Lorentz Center - Uncertainty Analysis in Geophysical Inverse Problems from 7 Nov 2011 through 11 Nov 2011
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    Uncertainty Analysis in Geophysical Inverse Problems
    from 7 Nov 2011 through 11 Nov 2011


Workshop Report

Uncertainty Analysis in Geophysical Inverse Problems


Aims and Scope: Our workshop was motivated by recent advances in computer science and applied mathematics that enabled us to start solving realistic large-scale inverse problems in the Earth sciences, including weather and climate forecasting, imaging the Earth’s internal structure, predicting ocean currents, and estimating flow patterns in the Earth’s mantle and outer core. The finite amount of data, the presence of noise and incomplete forward models introduce uncertainties in the solution of inverse problems that are often not properly quantified, despite their undisputed social and economic relevance, for instance in the context of geophysical exploration or the prediction of extreme local weather conditions.

Significant progress in uncertainty analysis can be made by realising that most inverse problems are very similar on an abstract mathematical level, and by fostering the communication between applied mathematics and various geophysical disciplines that use different approaches.

The principal objective of the workshop was thus to provide a communication platform for mathematicians, seismologists, meteorologists, oceanographers and geodynamicists that promotes the transfer of methodologies across the disciplines and the homogenisation of the diverse scientific vocabularies.


Tangible outcomes: The most concrete outcome for all participants was the recognition that inverse problems across the geosciences are indeed similar to a degree that allows for an easy transfer of methodologies and concepts. For instance, a sampling strategy for high-dimensional probability densities mostly used in solid-Earth geophysics (the so-called Neighbourhood algorithm) was found to be applicable in data assimilation applications such as weather forecasting. We furthermore recognized how to translate inverse problem formulations typically used in meteorology and oceanography to seismic tomography, thereby opening entirely new perspectives for uncertainty analysis in tomographic applications.

Our workshop was marked by a continuous learning process that started with major problems understanding each other and ended with an increased interest and ability to communicate across the disciplines. The establishment of many new research connections is probably the most important outcome of our workshop. With the help of our newly developed common language, we were able to formulate a list of key problems that we think our communities should address and solve in the new future. Our plan is to assess our progress in a second workshop that should take place in 2 to 3 years.

Finally, the discussions of our workshop will be summarised in a review paper entitled Uncertainty Analysis in Geophysical Inverse Problems, that we hope to publish in Annual Reviews of Earth and Planetary Sciences.


Organisation and Format: The participants generally appreciated the informal organisation and very much enjoyed the academic atmosphere at the Lorentz Center. The format was ideal for what we wanted to achieve. We quickly developed a culture of vivid discussions that lasted throughout the week. We often used the allocated discussion time during the talks already, continued during the coffee and lunch breaks and indeed dinner time. The visibility of the posters from Monday to Friday was very helpful, especially for the students who used the opportunity to establish connections with the more senior scientists.

A key element of our workshop was the daily morning lecture that introduced one specific field, e.g. seismic tomography. The lectures completely fulfilled their purpose of enabling a very diverse audience to engage in discussions


In summary, our workshop was a great success, and it was a pleasure for everybody to enjoy science at the Lorentz Center.