Sanyi Yuan

Effect of inaccurate wavelet phase on prestack waveform inversion

Wavelets are critical to inversion methods. Incorrect phase estimation will affect the objective function and cause convergence to local minima, and thus produce biased or incorrect results. Based on two simple models and ignoring all other factors, we studied the variation of the wavelet phase as a function of frequency and its effect on the prestack waveform inversion. Numerical experiments show that an incorrect phase may result in large deviations from the real solution, even if there is a high similarity between the model and real wavelets. The precision of the inversion slightly improves by using the constant-phase rotation; however, the effect of phase inaccuracy is not eliminated, which limits the precision of prestack inversion.

The influence of errors in the source wavelet on inversion-based surface-related multiple attenuation

We investigate the influence of source wavelet errors on inversion-based surface-related multiple attenuation, in order to address how the inverted primary impulse response, estimated primaries and predicted multiples are affected by the estimated wavelet. In theory, errors in estimated wavelet can lead to errors in the upgoing waves. Because of smoothness and band-limitedness characteristics of the estimated wavelet, errors in the upgoing waves are usually not white and random. Theoretical analysis and two synthetic examples demonstrate that (1) when the overall amplitude scalar of the estimated wavelet is under-estimated, the inversion of the primary impulse response suffers from instability which will distort the estimation of primaries, and (2) when wavelet is over-estimated, the estimated primaries will simply mimic the recorded upgoing waves. Nevertheless, the quality of the estimated primaries in the region above the first-order water-bottom multiples is independent of the estimated wavelet. Synthetic results illustrate that inversion-based surface-related multiple attenuation with a known wavelet is stable, since slight inaccuracy in amplitude spectrum and/or phase spectrum of the given wavelet or the corresponding upgoing waves will not lead to considerable deviation in the waveforms of the inverted results from those of the references. Furthermore, shot-to-shot wavelet variations, with maximum amplitude difference of 5% and maximum phase difference of 10 degrees, create just slight artifacts in both the inverted primary impulse response and estimated primaries. Moreover, the sensitivity test of estimation of primaries by sparse inversion method involving wavelet estimation shows that this method can stably and alternately update the wavelet and the primary impulse response, however, different choices of the initial wavelet can lead to different final inverted results. This article is protected by copyright. All rights reserved

A Fast Hybrid Algorithm For Spectral Inversion

Summary A matrix equation of spectral inversion was derived, which is essentially a simultaneous inversion of nonlinear problem aiming at layer positions and linear problem aiming at reflection coefficients. If linearization inversion techniques are used to invert these parameters, the ultimate solution is heavily dependent on the choice of initial model. If global inversion techniques are used, not only is the accuracy low, but also the convergence speed is slow. In view of these defects, a fast hybrid algorithm for spectral inversion was proposed. As to reflection coefficients, generalized inverse method, which makes the parameters need searching globally reduced by half, was adopted. By doing this, inversion speed can be improved greatly. Meanwhile, Particle Swarm Optimization (PSO) with constriction factor was adopted to globally invert layer positions for the purpose that the probability of converging to global solution can be improved. In this process, if particles hardly update to the vicinity of global solution as iteration time increases, random scattering was conducted. On the basis of best-so-far layer positions and reflection coefficients, Levenberg-Marquardt (L-M) algorithm was followed so as to make the accuracy further higher. The model results validated the fast hybrid algorithm’s feasibility and efficiency. Compared with pure PSO and pure L-M method, it has the attributes of faster convergence speed as well as higher accuracy.

Study on uncertainty of inversion and resolution limit in the presence of noise

This study analyzed the uncertainty of inversion and the resolution limit in the presence of noise by means of statistical experiments. The exhaustive method is adopted to obtain the global optimal solution in each experiment. We found that even with small level of noise, solutions fluctuate in a large range for the thin bed. The distribution of solutions in the presence of noise is closely related to the spread of the cost function in the absence of noise. As a result, the area of a certain neighborhood around the true solution on the spread of the cost function in the absence of noise is used to evaluate the uncertainty of inversion and the resolution limit in the presence of noise. In the case that the SNR (signal-to-noise ratio) is 5 in this study, solutions focus around the true solution with a very small uncertainty only when the bed thickness is greater than the reciprocal of the double predominant frequency of the convoluting wavelet.