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.