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Multi-trace nonstationary sparse inversion with structural constraints

Cheng Liang, Wang Shangxu, Li Shengjun, Ji Yongzhen

Acta Geophysica

2020

Vol. 68, no. 3

675--685

The recorded seismic signals are attenuated and spatially correlated due to their propagation through an elastic earth and the sedimentary rule of strata. This attenuation phenomenon is quantifed by means of the earth quality factor (Q) or the attenuation factor (1∕Q). Nowadays, the related Q-compensation and multi-trace inversion for the seismic data are two challenging problems when used for enhancing the temporal resolution and preserving the spatial continuity. Separately estimating Q and refectivity are difcult and produce the uncertainty or ill-condition problems. To overcome these limitations, we have developed a multi-trace nonstationary sparse inversion with structural constraint. Using prior dipping-angle information and refectivity sparsity property, the proposed method simultaneously estimates equivalent-Q and refectivity with structural constraint. Constructed by the source wavelet and diferent scanned equivalent-Q, a series of time-varying (nonstationary) wavelet matrices are provided for the forward-modeling schemes and the corresponding inversions. When the Q-model is infnitely close to the true attenuation mechanism, the corresponding inverted refectivity is comparatively sparse and quantifed as maximum sparsity or minimum sparse representation. A sparse representation function, such as l0.1-norm, is used for sparsity measurement of the inverted refectivity corresponding to each scanned Q. Through optimizing these sparse representation values, a suitable equivalent-Q, as well as the corresponding inverted refectivity with structural preservation and Q-attenuation, is determined. The synthetic and feld examples both confrmed a substantial improvement on seismic records, especially for Q-estimation, structure preservation and Q-compensation.

The influence of the frequency‑dependent spherical‑wave effect on the near‑surface attenuation estimation

Ji Yongzhen, Wang Shangxu, Yuan Sanyi, Yan Binpeng

Acta Geophysica

2019

Vol. 67, no. 2

577--587

The knowledge of Q is desirable for improving seismic resolution, facilitating amplitude analysis and seismic interpretation. The most commonly used methods for Q estimation are the frequency-spectrum-based methods. Generally, these methods are based on the plane wave theory assuming that the transmission/reflection loss is frequency independent. This assumption is reasonable in the far-field situation and makes the transmission/reflection coefficient irrelevant with the Q estimation result. However, in the near-surface context, this assumption is invalid because the seismic wave propagates in the form of spherical wave in the real seismic surveys and the spherical-wave transmission/reflection coefficient is frequency dependent. As a result, deviation will exist. In this paper, the influence of the spherical-wave effect on the Q estimation in the near-surface context was proved in both synthetic data and field data for the first time, and it was found that the deviation due to the sphericalwave effect is of order comparable to the intrinsic attenuation. The compensation method based on the forward modeling is then proposed to correct this deviation, and the effectiveness of the proposed method is proved by the reasonable estimated results of both synthetic data and field data example. These results raise caution for the interpretation of the extracted Q in the near-surface context if they do not account for the spherical-wave effect and point to the necessity of incorporating a frequency-dependent term in the frequency-spectrum-based method when applied to the Q estimation in the near surface.