正演子波响应特征及逆时成像分析

采用一阶形式和二阶形式的地震波动方程，开展了二维地震子波正演响应理论研究，并以二维均匀介质速度模型为例，将不同相位的 Ricker子波作为输入子波，进行了数值模拟。结果表明，一阶形式的子波响应与输入子波波形差异较大，且存在较大的相位移，同时，其比值 谱与频率呈线性正比关系；而二阶形式的子波响应与输入子波波形差异较小，相位移较小，其比值谱几乎不随频率变化。因此二阶形式的波动 方程具有更好的保形特征，可以实现任意期望子波波形的正演数值模拟。在上述研究的基础上，讨论了逆时子波波场响应特征，并以一维层状 介质反射系数模型为例，进行了一阶形式和二阶形式波动方程的相关型和反射率型逆时偏移成像试验，结果表明，当震源波场与接收波场的子 波波形相一致时，低频逆时噪声能量最弱，成像效果最佳；反之，成像剖面中的反射界面与真实的地层界面位置会存在时差，同时，低频逆时 噪声能量较强。因此，保持子波波形的一致性是实现高精度相关型、反射率型逆时偏移成像的前提。

Seismic wavelet response characteristic and reverse-time migration analysis

Taking 2D homogeneous medium velocity model as example,by using the first-order and second-order wave equation with input wavelet of different phase Ricker wavelet,we carried out numerical simulation.The computation results show that there is a large difference between the wave field response of the first-order wave equation and the input wavelet waveform,as well as the phase shift.Meanwhile,the ratio amplitude spectrum has linear proportional relationship with frequency.However,the wave field response characteristics of the second-order wave equation and the input wavelet waveform are almost the same with small phase shift,and the ratio amplitude spectrum is almost not changed with the frequency.Therefore,the second-order wave equation has the property of shape preservation,and can achieve forward modeling with expected wavelet form.Based on the above analysis,the response characteristic of inverse time wavefield was discussed,then,the correlation type and reflectivity type reverse-time migration on the 1D layered model was carried out.The results show that if the wavelet waveform of the source wave field and receive wave field are consistent,the image results are the best with lowest low frequency reverse-time noise;otherwise,there is a time shift between the reflection interface on the imaging section and actual formation interface,and the energy of the low frequency reverse-time noise is stronger.Therefore,maintaining the consistence of wavelet waveform is the prerequisite of the high-precision correlation and reflectivity reverse-time migration.