Horizons are geologically significant surfaces that can be extracted from seismic images. Color coding of horizons based on amplitude or other attributes can help reveal ancient sedimentary environments and structural features. Extracted horizons are also used for building structure models and stratigraphic interpretations. We propose two methods for constructing seismic horizons aligned with r...

In this paper, we describe an application of the planar conjugate gradient method introduced in Part 1 (Ref. 1) and aimed at solving indefinite nonsingular sets of linear equations. We prove that it can be used fruitfully within optimization frameworks; in particular, we present a globally convergent truncated Newton scheme, which uses the above planar method for solving the Newton equation. Fi...

An efficient multiresolution method to compute global conformal structures of nonzero genus triangle meshes is introduced. The homology, cohomology groups of meshes are computed explicitly, then a basis of harmonic one forms and a basis of holomorphic one forms are constructed. A progressive mesh is generated to represent the original surface at different resolutions. The conformal structure is...

Thus we can apply any optimization algorithm to solve this minimization problem and obtain a method for solving (1.1). At the point, let us consider the steepest descent method and select any initial guess x0. With xk available we try to find the direction along which φ(x) decreases most rapidly starting from xk and compute the next point xk+1 by minimizing φ(x) in this direction. By Taylor ser...

In this paper, we survey some of latest developments in using preconditioned conjugate gradient methods for solving mildly ill-conditioned Toeplitz systems where the condition numbers of the systems grow like O(n) for some > 0. This corresponds to Toeplitz matrices generated by functions having zeros of order. Because of the ill-conditioning, the number of iterations required for convergence in...

A time dependent minimization problem for the computation of a mixed L 2 /Wasserstein distance between two prescribed density functions is introduced (in the spirit of 1] for the \classical" Wasserstein distance). The optimum of the cost function corresponds to an optimal mapping between prescribed initial and nal densities. We propose to enforce the nal density conditions through a penalizatio...

We present an efficient and accurate variant of the conjugate gradient method for solving families of shifted systems. In particular we are interested in shifted systems that occur in Tikhonov regularization for inverse problems since these problems can be sensitive to roundoff errors. The success of our method in achieving accurate approximations is supported by theoretical arguments as well a...

This paper describes gradient methods based on a scaled metric on the Grassmann manifold for low-rank matrix completion. The proposed methods significantly improve canonical gradient methods, especially on ill-conditioned matrices, while maintaining established global convegence and exact recovery guarantees. A connection between a form of subspace iteration for matrix completion and the scaled...

abstract among activities that can be used to prevent piping phenomena and reduce seepage and exit gradient are installation of cutoff wall and drain under hydraulic structures. hence in this study, to investigating the influence of each mentioned parameter on uplift force and exit gradient a computer model has developed in which general equation of fluid flow into the isotropic and anisotropic...