The full waveform inversion (FWI)method utilizes kinematic and dynamic information of pre-stack seismic data to rebuild underground velocity structure.However, the large amount of calculation is a bottleneck problem for its development.Therefore,Researchers proposed the techniques of the source-encoding in order to reduce calculation amount,but this method would introduce random crosstalk in model updates.The paper uses decreasing random shot subsampling method to invert full waveform effectively in the case of guaranteeing the calculation accuracy.The paper applied the method into frequency-domain full waveform inversion of 2D viscous acoustic wave equation,and research the type of random shot sampling method in the frequency domain.We totally use eight gradually increased frequencies in FWI process,and apply overthrust model to demonstrate the validity of such random shot sampling method.Through the experiment,we can see that the fitting error between inversion results based on decreasing random shot subsampling method and the actual overthrust model is 0.065 65,and the fitting error between inversion results based on all the shots and the actual overthrust model is 0.064 64.Namely the inversion results of the two methods have little difference.However, the calculated time reduces from 740 min to 291.2 min.Namely the computational efficiency increased 2.54 times.In order to better determine the validity of the method,we apply it to Marmousi model.The fitting error between inversion results based on decreasing random shot subsampling method and the actual Marmousi model is 0.080 12,and the fitting error between inversion results based on all the shots and the actual Marmousi model is 0.078 97.Namely the inversion results of the two methods have little difference.However, the calculated time reduces from 1 218.9 min to 274.4 min.Namely the computational efficiency increased 4.44 times.In conclusion,under the condition of the inversion accuracy,the full waveform inversion based on the decreasing random shot sampling method in frequency domain greatly reduces the amount of calculation.Namely it has irreplaceable computing advantage.Therefore there is no introduction of random crosstalk noise.%全波形反演方法利用叠前地震波场的运动学和动力学信息重建地下速度结构,具有揭示复杂地质背景下构造与岩性细节信息的潜力.然而,巨大的计算量是阻碍其发展的一个瓶颈问题.为此,研究者们提出了震源编码技术来减少计算量,但是此方法在模型更新过程中会引进随机串扰噪声,降低反演结果准确性.所以,在保证计算精度的情况下,本文提出了采用逐减随机震源采样的方法来高效计算全波形反演问题.笔者将此方法应用于频率域二维黏滞声波波动方程全波形反演,开始了在频率域进行随机震源采样类方法的研究,计算过程中共使用了依次增大的8个频率段；并应用 Overthrust模型来验证此类随机震源采样法的正确性.实验结果表明：基于逐减随机震源采样法的反演结果与实际 Overthrust 模型的拟合误差为0．06565,而应用基于全部震源的全波形反演方法得到的反演结果与实际Overthrust模型的拟合误差为0．06464,两者差别不大；但计算用时由740 min减少到291．2 min,即计算效率提高了2．54倍.为了更好地确定方法的有效性,将其应用于 Marmousi模型进行试算.模型试算结果表明：基于逐减随机震源和基于全部震源得到的反演结果与实际 Marmousi模型的拟合误差分别为0．08012和0．07897,相差不大；但计算用时由1218．9 min减少到274．4 min,计算效率提高了4．44倍.综上,在保证反演精度的情况下,基于逐减随机震源采样法的频率域全波形反演方法大大减少了计算量,具有不可替代的计算优势,并且没有引进随机串扰噪声.
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