38 research outputs found
Large Scale Inverse Problems
This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences
Seismic Waves
The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni
3D reconstruction and object recognition from 2D SONAR data
Accurate and meaningful representations of the environment are required for autonomy in underwater applications. Thanks to favourable propagation properties in water, acoustic sensors are commonly preferred to video cameras and lasers but do not provide direct 3D information. This thesis addresses the 3D reconstruction of underwater scenes from 2D imaging SONAR data as well as the recognition of objects of interest in the reconstructed scene. We present two 3D reconstruction methods and two model-based object recognition methods. We evaluate our algorithms on multiple scenarios including data gathered by an AUV. We show the ability to reconstruct underwater environments at centimetre-level accuracy using 2D SONARs of any aperture. We demonstrate the recognition of structures of interest on a medium-sized oil-field type environment providing accurate yet low memory footprint semantic world models. We conclude that accurate 3D semantic representations of partially-structured marine environments can be obtained from commonly embedded 2D SONARs, enabling online world modelling, relocalisation and model-based applications
Reciprocity-based imaging using multiply scattered waves
In exploration seismology, seismic waves are emitted into the structurally complex
Earth. Its response, consisting of a mixture of arrivals including primary reflections,
conversions, multiples, and transmissions, is used to infer the internal structure and
properties. Waves that interact multiple times with the inhomogeneities in the medium
probe areas of the subsurface that are sometimes inaccessible to singly scattered waves.
However, these contributions are notoriously difficult to use for imaging because multiple
scattering turns out to be a highly nonlinear process. Conventionally, imaging
algorithms assume singly scattered energy dominates data. Hence these require that
energy that scatters more than once is attenuated.
The principal focus of this thesis is to incorporate the effect of complex nonlinear
scattering in the construction of subsurface elastic images. Reciprocity theory is used
to establish an exact relation between the full recorded data and the local (zero-offset,
zero-time) scattering response in the subsurface which constitutes our image. Fully
nonlinear, elastic imaging conditions are shown to lead to better illumination, higher
resolution and improved amplitudes in pure-mode imaging. Strikingly it is also observed
that when multiple scattering is correctly handled, no converted-wave energy is mapped
to any image point. I explain this result by noting that conversions require finite time
and space to manifest.
The construction of wavefield propagators (Green’s functions) that are used to extrapolate
recorded data from the surface to points in the Earth’s interior is a crucial component
of any imaging technique. Classical approaches are based on strong assumptions
about the propagation direction of recorded data, and their polarization; preliminary
steps of wavefield decomposition (directional and modal) are required to extract upward
propagating waves at the recording surface and separate different wave modes.
These algorithms also generally fail to explain the trajectories of multiply scattered
and converted waves, representing a major problem when constructing nonlinear images
as we do not know where such energy interacted with the scatterers to be imaged.
A secondary aim of this thesis is to improve on the practice of wavefield extrapolation
or redatuming by taking advantage of the different nature of multi-component
data compared with single-mode acoustic data. Two-way representation theorems are
used to define novel formulations in elastic media which allow both up- and downward
propagating fields to be back-propagated correctly without ambiguity in the direction,
and such that no cross-talk between wave modes is generated. As an application of
directional extrapolation, the acoustic counterpart of the new approach is tested on an
ocean-bottom cable field dataset acquired over the Volve field, North Sea. Interestingly,
the process of redatuming sources to locations beneath a complex overburden by means
of multi-dimensional deconvolution also requires preliminary wavefield separation to be
successful: I propose to use the two-way convolution-type representation as a way to
combine full pressure and particle velocity recordings. Accurate redatumed wavefields
can then be obtained directly from multi-component data without separation.
Another major challenge in seismic imaging is to construct detailed velocity models
through which recorded data will be extrapolated. Nowadays the information contained
in the extension of subsurface images along either the time or space axis is commonly
exploited by velocity model building techniques acting in the image domain. Recent
research has shown that when both extensions are taken into account, it is possible to
estimate the data that would have been recorded if a small, local seismic survey was
conducted around any image point in the subsurface. I elaborate on the use of nonlinear
elastic imaging conditions to construct such so-called extended image gathers:
missing events, incorrect amplitudes, and spurious energy generated from the use of
only primary arrivals are shown to be mitigated when multiple scattering is included
in the migration process. Finally, having access to virtual recordings in the subsurface
is also very useful for target-oriented imaging applications. In the context of one-way
representation, I apply the novel methodology of Marchenko redatuming to the Volve
field dataset as a way to unravel propagation effects in the overburden structure. Constructed
wavefields are then used to synthesize local, subsurface reflection responses
that are only sensitive to local heterogeneities, and detailed images of target areas of
the subsurface are ultimately produced.
Overall the findings of this thesis demonstrate that, while incorporating multiply scattered
waves as well as multi-component data in imaging may be not a trivial task, such information
is vital for achieving high-resolution and true-amplitude seismic imaging