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Aims of the TOAST project

For an improved estimation of subsurface parameters we need to exploit the full information contained in three-component seismic waveforms. Of particular importance is the estimation of the independent elastic parameters that characterize the properties of the subsurface. Waveform tomography is a cutting-edge inverse method that accounts for the full seismic waveform recorded over a broad range of frequencies and apertures. It iteratively retrieves multiparameter models of the subsurface by solving the full viscoelastic wave equations each time. It allows for a mapping of structures on spatial scales down to less than the seismic wavelength, hence providing a tremendous improvement of resolution compared to traveltime tomography based on ray theory.

Many examples published in recent years demonstrate that waveform tomography can image the interior of the earth and of material specimens on a wide range of scales. It has successfully been applied to seismological scales (Friederich 2003), subduction zones (Operto et al., 2006), basalt structures (Chironi et al., 2006), shallow environments (Forbriger 2003; Gao et al., 2007), material testing (Pratt 1999), and even breast tissues (Pratt et al., 2007). We can therefore anticipate a rich future of this approach for a wide range of applications.

Tomographic problems are commonly solved by using highly-specialized monolithic computer applications at the expense of flexiblity, transparency, portability and extendibility. Within the TOAST project, a flexible and modular toolbox for 1D, 2D, and 3D full waveform inversion will be created.

Existing software that has been developed and maintained by the participating partners will be assembled and grouped into three modules, which will interface through appropriate definitions of data and parameterization formats, input/output routines and parameter file translation tools. The whole collection of software will establish the toolbox which will be used to design and solve applied inverse problems. The toolbox will also contain components to prepare initial models from field data for subsequent waveform inversion. It will further contain tools to explore the null-space of the model, as well as tools to perform a quantitative resolution analysis. A deliberate definition of the representation of model parameters will allow for future extension to non-seismic observables, which is beyond the scope of the present project.

On one hand, the toolbox strives to facilitate access to tomographic methods for users from fields of applied science and engineering. On the other hand, it is designed to assist the expert scientist in solving highly demanding inverse problems. To all users, the added value of a modular product such as TOAST will be the freedom to start data exploration with very basic tools, and to gradually escalate the level of sophistication as their experience, the amount and understanding of their data, and their computational resources increase. Studies on the spatial scales adressed by TOAST will benefit in particular because they often start from a very vague understanding of the structure under investigation. Here, the modular toolbox will develop its full strength by supporting the scientist from the first simple model to a final high-end waveform tomography.

The success of this approach relies on professional code management. Format definition standards and best practices must be established. Interaction between working groups will be supported by a version-controlled software repository and documentation standards. Parallelized code must be implemented on several platforms. Code benchmarking and scalability will be accounted for.

The toolbox will be benchmarked through application to field data. Within the project, it will be tested on different scales from centimeters to meters in ultrasonic studies, and over tens of meters to kilometers in seismic studies. The requirements for seismic inversion at different scales differ significantly. While solutions to 1D problems on the seismological scale are standard nowadays, they are still challenging on the shallow seimics or ultrasonic scale, where initial models are missing for each individual sample or site. The variety of heterogeneity encountered (predominantly horizontal layering, full 3D heterogeneity, or even holes in the samples) calls for very flexible inversion tools.

The results of these studies will be compared to other observations (dynamic probing, resonant columns, etc.), thus providing a benchmark and calibration of seismic results to petrophysical parameters. Through close cooperation with industrial partners, exemplary datasets for all spatial scales will become available to the project. Additionally, exemplary data sets will be acquired at low cost in a field laboratory, and optimal acquisition strategies for waveform inversion will be developed. In return, the industrial partners will benefit from the tools created by the project for their future applications.