Trace interpolation and elevation statics by conjugate gradients

Marcus R. Wilson, Robert James Ferguson

We present a conjugate-gradient based inversion to correct for surface statics and irregular trace spacing. The algorithm returns a rough solution to the extrapolated wavefield with complexity O(n2.5). Convergence is fast in the wavelike region, and very slow in the evanescent region. Decimated traces are reconstructed even though no smoothing operator is applied, but recovered wavefields do not approach known source wavefields at low frequencies. We suggest that speed and accuracy of inversion by conjugate gradients can be improved through careful smoothing, or separate treatment of the wavelike and evanescent regions. Computing operators by series expansion for fast application during conjugate gradient iterations is suggested to optimize runtime.