Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis

The molecule solution of an extended discrete Lotka-Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is proved that our new sequence transformation accelerates some kinds of linear sequences and factorial sequences with good numerical stability. Some numerical e...

Shanks' convergence acceleration transform, Padé approximants and partitions

Acceleration of convergence of general linear sequences by the Shanks transformation

The Shanks transformation is a powerful nonlinear extrapolation method that is used to accelerate the convergence of slowly converging, and even diverging, sequences {An}. It generates a two-dimensional array of approximations A j) n to the limit or anti-limit of {An} defined as solutions of the linear systems Al = A j) n + n ∑ k=1 β̄k( Al+k−1), j ≤ l ≤ j + n, where β̄k are additional unknowns. I...

Full waveform inversion of crosswell seismic data using automatic differentiation

Full waveform inversion (FWI) is an effective and efficient data-fitting technique that has been widely used to produce accurate estimation of model parameters in Geophysics. The efficiency and accuracy of FWI are determined by the three main components: numerical solution for forward problem, gradient calculation and model update which usually involves the optimization method. The success of t...

Full waveform seismic inversion using a distributed system of computers

The aim of seismic waveform inversion is to estimate the elastic properties of the Earth’s subsurface layers from recordings of seismic waveform data. This is usually accomplished by using constrained optimization often based on very simplistic assumptions. Full waveform inversion uses a more accurate wave propagation model but is extremely difficult to use for routine analysis and interpretati...