Reply to Comment on: 'Non-minimum-phase wavelet estimation using second-and third-order moments' by Wenkai Lu

摘要

We first wish to correct a mistake indicated by Dr Velis and Dr Sacchi. Equation (23) in the original paper should be m_4~b(τ_1, τ_2, τ_3) = a(τ_1, τ_2, τ_3)c_4~x(τ_1, τ_2, τ_3), (1) where c_4~x (τ_1, τ_2, τ_3) is the fourth-order cumulant of the seismic signal. Since the seismic signal is zero-mean, its cumulant is c_4~x(τ_1, τ_2, τ_3) = m_4~x(τ_1, τ_2, τ_3) - m_2~x(τ_1) -m_2~x(τ_3-τ_2)-m_2~x(τ_2)m_2~x(τ_3- τ_1)-m_2~x(τ_3)m_2~x(τ_2-τ_1). (2)