二维随机介质等效裂缝建模及波动方程正演模拟

针对裂缝预测问题,可以通过建立二维随机介质小尺度等效裂缝模型研究碳酸盐岩地层中裂缝的地震响应特征,从而为碳酸盐岩地层裂缝地震预测提供依据。采用指数型椭圆自相关函数随机介质模型建立等效裂缝模型(x、z方向的自相关长度分别为0.5m,1~15m),对其进行波动方程正演模拟得到包含绕射波的零偏移距地震剖面,利用叠后逆时偏移方法分析等效裂缝模型的地震响应特征。当纵向分辨率足够高时(主频100Hz),纵向3m规模的等效裂缝在零偏移距地震剖面上有响应,呈现“扁圆”状杂乱反射特征;当纵向分辨率较小时(主频30Hz),横向累计40m、纵向10m规模等效裂缝在零偏移距地震剖面上有响应,呈现“短轴”状杂乱地震反射特征。裂缝密度大小与叠加振幅呈正相关关系。这些认识对指导包括小规模缝洞储层在内的裂缝型储层地震预测具有重要的意义。

Building an equivalent fracture model and performing forward modeling of wave equations in a 2D random medium

To investigate the characteristics of the seismic response of equivalent fractures in carbonate formations,small-scale,equivalent fracture models in a two-dimensional(2D)random medium can be utilized to perform forward modeling of the wave equations.In this study,a 2D small-scale fracture model(with autocorrelation lengths in the x and z directions of 0.5m and 1~15m,respectively)was generated using a random medium model with an exponential elliptic autocorrelation function.Forward modeling of the wave equations was carried out to obtain the stacked seismic profile containing the diffracted waves.Then,post-stack reverse time migration was conducted to analyze the seismic response of the equivalent fracture model.When the vertical resolution of the seismic data was sufficient(e.g.,when the main frequency was 100Hz),3m long equivalent vertical cracks in the model could be imaged.These cracks exhibited round-dot-shaped cluttered reflections.Conversely,when the vertical resolution of the seismic data was low(e.g.,when the main frequency was 30Hz),equivalent cracks,40m long in horizontal direction and 10m long in vertical direction could be imaged in the model.These cracks exhibited short-axis-shaped cluttered reflections.It was also found that the crack density is positively correlated with the stack amplitude.These research results are significant for improving the prediction of fractured reservoirs through seismic imaging.