Throughout this book there are numerous cases where geophysics has been used to help
solve practical environmental, geotechnical, and exploration problems. The typical scenario …

Regularization algorithms are often used to produce reasonable solutions to ill-posed
problems. The L-curve is a plot—for all valid regularization parameters—of the size of the …

Many recent computational photography techniques decompose an image into a piecewise
smooth base layer, containing large scale variations in intensity, and a residual detail layer …

We present four numerical methods for computing the singular value decomposition (SVD)
of large sparse matrices on a multiprocessor architecture. We emphasize Lanczos and …

Over the past 10 years, ray-based postmigration grid tomography has become the standard
model-building tool for seismic depth imaging. While the basics of the method have …

This book describes the theory and practice of inverting seismic data for the subsurface rock
properties of the earth. The primary application is for inverting reflection and/or transmission …

The “Huber function”(or “Huber norm”) is one of several robust error measures which
interpolates between smooth (ℓ2) treatment of small residuals and robust (ℓ1) treatment of …

AVO inversion is a well established seismic exploration methodology to predict the earthos
elastic parameters and thus rock and fluid properties. This thesis in'troduces a series of …

Replacing the lscr 2 data fidelity term of the standard total variation (TV) functional with an
lscr 1 data fidelity term has been found to offer a number of theoretical and practical benefits …

Least squares or ℓ 2 solutions of seismic inversion and tomography problems tend to be
very sensitive to data points with large errors. The ℓ p minimization for 1≤ p< 2 gives more …