Seismic borehole tomography—Theory and computational methods

Non Invasive Acoustic Measurements for Faults Detecting in Building Materials and Structures

“…A common method to obtain the solution of equations system (5) in the least square sense is the Singular Value Decomposition (SVD) (Berryman, 1991;Herman, 1980;Ivansson, 1986). The SVD can be used for computing the pseudo-inverse of the coefficient matrix P. Indeed, this method produces a diagonal matrix D, of the same dimension of P and with nonnegative diagonal elements in decreasing order, and two unitary matrices U and V so that P = UDV T .…”

Acoustic tomography for qualitative nondestructive evaluation (QNDE) of structural concrete using a new ultrasonic scanner source

“…In this paper, we have sought to solve (4) by using two series expansion approaches from geotomography: an optimized and efficient matrix inversion approach based on the Conjugate Gradient (CG) inversion technique [4,5]; and another "backprojection" approach, adapted from medical tomography [2,3] of Simultaneous Iterative Reconstruction Technique (SIRT).…”

Conjugate Gradient Method for the Solution of Inverse Problems: Application in Linear Seismic Tomography

“…However, since the matrix G is usually sparse, iterative methods are the usual choices for large-scale problems [8,9,16]. Taking into account that several authors reported that iterative methods based on Krylov subspaces, such as the conjugate gradient method for the normal equations and the LSQR method [10], performed better than stationary iterative methods such as SIRT and ART techniques [9,7,19], we focus on conjugate gradient methods in this work.…”