Practical Geostatistics Isobel Clark. William V Harper

Transcription

1 Practical Geostatistics 2000 Answers to the Exercises Isobel Clark Geostokos (Ecosse) Limited, Scotland William V Harper Otterbein College, Westerville, Ohio, USA

2 Ecosse North America LLC, Columbus, Ohio, USA.

3 umpteenth Reprint, October 2008 Copyright c 2007 by Geostokos (Ecosse) Limited, Scotland. All rights reserved. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to Permissions Department, Geostokos (Ecosse) Limited, Alloa Business Centre, Whins Road, Alloa FK10 3SA, Central Scotland. Tel: Fax: AttE@kriging.com Library of Congress Cataloging-in-Publication Data: Clark, Isobel Practical geostatistics 2000, answers to exercises / Isobel Clark, William V. Harper. 382p. 2.5cm. ISBN: Geology Statistical methods. 2. Mining engineering. 3. Environmental engineering I. Harper, William V. II. Title. QE33.2.S82 C dc21 Ecosse North America LLC, Columbus, Ohio USA, publishers. Typeset using Scientific Word 5.5, MacKichan Software Inc,

4 This one is for Audun whose every question was answered fully if not always accurately and for Rachel, who did not believe that people in Australia walk around upside down For those who seek definitive answers: Let us all be quiet in unison and hear what the oracle has to tell us. The oracle says, when winter comes theautumnisover.arewecomforted? Edwin Morgan

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6 CONTENTS Preface Notation 1. Introduction Page Background 1.2 Data sets 1.3 Note for teachers 1.4 Cautionary note 1.5 Exercises from each Chapter of Practical Geostatistics Introduction Why a statistical approach? Normal (Gaussian) distributions Lognormal distributions (and others) Discrete distributions Hypothesis Testing Relationships The spatial element The semi-variogram Estimation and kriging 2. Answers to: Why a statistical approach? Page Answers to: Normal (Gaussian) distributions Page Answers to: Lognormal distributions (and others) Page Answers to: Discrete distributions Page Answers to: Hypothesis testing Page Answers to: Relationships Page Answers to: The spatial element Page Answers to: The semi-variogram Page Answers to: Estimation and Kriging Page 255

7 11. Bonus Answer: Estimation over a mining block Page estimating a mining block the inter-sample relationships the relationship between sample and block the within block the estimation variance 11.2 Alternative answer estimating the block from face averages estimating the average value over the face combining the components of the error 11.3 Summary Tables Data Sets

8 Preface This is a companion volume to Practical Geostatistics Here we present the exercises suggested in the book with model answers for each one. If you have questions please contact one or other of us or visit or to check whether your question has already been asked and answered. Given the nature of the universe, we can give no guarantee that this volume is typo free. We have taken as much care as we can but none of us are perfect. We apologise for any stress caused by any remaining errors in the text. Isobel Clark Geostokos (Ecosse) Limited Alloa Business Centre Whins Road, Alloa, FK10 3SA Central Scotland Tel: Fax: PG2000_AttE@kriging.com William V. Harper Otterbein College, Mathematical Sciences Towers Hall 139, 1 Otterbein College Westerville, OH U.S.A Phone: Fax: WHarper@otterbein.edu

9 In addition to full worked examples, the first 10 chapters of Practical Geostatistics 2000 finish with a set of exercises for the reader to tackle. This second volume presents Answers to the Exercises. It is not exactly a slim volume, being 382 pages long. If your idea of an answer book reads like: Q: the ultimate question of life, the universe and everything A: 42 Then this is not the book for you. The answers here are detailed, wordy and tackle the real problem rather than present some idealised pat solution to each exercise. If you have a problem that does not follow the flock, you may find some help amongst the definitely non-standard real-life problems here. Ecosse North America, LLC Attn: William V. Harper, wharper@otterbein.edu Mathematical Sciences, Towers Hall 139 Otterbein College One Grove Street Westerville, OH USA