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    黏声介质整数阶微分算子逆时偏移成像方法研究与应用

    Research and application of reverse time migration using integer-order differential operator for viscoacoustic media

    • 摘要: 地震波在黏声介质中传播时不仅会发生振幅能量的衰减,还会造成相位的畸变,影响偏移能量聚焦的同时也会降低成像分辨率。目前,黏声介质逆时偏移算法主要基于分数阶微分方程进行求解,通过在频率−波数域将振幅衰减部分与相位频散部分解耦,从而在补偿振幅的同时校正相位。常规方法通常采用伪谱法进行数值计算,在三维情况下其计算效率难以满足实际数据大规模应用的需求。为此,基于广义标准线性体模型,在一定频率范围内对Q值进行多参数高精度表征,实现了整数阶微分算子的求解。本方法实现过程中采用高阶有限差分法,具有易于灵活地进行计算区域分解,又可借助GPU加速计算的优势,兼顾了成像效果与计算效率。理论模型测试与实际数据的应用结果表明,该方法在时空域实现了黏声介质逆时偏移成像,实现了振幅能量补偿和相位校正,提升了成像精度与分辨率,具有在实际数据中工业化规模应用的潜力。

       

      Abstract: Seismic wave propagation in viscoacoustic media results in amplitude attenuation and phase distortion, which degrade energy focusing and final resolution of imaging. Current reverse time migration (RTM) for viscoacoustic media is predominantly based on fractional-order differential equations. These approaches operate in the frequency-wavenumber domain to decouple amplitude attenuation from phase dispersion, thereby compensating for amplitude loss while correcting phase distortion. The pseudospectral method is routinely employed for numerical computation; however, its efficiency in a 3D setting is insufficient for field data application. To address this limitation, this paper adopts the generalized standard linear solid (GSLS) model to achieve a multi-parameter, high-accuracy characterization of the quality factor (Q) within a defined frequency range and thereby enable the implementation using an integer-order differential operator. The computation is performed using a high-order finite-difference scheme, which offers flexibility in computational domain decomposition and is well-suited for GPU acceleration, thereby achieving an effective balance between imaging quality and computational efficiency. Application to synthetic and field data demonstrates that this method successfully implements viscoacoustic RTM in the time-space domain with enhanced imaging accuracy and resolution via effective amplitude compensation and phase correction. The proposed method exhibits the capability for industrial-scale application to field data.

       

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