Sine-Cosine Wavelets Approach in Numerical Evaluation of Hankel Transform for Seismology

•Sine–Cosine wavelet method has fast response and high precision.•Sine–Cosine wavelet is proposed for numerical evaluation of the Hankel transform.•In few examples our method is better than earlier approaches.•With the help of figures different results are shown.•Accuracy of proposed method is illustrated by computing absolute error graphically.

The computation of electromagnetic (EM) fields for 1-Dlayered 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 Sine-Cosine wavelets arising in seismology. We have projected an approach depending on separating the integrand rf(r)Jν(pr) into two components; the slowly varying components rf(r) and the rapidly oscillating component Jν(pr). Then either rf(r) is expanded into wavelet series using Sine-Cosine wavelets orthonormal basis and truncating the series at an optimal level or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed Sine-Cosine wavelet method applied on 5 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.