This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo spheric physics, fluid mechanics, seismology, and oceanography. The com mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas."

Hurricanes of the North Atlantic Ocean have left their imprint on the landscape and human cultures for thousands of years. In modern times, fewer lifes have been lost due, in part, to the development of modern communication systems, and to improved understanding of the mechanisms of storm formation and movement. However, the immense growth of human populations in coastal areas, which are at risk to hurricanes, has resulted in very large increases in the amount of property damage sustained in the last decade in the Atlantic, Gulf of Mexico and Caribbean regions. This book is of interest to climatologists and meteorologists and as source of information for policymakers and emergency management planners.

Advances in seismology and extensions of its application have made it increasingly necessary to perform high-sensitivity observationsonartificial earth tremors (explosions) or on natural ones. This implies in particular to investigating the seismic conditions in large industrial centres. There are many major cities with a million inhabitants or more in seismically-active regions. In the USSR, this applies to the capitals of the Union Republics such as Alma Ata, Frunze, Tashkent, Dushanbe, and Ashkhabad, as well as to dozens of local entres and cities with extensive industrial development. Seismic classification and earthquake forecasting have to be considered in relation to the extension or building of cities in such regions, and this would be impossible without detailed investigation of the seismicity, which involves upgrading the instru mental observation network. The demand for detailed information on the seismicity increases with every extension to the construction. A successful solution here can be implemented only by taking account of some specific factors, the main one being the high level of seismic noise due to the activities in large centres, which restricts the sensitivity of the apparatus and makes it impossible to record weak local earth tremors, which are of particular interest in periods of relative seismic calm. Stations at sufficiently great distances from the city do not sense the city noise, but they also fail to record weak local earth tremors. Also, the accuracy ofobservation falls for those tremors that can be recorded because of the great distances between stations."

Historically, the discovery of tools, or evidence that tools have been used, has been taken as proof of human activity; certainly the invention and spread of new tools has been a critical marker of human progress and has increased our ability to observe, measure, and understand the physical world. In astronomy the tools are telescopes and the optical and electronic instruments that support them. The use of the telescope by Galileo marked the beginning of a new and productive way to study and understand the universe in which we live. The effects of this new tool on what we can see, and how we see ourselves, are well known. However, after almost four centuries of developing ever more sensitive and subtle instruments as tools for astronomy, it might have been expected that only a few minor improvements would remain to be made, or that possibly the law of diminishing returns would have taken effect. On the contrary, the new instruments and ideas for new instruments described in this book make it clear that the rate of progress has not diminished, and that this subject is still as exciting and productive as ever. Instrumentation for Ground-Based Optical Astronomy was chosen as the theme for the Ninth Santa Cruz Summer Workshop in Astronomy and Astrophysics.

Surface waves form the longest and strongest portion of a seismic record excited by explosions and shallow earthquakes. Traversing areas with diverse geologic structures, they 'absorb' information on the properties of these areas which is best retlected in dispersion, the dependence of velocity on frequency. The other prop erties of these waves - polarization, frequency content, attenuation, azimuthal variation of the amplitude and phase - arc also controlled by the medium between the source and the recording station; some of these are affected by the properties of the source itself and by the conditions around it. In recent years surface wave seismology has become an indispensable part of seismological practice. The maximum amplitude in the surface wave train of virtually every earthquake or major explosion is being measured and used by all national and international seismological surveys in the determination of the most important energy parameter of a seismic source, namely, the magnitude M, . The relationship between M, and the body wave magnitude fI1t, is routinely employed in identification of underground nuclear explosions. Surface waves of hundreds of earthquakes recorded every year are being analysed to estimate the seismic moment tensor of earthquake sources, to determine the periods of free oscillations of the Earth, to construct regional dispersion curves from which in turn the crustal and upper mantle structure in various areas is derived, and to evaluate the dissipative parameters of the mantle material."

In the Fall of 1988, 64 geologists and geophysicists from 11 countries met in Killarney, Ontario, on the north shore of Lake Huron to examine evidence that suggests that the continental crust is exposed in cross-section at several key locations on the Earth's surface. The meeting, which was held under NATO auspices as an Advanced Study Institute, was a landmark event in that it was the first time that many of the lead scientists working on these complexes in relative isolation around the world had' ever gathered together to compare results. The present volume is a compendium of the invited lectures given on the principle sections, plus an array of supporting papers on these and other sections as well as on related topics such as crustal emplacement mechanisms, deformation and rheology. Nearly all of the best known sections are represented, including the Ivrea Zone, Calabria, the Kapuskasing Zone, Fiordland and many others. It is our hope that this Volume will serve as a reference for Earth scientists who are trying to understand levels of the crust not normally exposed to view, as well as a point of departure for new research and a teaching aid to new entrants in this relatively new field of study.

Recent developments in Science and Technology have removed the boundaries betwe n the so-called 'fundamental' and 'applied' fields of research. This has been particularly evident in the rapidly expanding geophysical sciences with their far reaching applications. Fundamental geophysical studies of surface, subsurface and crustal structures where gravity investigations play an important role, are of immediate potential importance in defining major structural features or geological units which may control or influence the development of metallogenic provinces, petroleum potential areas or coal fields. Gravity studies in India have a long history and tradition. The earliest gravity measurements were made with two brass pendulums loaned by the Royal Society of England, when Basevi and Heaviside established 30 gravity pendulum stations between Cape Comorin and Ladakh during 1865 to 1873. Over the subsequent years, large areas of the country have been systematically covered through gravimeters and a number of regional and detailed studies have been undertaken by various agencies like Survey of India, Geological Survey of India (GSI), Oil and Natural Gas Commission (ONGC), National Geophysical Research Institute (NGRI) and a number of universities. Assistance was provided by late Prof. G. P. Woollard and his former students Muckenfuss, Bonini, Shankaranarayan and Murali Manghnani, who have connected India to the international gravity net work. Gravity studies carried out by the Survey of India have been of great value in geodetic studies.

Earthquake Hazard and Risk is a book summarizing selected papers presented at the 27th General Assembly of the International Association of Seismology and Physics of the Earth's Interior (Wellington, January 1994). The papers, rigorously scrutinized by an international board of referees, cover some recent aspects of current research in earthquake hazard and seismic risk. They address the algorithms and methodology used in seismological applications, the reliability of these techniques with the decreasing level of probability and uncertainty associated with various seismotectonic settings, the physical and statistical nature of earthquake occurrences, strong ground motions and effects of surface seismogeological conditions. A special effort has been made to include papers that illustrate the assessment of earthquake hazard and seismic risk through applications at sites in either inter-plate or intra-plate tectonic settings. Of particular interest is hazard assessment in regions of rare large earthquakes. The book is suitable for those interested in earthquake hazard and seismic risk research as well as a more general audience of seismologists, geophysicists and Earth scientists. It is also useful for authorities responsible for public safety and natural hazard mitigation plans and for insurance companies.

This book consists of a collection of papers presented at the NATO Advanced Research Workshop (ARW) on "Crust/mantle Recycl ing at Convergence Zones," held in Antalya, Turkey, between May 25 to 29, 1987. The workshop was attended by 36 earth scientists from ten countries and 28 papers were presented. Crust/mantle recycling is one of the most fundamental processes in the Earth. The study and understanding of this process requires the consideration of the Earth as a whole system including the atmosphere, the hydrosphere and the core, as well as the crust and the mantle; effective interdisciplinary collaboration is therefore essential to our progress. The Antalya ARW gave us the opportunity to assemble key specialists from relevant branches of the earth sciences and to address our state of knowledge. This ARW proved to be very useful in attaining an interdisciplinary, mutual understanding among specialists from diverse fields such as isotope and trace element geochemistry, mineral physics, theoretical geophysics, seismology, experimental petrology, and structural geology.

This volume presents lectures given at the NATO Advanced Study Institute held 11-22 April 1988 at Newcastle upon Tyne, England. The aim of the Institute was to improve the interaction between workers in observational geomagnetism (using historical data) and archaeo- and palaeo-magnetism (using the remanent magnetization of man-made artefacts and of natural sediments and rocks) and those trying to interpret the data in terms of mechanisms inside or outside the Earth, particularly those developing dynamo theories of the field. The material discussed ranged from magnetic bacteria swimming round a circle in a few seconds, the effect of El Nino, through secular variation with time scales of tens to thousands of years and the'mechanics of individual field reversals and excursions (aborted reversals?) to possible modulation of average reversal frequency on the hundred million year time scale. Many members of the Physics Department helped with the organization, and we are most grateful to them, and in particular to Anne Codling for her very many contributions. We also gratefully acknowledge the painstaking work of Aileen Dryburgh and Lynn Whiteford in so carefully typing the manuscript.

Recent advances in the power of inversion methods, the accuracy of acoustic field prediction codes, and the speed of digital computers have made the full field inversion of ocean and seismic parameters on a large scale a practical possibility. These methods exploit amplitude and phase information detected on hydrophone/geophone arrays, thereby extending traditional inversion schemes based on time of flight measurements. Full field inversion methods provide environmental information by minimising the mismatch between measured and predicted acoustic fields through a global search of possible environmental parameters. Full Field Inversion Methods in Ocean and Seismo-Acoustics is the formal record of a conference held in Italy in June 1994, sponsored by NATO SACLANT Undersea Research Centre. It includes papers by NATO specialists and others. Topics covered include: . speed and accuracy of acoustic field prediction codes . signal processing strategies . global inversion algorithms . search spaces of environmental parameters . environmental stochastic limitations . special purpose computer architectures . measurement geometries . source and receiving sensor technologies. "

The Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, April 10-12, 1995, was organized to bring to gether an interdisciplinary group drawn from the areas of science, engineering and mathematics for the following purposes: - to promote, encourage and influence more understanding and cooperation in the community of parameter identifiers from various disciplines, - to forge unity in diversity by bringing together a variety of disciplines that attempt to understand the reconstruction of inner model parameters, un known nonlinear constitutive relations, heterogeneous structures inside of geological objects, sources or sinks from observational data, - to discuss modern regularization tools for handling improperly posed pro blems and strategies of incorporating a priori knowledge from the applied problem into the model and its treatment. These proceedings contain some of the results of the workshop, representing a bal anced selection of contributions from the various groups of participants. The reviewed invited and contributed articles are grouped according to the broad headings of hydrology, non-linear diffusion and soil physics, geophysical methods, mathematical analysis of inverse and ill-posed problems and parallel algorithms for inverse problems. Some of the issues adressed by the articles in these proceedings include the rela tion between least squares and direct formulations of inverse problems for partial differential equations, nonlinear regularization, identification of nonlinear consti tutive relations, fast parallel algorithms for large scale inverse problems, reduction of model structures, geostatistical inversion techniques.

General circulation models (GCMs) predict certain changes in the amounts and distribution of precipitation, but the conversion of these predictions of impacts on water resources presents novel problems in hydrologic modeling, particularly with regard to the scale of the processes involved. Therefore improved, distributed GCMs are required. New remote sensing technologies provide the necessary spatially distributed data. However, there are many attendant problems with the translation of remotely sensed signals into hydrologically relevant information. This book elucidates how to improve the representation of land surface hydrologic processes in GCMs and in regional and global scale climate studies. It is divided into five sections: Models and Data; Precipitation; Soil Moisture; Evapotranspiration; Runoff.

The collection of papers in this volume is a direct result of the Society of Economic Paleontologists and Mineralogists Research Symposium on "Thermal History of Sedimentary Basins: Methods and Case Histories" held as part of the American Association of Petroleum Geologists Annual Convention in New Orleans in March 1985. The original goal of the sym posium was to provide a forum where specialists from a variety of dis ciplines could present their views of methods that can be used to study the thermal history of a sedimentary basin or an important portion of a basin. An explicit part of that goal was to illustrate each method by presentation of a case history application. The original goal is addressed by the chapters in this volume, each of which emphasizes a somewhat different approach and gives field data in one way or another to illustrate the practical useful ness ofthe method. The significance of our relative ignorance of the thermal conductivities of sedimentary rocks, especially shales, in efforts to understand or model sedimentary basin thermal histories and maturation levels is a major thrust of the chapter by Blackwell and Steele. Creaney focuses on variations in kerogen composition in source rocks of different depositional environments and the degree to which these chem- . ically distinct kerogens respond differently to progressive burial heating."

In the two decades since the development of the first eclipsing-binary modeling code, new analytic techniques and the availability of powerful, sometimes dedicated computing facilities have made possible vastly improved determinations of fundamental and even transient stellar parameters. The scale of these developments, of course, raises questions about modeling tools, techniques, and philosophies, such as: Who will maintain and upgrade the codes? Will the codes be open to improvement by outsiders, and if so, how? And, indeed, what should be the goals of a modeling program? Such questions had not been aired for a long time and, for this reason alone, deserved to be discussed in as general a forum as the community provides. This volume contains material presented by Commission 42 (Close Binary Stars) during the International Astronomical Union's XXI General Assembly in Argentina, July 1991, and during IAU Colloquium 151, Cordoba, Argentina, August 1991. The techniques discussed include simulations of stellar bright and dark spots, streams, partial and complete stellar disks, prominences, and other features characterizing active stars; modeling of polarization parameters; models that use radial velocities as well as line profile simulations to model velocity field variation across stellar disks; the weighted effects of brightness asymmetries; and models for translucent eclipsing agents such as stellar winds.

Three symposia on environmental geochemistry in tropical countries, held in Niter6i, Brazil (1993), in Cartagena, Colombia (1996) and in Nova Friburgo, Brazil (1999), made it very clear that tropical geochemistry is of world standard and fast increasing in multi disciplinarily and impact on important geochemical paradigms. It has additionally strong links with the economy of tropical countries, such as mining and industrialisa tion and is in full development for treating environmental problems caused by human activities of urban or industrial origin. We must compliment Prof. Jorge Abriio and his colleagues in Brazil and Dr. Gloria Prieto and her colleagues in Colombia for these ini tiatives. The participation of respectively 180 and 150 scientists, coming from 15 different countries for the first and second symposia, has shown that a large interest exists for tropical environmental geochemistry. It also demonstrates the necessity to understand tropical environmental problems. The organisation of a large international symposium is not possible without the assistance of state and federal authorities, for which those of Brazil and Colombia have to be complimented. The 3rd Symposium on Environmental Geochemistry in Tropical Countries was the last of the series and was attended by 22 countries and 170 participants and treated a number of related environmental and economic problems."

This book is aimed at studying the scattering of monochromatic radiation in plane inhomogeneous media. We are dealing with the media whose optical properties depend on a single spatial coordinate, namely of a depth. The most widely known books on radiation transfer, for instance 1. S. Chandrasekhar, Radiative Transfer, Oxford, Clarendon Press, 1950, (RT), 2. V. V. Sobolev, Light Scattering in Planetary Atmospheres, New York, Pergamon Press, 1975, (LSPA), 3. H. C. van de Hulst, Multiple Light Scattering. Tables, Formulas and - plications. Vol. 1,2, New York, Academic Press, 1980, (MLS), treat mainly the homogeneous atmospheres. However, as known, the actual atmospheres of stars and planets, basins of water, and other artificial and nat ural media are not homogeneous. This book deals with the model of vertically inhomogeneous atmosphere, which is closer to reality than the homogeneous models. This book is close to the aforementioned monographs in its scope of prob lems and style. Therefore, I guess that a preliminary knowledge of the con tents of these books, particularly of the book by Sobolev, would facilitate the readers' task substantially. On the other hand, all concepts, problems, and equations used in this book are considered in full in Chap. 1. So, it will be possible for those readers who do not possess the above knowledge to understand this book. A general idea about the content of the book can be gained from both the Introduction and the Table of Contents."

This book is the first volume of a new interdisciplinary series on "Impact Studies". The volumes of this series aim to include all aspects of research related to impact cratering - geology, geophysics, paleontology, geochemistry, mineralogy, petrology, planetolgy, etc. Future volumes will include monographs, field guides, conference proceedings, etc. All contributions in this book were peer-reviewed to ensure high scientific quality. The thirteen papers in the present volume result from a workshop of the European Science Foundation (ESF) IMPACT programme ("Response of the Earth System to Impact Processes"). This programme is an interdisciplinary effort aimed at understanding impact processes and their effects on the Earth System, including environmental, biological, and geological changes, and consequences for the biodiversity of ecosystems. The goals of the programme, and details about our activities, can be found on the web at . The IMPACT programme has currently 15 member nations from allover Europe. The activities of the programme range from workshops to specific topics regarding impact cratering, short courses on impact stratigraphy, shock metamorphism, etc. , mobility grants for students and young researchers, development of teaching aids, and publications. The third IMPACT workshop was held in Quillan, in the foothills of the French Pyrenees, in September 1999.

The Workshop on the Seismicity and Seismic Risk in the Off shore North Sea Area was intended to bring together experts from a variety of disciplines as well as interest groups with involve ment in siting, design and construction of offshore structures in the region. Participants came from the fields of geology, seismology, oceanography, geotechnical and structural engineering and risk analysis. The wide range of participant affiliations included institutes, Observatories, universities, oil companies, consultants and insurance firms. All nationalities around the North Sea were present, in addition to some experts from outside the region. All participants were present on the basis of personal invitation. The idea of organizing the Workshop stemmed from conside- tions, such as: the rapidly increasing material and personel investments and versatility of type of structures in the basin.during the past decade; - the present-day important role Jf the North Sea oil and gas production in the economy of Western Europe; and - the increase of potential environmental risks in the region. Although devastating earthquakes are almost unknown in the area and seismic hazard is not great, the seismic risk grows with the growing size and number of structures in the area. The study of the potential seismic risks, therefore, cannot be neglected any more. The siting and design of offshore platforms and submarine pipelines are controlled by the degree of their vulnerability as well as the seismic hazard. in the region."

Electrical conductivity is a parameter which characterizes composition and physical state of the Earth's interior. Studies of the state equations of solids at high temperature and pressure indicate that there is a close relation be tween the electrical conductivity of rocks and temperature. Therefore, measurements of deep conductivity can provide knowledge of the present state and temperature of the Earth's crust and upper mantle matter. Infor mation about the temperature of the Earth's interior in the remote past is derived from heat flow data. Experimental investigation of water-containing rocks has revealed a pronounced increase of electrical conductivity in the temperature range D from 500 to 700 DC which may be attributed to the beginning of fractional melting. Hence, anomalies of electrical conductivity may be helpful in identitying zones of melting and dehydration. The studies of these zones are perspective in the scientific research of the mobile areas of the Earth's crust and upper mantle where tectonic movements, processes ofthe region al metamorphism and of forming mineral deposits are most intensive. Thus, in the whole set of research on physics of the Earth the studies of electrical conductivity of deep-seated rocks appear, beyond doubt, very important."

This volume, derived from the 1999 International Tsunami Symposium, presents a unique look at the state of tsunami research at the end of the 20th century. It displays recent progress both in data recovery and reconstructions of historical tsunamis and in detail examination of recent disasters. It shows the tsunami community using both traditional methods of data gathering - searching archives and attempting to simulate past events - and integrating modern technologies - side-scan sonar, GPS, global communications, supercomputers - in the quest to understand tsunamis and improve mankind's ability to mitigate the disastrous consequences of these unpredictable and unstoppable events. It chronicles recent advances in mitigation efforts while illuminating the continuing need for increased efforts. The papers range from descriptive texts for the non-specialists to fairly technical discussions for those familiar with tsunami research. Audience: This book will be of interest to researchers and graduate students involved in natural hazards research, physical oceanography, seismology, environmental impact assessment and risk assessment.

A profound knowledge of the past climate is vital for our understanding of global warming. The past 2000 years are both the period which is of most relevance to the next century and that for which there is the most evidence. High-resolution proxy records for this period are available from a variety of sources. Five sections consider dendroclimatology, ice cores, corals, historical records, lake varves, and other indicators. The final two sections cover the histories of various forcing factors and attempt to bring together records from a variety of sources and provide explanations.

Global risk potentials and their interplay with economic, social and ecological processes of change have emerged as a challenge to the international community. By presenting this report, the Council hopes to contribute constructively to an effective, efficient and objective management of the risks of global change. The approach taken by the Council is first to classify globally relevant risks and then to assign to these classes of risk both established and innovative risk assessment strategies and risk management tools. On this basis, management priorities can be set. The Council further recommends a number of cross-cutting strategies for international policies. These include worldwide alignment of liability law, creation of environmental liability funds, establishment of a United Nations Risk Assessment Panel and implementation of strategies aimed at reducing vulnerability to risk.

Causes of major disasters are many and diverse, and the risks associated with them endanger human lives, property, the environment, the economy, and even the country's political and social well-being. It is clear that, with rapid population growth, environmental degradation, climate change, poorly regulated industries, and continued economic uncertainty, the chances are that communities may become more vulnerable to disasters. The dramatic losses in recent years from volcanic eruptions, earthquakes and landslides, wildland fires, droughts and floods, cyclones and storm surges attest to the fact that we are still a long way from applying even the knowledge we have today to make communities safe. Tackling this problem requires a sound evaluation of disaster mitigation policies and tools. As a contribution to the International Decade for Natural Disasters Reduction (IDNDR), the fifth international symposium HAZARDS-93 was held in Qingdao, P.R. China on 29 August - 3 September, 1993. China is a country frequently hit by almost all kinds of disasters. Its history is one of combating natural disasters and working towards their reduction. More than 250 scientists, engineers and government officials from 20 countries met for the purpose of engaging in a free exchange of knowledge, experience and ideas regarding the scientific and socio-economic aspects of mitigating losses from natural and man- made disasters. A total of 180 papers were presented at 28 sessions covering a very broad range of topics related to disaster management. The twenty-one articles included in this book deal with the scientific and management issues of land-based and marine hazards which cause the most severe economic losses, deaths and environmental degradation in many parts of the world. The book also includes specific recommendations addressed to the IDNDR Secretariat, national governments and scientific experts to increase the effectiveness and efficiency of disaster management. Thus, Land-Based and Marine Hazards: Scientific and Management Issues forms an excellent reference for scientists, engineers, policy-makers and the insurance industry.

Although international scientific cooperation - particularly in meteorology - was established previous to the first International Polar Year, the IPY-1 (1882-83) is considered to be the first revolutionary step towards an extensive international cooperation in the polar areas for the benefit of science rather than national prestige and territorial gain. This was followed by IPY-2 (1932-33) and IPY-3 - actually the International Geophysical Year (1957-58) - before the crowning effort of IPY-4 (2007-08). The history of these years is recounted here and explains the political, economic, technical and scientific conditions and expectations that laid the basis for each IPY and which gradually expanded both the scope and extent of our understanding of the complexities in polar regions