*GEO-MATHEMATICS*
*INVERSE MODELLING IN THE NATURAL SCIENCES *
*Final Announcement! !*
15 – 26 January 2007, Bandung
Organised by
*Laboratorium Matematika Indonesia*
*( LabMath-Indonesia) *
*www.labmath- indonesia. or.id*
in collaboration with
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University of Delft, Netherlands
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Alfred Wegener Institute, Bremerhaven, Germany
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GeoPhysics Group, Institut Teknologi Bandung
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GITEWS consortium
*AIM AND DESCRIPTION*
The aim of the two-week Research Work Shop (RWS) is to provide some background of methods and ideas in Inverse Modelling. For the best performing participants, this may be the start of continued research, guided by one of the lecturers of the RWS.
In many problems from natural and physical sciences one has to solve a *direct *problem. That means that mathematical model equations describing the state or dynamics of the problem have to be solved. This will be possible if the data of the problem, such as the parameters and/or initial/boundary values are (assumed to be) known. If these data are inaccurate or uncertain, the problem is not well posed: information is missing to get a unique solution. *Data-assimilation* is the set of methods to use available measurements to compensate as much as possible for the missing information. If measurements are used to determine a-priori unknown data, such as material properties or the source, this is called an *inverse* problem.
In many areas important examples can be found. For instance, *Tomography* which 'determines the inside from outside', uses the fact the speed (and deformation) of light-, pressure- and sound- waves is determined by the material properties through which it propagates. From measurements on waves at the outside of a domain that are caused by external sources one can determine (partly) the interior material composition. Applications: the interior of the earth from volcano eruptions and seismic signals, positioning (extent of) oil fields from acoustically generated waves, detecting tumors in the body from X-rays, reconstruction of oceanic tectonic
plate motions from measurements on tsunamis, positioning fish shoals from acoustic reflections, etc. An example of data-assimilation is weather prediction that is constantly 'updated' with new measurements.
There is a whole (ever-increasing) set of mathematical techniques to tackle such problems, and research is still very active in this field. The aim is to introduce basic techniques and ideas, and to illustrate these to several examples mentioned above.
*PROJECTS*
A short description of the five projects is as follows.
*Project 1* INVERSE MODELING OF POLLUTION TRANSPORT IN GROUND WATER (Heemink)
We consider a ground water system where at a certain time at a certain location there has been a release of pollutant. We want to combine the results of a numerical ground water model with available measurements in order to reconstruct the pollution plume and the time and location of the pollution release. The Euler-Lagrange equations provide the optimal solution to this problem.
In this project we will use the representer method to solve the Euler-Lagrange equations in order to determine an optimal estimate of the initial release of the pollutant.
*Project 2* THE ESTIMATION OF THE PERMEABILITY FIELD IN RESERVOIR MODELS (Hanea)
Data assimilation can be used to combine the results of a numerical reservoir model with the measurement information available in order to obtain an optimal reconstruction of the dynamic behaviour of the model state. Data assimilation schemes are based on ensemble Kalman filtering. These recursive schemes are very powerfull and relatively easy to implement.
The permeability field is one of the key parameters in large scale reservoir models. In this project we will develop a ensemble-type data assimilation scheme for estimating the permeability field in a relatively simple reservoir model. In the project we will apply and evaluate the performance of the ensemble-type method for these type of estimation problems.
*Project 3* SEISMIC TOMOGRAPHY INVERSION (Widiyantoro)
Tomographic imaging represents the reconstruction of an object from observations of physical quantities which represent the effect of the passage of some form of radiation through the object, where each quantity represents the integrated effect of interaction along a slice through the object. A major development has been in the field of medical research, where this approach forms the basis for Computer Tomographic (CT) scanning which has been successfully applied to retrieve high resolution tomograms (slice pictures) of a human body allowing e.g. the size and shape of a tumour to be measured. In medical tomographic imaging, the three-dimensional structure of the body of a patient is usually imaged in terms of spatial absorption anomalies of the intensity of X-ray energy.
The word tomography has been adopted in seismology as a synonym for methods of extracting two- or three-dimensional images of structure. In seismic tomographic studies the Earth's interior structure is investigated through the inversion of either seismic-wave travel-time residuals (delay times) or full waveforms to determine seismic velocities. In this project, we will apply a method of inversion using delay-time data in order to delineate sub-surface structures on local and regional scales such as volcanoes and subduction zones, respectively.
*Project 4. INVERSE METHODS FOR TSUNAMI EARLY WARNING (Behrens)*
A critical component in tsunami early warning systems is the timely and accurate reconstruction of the wave source parameters. The source plays a key role in determining the arrival time and wave height, and therefore the impact at vulnerable coastal areas. Wave dispersion is commonly modelled by the non-linear shallow water equations with some run-up parameterization, taken as an initial value problem. In order to determine the initial source for the computation, seismic data, gauge data, GPS data, etc. have to be considered. The inversion procedure based on such a diversity of data is non-trivial and will be further developed in this project.
*Project 5. SEISMOTECTONIC ACTIVITY MODELLING AROUND SUNDA ARC (Triyoso)*
This project deals with a new algorithm to estimate the magnitude using The Present Day Instrumentally recorded Earthquake Catalogue. We take as special case The December 26th 2004 Giant Thrust Event, and use Co-Seismic and Pre-Seismic data to compare the estimates. The algorithm can be of help in estimating Earthquake & Tsunami Hazard and thereby reducing possible losses and damages.
*LECTURERS*
Prof. Dr. Arnold Heemink, Univ. of Delft, Netherlands
Dr. Remus Hanea, Univ. of Delft, Netherlands
PD Dr. Jörn Behrens, AWI Bremerhaven, Germany
Dr. Sri Widiyantoro, Institut Teknologi Bandung, Indonesia
Dr. Wahyu Triyoso, , Institut Teknologi Bandung, Indonesia
*PROGRAMME LAY-OUT*
The first week is a Course week, with lectures and exercise classes. This Course week can be attended by maximal 30 participants. At the end of this week, the projects will be introduced and Project groups will be formed. At most 20 participants can continue with these projects, when necessary selected based on their performance during the Course week. This project work will be executed during the whole second week with close guidance by the RWS lecturers. A special lecture will deal with the 'art' of grant hunting and project writing. Participants will prepare written and oral presentations of their work. Arrangements for further activities will be made if applicable.
*AWARD/CONTINUATION *
For at most five of the best performing participants, a continued activity will be designed. Such a continuation may consist of further study and own research investigations in a specific topic. Working on the topic may include a period of several months as guest of *LabMath-Indonesia* in Bandung. During these periods, and as much as possible also during other periods using email for correspondence, tutorial guidance will be provided by one of the lecturers of the RWS. When achievements are good, sooner or later the results will lead to an application for a research grant, to an international publication, and/or to a visit or following a study programme at a university abroad, whatever is possible and desired. The best
performing participants will be invited and guided to write a research proposal to be submitted to (inter-) national funding agencies.
*PARTICIPATION*
Students and staff from governmental or private universities and organisations, and employees of companies can apply for participation. *Especially young S1 students in their final year and S2 students are strongly encouraged to participate. *
To profit from the course, participants should be eager to learn new topics, both the theoretical background as well as the specific applications. In general, knowledge in analysis, and in ordinary and partial differential equations, is required. Students with a math, physics, engineering or natural science (oceanography, geophysics, etc) back ground will be able to enjoy the lectures and projects. Programming skills (Matlab, Maple), will be needed in the execution of most of the projects. The applications will be critically examined, and at most 30 participants will be allowed to participate in the first Course Week, and 20 in the Project week.
*DEADLINE FOR APPLICATION: 21 December 2006*
*NOTIFICATION OF PARTICIPATION: before 9 January 2007*
*FEE AND SUPPORT*
For participation a fee is requested of 1.000.000 Rp for registration before 15 December 2006, and 1.500.000 Rp thereafter. This fee includes the workshop material, lunch and coffee/tea during breaks, and the workshop dinner. *For young students and university staff the fee may be (partly) exempted;* please indicate and motivate the amount of support needed in a separate letter, added to the other application documents.
*VENUE*
Lecture room to be announced.
*REGISTRATION FORM*
Fill out the items below and send this together with CV, updated academic record, letter of motivation and request for financial support (if applicable), to the office of *LabMath-Indonesia* . This form can be copied as many times as you wish.
Alternatively: provide the details below in the main part of an email, with the documents as attachment, and email to: admin@labmath- indonesia. or.id .
*Name:*
*Position (student/lecturer Univ., other):*
*Address:*
*Tel: Fax:*
*E-mail:*
*Date: Signature: *
*LABMATH-INDONESIA*
*Office: Jl. Cigadung Raya Barat 7A Kav. A-2, *
*Bandung 40191*
*Phone: +62 (0)22 9127 1863*
*admin@labmath- indonesia. or.id*
*www.labmath- indonesia. or.id*
[sursa beasiswa]
