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    基于双差走时伴随状态法的时移地震层析成像方法研究

    Time-lapse seismic traveltime tomography using a double-difference adjoint-state method

    • 摘要: 时移地震走时层析成像是刻画地下介质动态变化的重要方法,但传统基于绝对走时差(absolute-difference, AD)的伴随状态法对震源时刻误差和近地表静校正误差较为敏感,在复杂近地表条件下容易将共模走时偏差错误映射为深部速度扰动,从而影响微弱时移异常的恢复效果。为此,研究聚焦复杂近地表静校正误差背景下的时移走时层析成像,引入基于双差走时(double-difference, DD)的伴随状态法,通过构造接收点对之间的相对走时残差,在数据层面削弱系统性共模误差对反演梯度和模型更新的影响。首先,通过两组简单模型实验对比分析了AD方法与DD方法在系统性走时扰动条件下的梯度稳定性。随后,围绕时移成像问题,分别构建理想近地表模型和包含空气层、起伏地表及近地表低速层的复杂模型,在连续反演和分别反演两种时移流程下,对比评估两种方法对时移速度异常的恢复能力。结果表明:在理想条件下,两种方法均能够较好恢复时移异常;而在复杂近地表条件下,DD方法表现出更稳定的梯度特征和更优的异常体恢复效果。定量分析显示,在所设计的静校正误差背景下,DD方法在异常体区域内的均方根误差相较AD方法降低35% ~ 40%。此外,基于国内油田实际资料的单期走时层析测试表明,在相同反演设置下,与AD方法相比,DD方法对地下局部速度剧烈变化区域的刻画更清晰,分辨能力更强。研究结果表明,DD伴随状态法在复杂近地表静校正误差背景下具有较好的抗误差能力和时移成像稳健性,可为复杂地表条件下的时移走时层析成像提供一种可行的方法。

       

      Abstract: Time-lapse seismic traveltime tomography is an important approach for characterizing subsurface changes. However, the conventional adjoint-state method based on absolute-difference (AD) traveltime residuals is sensitive to source-origin time errors and near-surface statics. Under complex near-surface conditions, such common-mode traveltime perturbations can be easily mis-mapped into deep velocity anomalies, thereby compromising the recovery of weak time-lapse signals. To address this issue, this study investigates time-lapse traveltime tomography under complex near-surface statics errors and introduces a double-difference (DD) adjoint-state method. By constructing relative traveltime residuals between receiver pairs, the proposed method systematically reduces common-mode errors at the data level and thereby mitigates their influence on inversion gradients and model updates. First, two simple numerical experiments are designed to compare the gradient stability of the AD and DD methods under systematic traveltime perturbations. Then, for the time-lapse imaging problem, two models are considered: an ideal near-surface model and a complex model containing an air layer, undulating topography, and a near-surface low-velocity layer. Under both sequential and independent inversion schemes, the two methods are evaluated in terms of their ability to recover time-lapse velocity anomalies. The results show that both methods satisfactorily recover the time-lapse anomalies under ideal conditions. Under complex near-surface conditions, however, the DD method achieves more stable gradients and better anomaly recovery. Quantitative analysis indicates that, under the designed statics-error scenarios, the DD method reduces the RMSE within the anomaly region by approximately 35%–40% compared with the AD method. In addition, a single-survey field data test shows that, under the same inversion settings, the DD method provides clearer imaging and higher resolution in areas with drastic local velocity variations than the AD method. These results suggest that the DD adjoint-state method exhibits strong robustness against statics errors under complex near-surface conditions and provides a feasible approach for time-lapse traveltime tomography under complex surface conditions.

       

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