Length分形维算法拾取地震波初至

Length fractal dimension method for picking seismic first break.

本文从理论上分析了 Hausdorff分形维和 Divider分形维算法 ,采用拓扑映射工具 ,提出了 Hausdorff分形维和 Divider分形维的统一简化算法—— L ength分形维算法。该算法的实现过程为 :1在地震道上确定一个窗口宽度 ,并计算窗口内地震道采样序列的分形维 ,将该值标记在工作窗右边界采样点上 ;2使窗口沿地震道以一个采样间隔步长向前移动 ,并计算每个窗口的分形维 ,从而得到一条分形维变化轨线 ;3随着初至逐渐进入窗口 ,局部轨线呈现清晰的“V”字形状 ,把“V”字形轨线左支顶端点的局部进行区域放大 ,第一个突降点即为初至开始进入工作窗的标志 ,亦即对应的初至到达。理论分析和实际资料试算表明 ,L ength分形维方法具有计算量小、无须设置度量 (覆盖 )尺度、可消除坐标标度的不协调性、对地震波初至反映敏感、窗口宽度对计算结果的稳定性和精度影响较小、抗噪能力较强等优点 ,而且在计算分形维数时对初至波的波型没有限定。

The paper theoretically analyzed Hausdorff fractal dimension and Divider fractal dimension algorithms and presented uniform simplified algorithm for Hausdorff fractal dimension and Divider fractal dimension algorithms—Length fractal dimension algorithm.The realizations of the method are follows:①defining a window width on a seismic trace,computing fractal dimension of sampled seismic data sequence within the window and labeling the value at the sample of right edge of working window;②moving the window forward along the seismic trace with step-length of one sample interval and computing fractal dimension at each window,then resulted in one variance track of fractal dimension;③the local track appeals a clear “V” form along with first break gradually enters the window,zooming regionally the local apex in left branch of “V” track,the first rapidly-dropping point is symbol of first break entering window,which corresponds the arrival of first break.The theoretical analysis and practical test showed that the Length fractal dimension method characterized by small computational efforts,without setting measure (fold) scale,removing inconsistent coordinate scale,sensitive to first break of seismic wave,small influence of window width on stability and precision of computed results and strong anti-noise ability,meanwhile,there is no limit to wave mode of first break when computing fractal dimension.