Phase inversion deconvolution for long and short period multiples attenuationl¹

A new approach to deconvolution has been developed to improve the attenuation of multiple energy. This approach to deconvolution is unique in that it not only eliminates the usual assumptions of a minimum phase lag wavelet and a random distribution of impulses, but also overcomes the noise limitation of the homomorphic deconvolution and its inherent instability to phase computation.

We attempt to analyse the continuous alteration of the acoustic waveform during the propagation through a linear system. Based on the results of this analysis, the surface‐related measurements are described as a convolution of the impulse response of the system with the non‐stationary forward wavelet which includes all multiple terms generated within the system.

The amplitude spectrum of the forward wavelet is recovered from the amplitude spectrum of the recorded signal, using the difference between the rate of decay of the source wavelet and the duration of the measurement.

The phase spectrum of the forward wavelet is estimated using the Hilbert transform and the fact that the mixed phase lag wavelet can be presented as a convolution of the minimum and maximum phase lag wavelets.

The multiples are discriminated from primaries by comparison of the phase spectrum of the seismic signal and the inverse of the forward wavelet. Therefore, the technique is called phase inversion deconvolution (PID). This approach requires no velocity information in order to recognize and attenuate multiple energy. Therefore, primary energy is recovered in the near‐offset region where the velocity differential between primary and multiple energies is very small.