Abstract
The computation of electromagnetic (EM) fields for 1-D layered earth model requires evaluation of Hankel transform. In this paper we propose a stable algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets arising in seismology. We have projected an approach depending on separating the integrand tf(t)J ν (pt) into two components; the slowly varying components tf(t) and the rapidly oscillating component J ν (pt). Then either tf(t) is expanded into wavelet series using wavelets orthonormal basis and truncating the series at an optimal level or approximating tf(t) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed wavelet method applied on three test functions indicate that the approach is easy to implement and computationally very attractive. We have supported a new efficient and stable technique based on compactly supported orthonormal wavelet bases.
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Irfan, N., Siddiqi, A.H. (2015). Application of Wavelets in Numerical Evaluation of Hankel Transform Arising in Seismology. In: Siddiqi, A., Manchanda, P., Bhardwaj, R. (eds) Mathematical Models, Methods and Applications. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-287-973-8_17
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