical astrogeodetic deflections led to some unrealistic values. 21 22 Keywords : Gravimetric geoid errors, vertical deflections, vertical datum errors 23 24 1. Introduction 25 Fitting regional gravimetric geoid or quasigeoid models to GPS-levelling data has 26 become a widespread practice. A principal objection to this is the inseparability of 27 errors among the levelling and local vertical datum (LVD), GPS and gravimetric 28 quasi/geoid model (cf. -
Geophysical Abstracts 156-159 January-December 1954
Geophysical Abstracts 156-159 January-December 1954 GEOLOGICAL SURVEY BULLETIN 1022 Abstracts of current literature pertaining to the physics of the solid earth and geophysicq,l exploration UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1955 UNITED STATESlDEPARTMENT OF THE INTERIOR Douglas McKay, Secretary GEOLOGICAL SURVEY W. ~· Wrather, Director CONTENTS [The letters in parentheses are those used to designate the chapters for separate publication] Page (A) Geophysical Abstracts 156, January-March------------------------ 1 (B) Geophysical Abstracts 157, April-June---------------------------- 71 (C) Geophysical Abstracts 158, July-September________________________ 135 (D) Geophysical Abstracts 159, October-December_____________________ 205 Under department orders, Geophysical Abstracts have been published at different times by the Bureau of Mines or the Geological Survey as noted below: 1-86, May 1929-June· 1936, Bureau of Mines Information Circulars. [Mimeo- graphed] 87, July-December 1936, Geological Survey Bulletin 887. 88-91, January-December 1937, Geological Survey Bulletin 895. 92-95, January-December 1938, Geological Survey Bulletin 909. 96-99, January-December 1939, Geological Survey Bulletin 915. 100-103, January-December 1940, Geological Survey Bulletin 925. 104-107, January-December 1941, Geological Survey Bulletin 932. 108-111, January-December 1942, Geological Survey Bulletin 939. 112-127, January 1943-December 1946, Bureau of Mines Information Circulars. [Mimeographed] 128-131, January-December 1947, Geological Survey Bulletin 957. 132-135, January-December 1948, Geological Survey Bulletin 959. 136-139, January-December 1949, Geological Survey Bulletin 966. 140-143, January-December 1950, Geological Survey Bulletin 976. 144-147, January-December 1951, Geological Survey Bulletin 981. 148-151, January-December 1952, Geological Survey Bulletin 991. 152-155, January-December 1953, Geological Survey Bulletin 1002. -
The Nature of Lunar Isostasy
45th Lunar and Planetary Science Conference (2014) 1630.pdf THE NATURE OF LUNAR ISOSTASY. Michael M. Sori1 and Maria T. Zuber1. 1Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA ([email protected]). Introduction: One way planetary topography can A key assumption in investigating the role of Pratt be supported is isostatic compensation, in which isostasy by looking at the relationship between crustal overburden pressure of rock is balanced at some depth. density and topography is that the density one observes The regions of the Moon that are not associated with near the surface is representative of the underlying maria or basins are generally isostatically compensated crustal column. We justify that assumption here by [1], an observation that was made when the first noting that calculation of the effective density of the detailed lunar gravity maps were constructed [2] and lunar crust as a function of spherical harmonic degree has held with each subsequently more precise data set considered results in a linear trend [14], supporting the [e.g., 3]. notion of a single-layer crust. There are two models of isostasy commonly Results: We make scatter plots of crustal density considered. In the Airy isostasy model [4], crustal as a function of elevation. One such scatter plot, for thickness is varied such that overburden pressures are the South Pole-Aitken basin, is shown in Figure 1. equal at some depth of compensation. The crust is a Points are sampled in a grid every ~8 km. For each layer of uniform density overlaying a mantle of higher scatter plot, we make a least-squared fit to the data and uniform density. -
Glacial Isostatic Adjustment and Sea-Level Change – State of the Art Report Technical Report TR-09-11
Glacial isostatic adjustment and sea-level change – State of the art report Glacial isostatic adjustment and sea-level change Technical Report TR-09-11 Glacial isostatic adjustment and sea-level change State of the art report Pippa Whitehouse, Durham University April 2009 Svensk Kärnbränslehantering AB Swedish Nuclear Fuel and Waste Management Co Box 250, SE-101 24 Stockholm Phone +46 8 459 84 00 TR-09-11 ISSN 1404-0344 CM Gruppen AB, Bromma, 2009 Tänd ett lager: P, R eller TR. Glacial isostatic adjustment and sea-level change State of the art report Pippa Whitehouse, Durham University April 2009 This report concerns a study which was conducted for SKB. The conclusions and viewpoints presented in the report are those of the author and do not necessarily coincide with those of the client. A pdf version of this document can be downloaded from www.skb.se. Preface This document contains information on the process of glacial isostatic adjustment (GIA) and how this affects sea-level and shore-line displacement, and the methods which are employed by researchers to study and understand these processes. The information will be used in e.g. the report “Climate and climate-related issues for the safety assessment SR-Site”. Stockholm, April 2009 Jens-Ove Näslund Person in charge of the SKB climate programme Contents 1 Introduction 7 1.1 Structure and purpose of this report 7 1.2 A brief introduction to GIA 7 1.2.1 Overview/general description 7 1.2.2 Governing factors 8 1.2.3 Observations of glacial isostatic adjustment 9 1.2.4 Time scales 9 2 Glacial -
Isostasy and Flexure of the Lithosphere
Isostasy and Flexure of the Lithosphere A. B. WATTS Department of Earth Sciences, Oxford University Oxford, United Kingdom PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge, United Kingdom http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011–4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Ruiz de Alarco´ n 13, 28014 Madrid, Spain # Cambridge University Press 2001 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2001 Printed in the United States of America Typeface Times Ten PS 10/12.5 System 3B2 [KW] A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Watts, A. B. (Anthony Brian), 1945– Isostasy and flexure of the lithosphere / A. B. Watts. p. cm. Includes bibliographical references and index. ISBN 0-521-62272 – ISBN 0-521-00600-7 (pb) 1. Isostasy. 2. Earth – Crust. I. Title. QE511.W38 2001 551 – dc21 00-065146 ISBN 0 521 62272 7 hardback ISBN 0 521 00600 7 paperback Contents Preface page xi Acknowledgments xiii Notation xvii 1 The Development of the Concept of Isostasy 1 1.1 Introduction 1 1.2 First Isostatic Ideas 2 1.3 The Deflection of the Vertical in India 9 1.4 Isostasy According to Airy -
The Deflection of the Vertical, from Bouguer to Vening-Meinesz, and Beyond – the Unsung Hero of Geodesy and Geophysics
EGU21-596 https://doi.org/10.5194/egusphere-egu21-596 EGU General Assembly 2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. The Deflection of the Vertical, from Bouguer to Vening-Meinesz, and Beyond – the unsung hero of geodesy and geophysics Christopher Jekeli Ohio State University, School of Earth Sciences, Division of Geodetic Science, United States of America ([email protected]) When thinking of gravity in geodesy and geophysics, one usually thinks of its magnitude, often referred to a reference field, the normal gravity. It is, after all, the free-air gravity anomaly that plays the significant role in terrestrial data bases that lead to Earth Gravitational Models (such as EGM96 or EGM2008) for a multitude of geodetic and geophysical applications. It is the Bouguer anomaly that geologists and exploration geophysicists use to infer deep crustal density anomalies. Yet, it was also Pierre Bouguer (1698-1758) who, using the measured direction of gravity, was the first to endeavor a determination of Earth’s mean density (to “weigh the Earth”), that is, by observing the deflection of the vertical due to Mount Chimborazo in Ecuador. Bouguer’s results, moreover, sowed initial seeds for the theories of isostasy. With these auspicious beginnings, the deflection of the vertical has been an important, if not illustrious, player in geodetic history that continues to the present day. Neglecting the vertical deflection in fundamental surveying campaigns in the mid to late 18th century (e.g., Lacaille in South Africa and Méchain and Delambre in France) led to errors in the perceived shape of the Earth, as well as its scale that influenced the definition of the length of a meter. -
Isostasy, Dynamic Topography, and the Elevation of the Apennines of Italy ∗ Claudio Faccenna A, , Thorsten W
Earth and Planetary Science Letters 407 (2014) 163–174 Contents lists available at ScienceDirect Earth and Planetary Science Letters www.elsevier.com/locate/epsl Isostasy, dynamic topography, and the elevation of the Apennines of Italy ∗ Claudio Faccenna a, , Thorsten W. Becker b, Meghan S. Miller b, Enrico Serpelloni c, Sean D. Willett d a Laboratory Experimental Tectonics, Università Roma TRE, Roma, Italy b Department of Earth Sciences, University of Southern California, Los Angeles, CA, USA c Istituto Nazionale Geofisica e Vulcanologia, Centro Nazionale Terremoti, Bologna, Italy d Department of Earth Sciences, Swiss Federal Institute of Technology, Zurich, Switzerland a r t i c l e i n f o a b s t r a c t Article history: The elevation of an orogenic belt is commonly related to crustal/lithosphere thickening. Here, we discuss Received 19 March 2014 the Apennines as an example to show that topography at a plate margin may be controlled not only by Received in revised form 28 August 2014 isostatic adjustment but also by dynamic, mantle-driven processes. Using recent structural constraints for Accepted 14 September 2014 the crust and mantle we find that the expected crustal isostatic component explains only a fraction of Available online xxxx the topography of the belt, indicating positive residual topography in the central Apennines and negative Editor: Y. Ricard residual topography in the northern Apennines and Calabria. The trend of the residual topography Keywords: matches the mantle flow induced dynamic topography estimated from regional tomography models. Apennines We infer that a large fraction of the Apennines topography is related to mantle dynamics, producing elevation relative upwellings in the central Apennines and downwellings in the northern Apennines and Calabria subduction where subduction is still ongoing. -
Isostasy and Its Meaning
SVENSKA GEOFYSISKA FORENINGEN VOLUME I, NUMBER 3 Te I L u s AUGUST 1949 A QUARTERLY JOURNAL OF GEOPHYSICS Isostasy and its Meaning By B. GUTENBERG, California Institute of Technology1 (Manuscript received June 25, 1949) Abstract The theory of isostasy supposes that, in regions which have not been disturbed recently, each vertical column of the earth's crust with a certain minimum radius and extending to a depth of about IOO km has approximately the same mass. To find the deviation from this approximation in a given region, the density must be assumed as a function of depth. Such assumptions used at present for calculations are discussed critically. The resulting errors are greater than it is normally beleaved; errors in the calculated isostatic gravity anomalies exceeding ten milligals must be expected in certain regions. Systematic errors result from the usual assumption in routine calculations that the mean density in the earth's crustal layers under the bottom of the Pacific and in the continental areas is the same, and that in both the difference between the density of the layers above about 30 km and the layers below this depth is 0.6. The processes producing and maintaining isostatic equilibrium are discussed. In the theory of isostasy it is assumed that available, there are two ways to approach this in regions that have not been disturbed re- uestion. The first is, to use observations of cently each vertical column of the earth's crust tx e density and distribution of rocks in the with a given radius (at least, say, 10 km) and earth's crust and of gravity at the earth's surface extending down to a sufficient specified depth and to calculate the residuals (the so-called (apparently at least 60 km), has approximately gravity anomalies) against an assumed equili- the same mass, regardless of the surface condi- brium condition; the second is to consider the tion (continental or oceanic) or of the surface processes involved in establishing isostasy. -
Application to the Mid-Norwegian Continental Margin
Downloaded from http://sp.lyellcollection.org/ by guest on September 28, 2021 Isostasy as a tool to validate interpretations of regional geophysical datasets – application to the mid-Norwegian continental margin SOFIE GRADMANN1*, CLAUDIA HAASE1 &JO¨ RG EBBING1,2 1Geological Survey of Norway, Leiv Eirikssons vei 39, 7040 Trondheim, Norway 2Present address: Department of Geosciences, Kiel University, 24118 Kiel, Germany *Correspondence: sofi[email protected] Abstract: Isostasy is a well understood concept, yet rarely applied to its full capacity in regional interpretations of crustal structures. In this study, we utilize a recent density model for the entire NE Atlantic, based on refraction seismic data and gravity inversion, to calculate isostatically balanced bathymetry along the mid-Norwegian margin. Since gravity and isostatically balanced elevation are independent observables but both depend on the underlying density model, consis- tencies and discrepancies point towards model deficits, erroneously interpreted or poorly understood areas. Four areas of large isostatic residuals are identified. Along the outer Vøring Margin, a mass deficit points to more extensive high-density bodies or a shallower Moho than currently mapped. Farther seaward, along the Vøring Marginal High, a mass excess indicates inaccurate mapping of the continent–ocean boundary and surrounding structures. A number of eclogitic bodies along the proximal mid-Norwegian margin have been described in recent publications and their presence is now also confirmed by isostatic calculations. Major elevation and gravity residuals along the transition between the Vøring and Møre margins signify that the structure of this region is poorly understood and modifications to the mapped continent–ocean transition may be required. -
Concepts of Isostasy
Unit 3 Interior of the Earth: Structure and Composition .................................................................................................................................................................................................................................... UNIT 4 CONCEPTS OF ISOSTASY Structure 4.1 Introduction 4.4 Views on Isostasy Expected Learning Outcomes Airy’s Theory 4.2 Basic Principles Pratt’s Theory Hayford and Bowie Principle of Buoyancy Joly Density Heiskanen Lithospheric Flexure Vening-Meinesz or Flexural The Concept of Equilibrium Isostasy The Isostatic Adjustments Isostasy v/s No Isostasy 4.3 Development of the Concept of 4.5 Summary Isostasy 4.6 Terminal Questions Determination of Latitudes Isostasy as the Earth’s Balance 4.7 Answers Isostatic Effects 4.8 References/Further Reading 4.1 INTRODUCTION In the previous units of this course, you have learnt about the origin of the Earth, its internal structure and composition as well as the life forms it supports. You must have realized that it is a very complex system. Now we turn our attention to understand how and which features of the Earth helps in achieving this delicate balance. In particular, this unit is devoted to the discussion of isostasy, which gives us information about the mechanical stability between the upstanding features and low lying basins of the Earth. In this unit, we will trace the evolution of the concept of isostasy, which originated in a survey initiated to determine the shape of the Earth. 65 Block 1 GEO-Tectonics .................................................................................................................................................................................................................................... You might have visited different places in India as well as abroad and observed some relief features present on the Earth’s surface, such as mountains, plains, plateaus, valleys, lakes and oceans etc. You might have also noticed that such features are of different shapes and sizes. -
Recent Global Sea Levels and Land Levels
3 Recent global sea levels and land levels D.G. Aubrey and K.O. Emery Abstract Tide-gauge records from around the world ambiguously document the rise and fall of relative sea levels during the past century. Analyses of these records, non-uniformly distributed in time and space, reveal that land levels as well as ocean levels are changing, complicating the estimation of the eustatic component of sea level change. Because most tide gauges are concentrated in the Nonhero Hemisphere instead of the Southern Hemisphere (where most ocean area is located), tide-gauge data reflect major continental motions due to glacio-isostasy and neo-tectonism, which suppress and mask the signal from eustatic sea level change. Estimation of the magnitude of sea level change is important for many reasons, including the interpretation of possible effects of global climate change resulting from carbon dioxide and other trace gas loading of the atmosphere. Proper interpretation of past sea level changes is valuable for the calibration and evaluation of certain global climate, ocean and geophysical Earth models. This interpretation can be accomplished using tide-gauge records and other records of relative sea levels only if land level changes are sufficiently distinguished from actual sea level changes. Introduction Past and future climate changes drive various responses in the oceans. One such response is variation in sea levels as the oceans wann or cool, and as water is removed from or returned to the ocean basins and glaciers. During the past 15.000--18,000 years following the last glacial maximum, the Earth has experienced an average warming of about 4-5 ·c. -
Dynamic Surface of the Earth
MODULE - 2 Changing face of the Earth 3 Notes DYNAMIC SURFACE OF THE EARTH In the previous lesson, we have learnt that the interior of the earth is very hot. Earthquakes and volcanoes are concentrated along a few narrow belts. The type and density of rocks of the crust are variable. The surface features are dynamic in character. This dynamism is due to two forces — endogenetic and exogenetic. Endogenetic forces are those which are caused from below the surface. Due to this, an area may get elevated or gets submerged. These forces try to make the surface irregular while exogenetic froces are those which operate from above the surface. They try to eliminate the irregulari- ties of the surface through the process of denudation about which we will be reading in lesson. In this lesson we will be studying about the endogenetic forces. OBJECTIVES After studying this lesson, you will be able to : define isostasy; describe the variation in relief features on the earth’s surface; explain the isostatic adjustment by various experiments; explain the views of Airy and Pratt and distinguish between the ideas of both; explain the concept of continental drift; enumerate the evidences of continental drift; explain the concept of plate tectonics; identify and locate different plates on the world map; GEOGRAPHY 45 MODULE - 2 Dynamic Surface of the Earth Changing face of the Earth explain the mechanism of plate movement; identify various plate boundaries and associated features; explain the distribution of land and water on the globe and associate earthquakes and volcanoes with plate boundaries. Notes 3.1 CONCEPT OF ISOSTASY The term “Isostasy” is derived from “Isostasios”, a word of Greek language meaning the state of being in balance.