Is the fast Hankel transform faster than quadrature?

• DOI: 10.1190/geo2011-0237.1
• Publication Date: 2012-04-05T18:44:59Z
• Authors: Kerry Key
• Keywords: Quadrature (astronomy); Hankel transform; Convolution (computer science)

The fast Hankel transform (FHT) implemented with digital filters has been the algorithm of choice in EM geophysics for a few decades. However, other disciplines have predominantly relied on methods that break up integral into sum partial integrals are each evaluated quadrature. convergence sums is then accelerated through nonlinear sequence transformation. While such method was proposed nearly three decades ago, it demonstrated to be much slower than FHT. This work revisits this problem by presenting new named quadrature-with-extrapolation (QWE). QWE recasts quadrature form conceptually similar FHT approach using fixed-point rule. efficiently Shanks transformation computed Wynn’s [Formula: see text] algorithm. A Matlab implementation compared accuracy and speed suite relevant modeling problems including frequency-domain controlled-source EM, time-domain large-loop magnetic source problem. Surprisingly, faster all problems. when needs at many offsets lagged convolution variant applicable, significantly method. For divergent as those encountered large loop problem, can provide an accurate answer fails.