﻿ 横纵向组合的卡尔曼地震资料迭代滤波方法
 石油地球物理勘探  2021, Vol. 56 Issue (3): 468-475  DOI: 10.13810/j.cnki.issn.1000-7210.2021.03.005 0
 文章快速检索 高级检索

### 引用本文

CHEN Gang, QI Hongyan, LI Wei, ZHANG Rong, XIAN Chenggang, WANG Zhenlin. A Kalman seismic iterative filtering method based on lateral and vertical combination. Oil Geophysical Prospecting, 2021, 56(3): 468-475. DOI: 10.13810/j.cnki.issn.1000-7210.2021.03.005.

### 文章历史

① 中国石油大学(北京)非常规油气科学技术研究院, 北京 102249;
② 中国石油新疆油田分公司勘探开发研究院, 新疆克拉玛依 834000

A Kalman seismic iterative filtering method based on lateral and vertical combination
CHEN Gang①② , QI Hongyan , LI Wei , ZHANG Rong , XIAN Chenggang , WANG Zhenlin①②
① Unconventional Oil and Gas Science and Technology Research Institute, China University of Petroleum(Beijing), Beijing 102249, China;
② Research Institute of Exploration and Development, PetroChina Xinjiang Oilfield Company, Karamay, Xinjiang 834000, China
Abstract: Low signal-to-noise ratio and lateral continuity of seismic data result in multiple solutions of horizon tracking and fault characterization in seismic interpretation. To improve the lateral continuity and signal to noise ratio of seismic data, this paper puts forward an effective Kalman seismic filtering method based on lateral and vertical combination. This method proposes an alternate iterative optimization model in space and time and obtains a formula of lateral and vertical combination for filtering seismic data. Specifically, 4N times of modified lateral Kalman seismic filtering is firstly performed in the seismic trace direction, then N times of modified vertical Kalman seismic filtering is performed in the time direction. and finally, multiple rounds of combined filtering are performed based on the ratio of lateral and vertical filtering times. Compared with smooth filtering and lateral or vertical kalman filter, our method can greatly improve the signal-to-noise ratio and lateral continuity of seismic data. Numerical test and a field data example have proved that our method is feasible and effective.
Keywords: Kalman filtering    lateral continuity    signal-to-noise ratio    lateral and vertical combination
0 引言

1 方法原理 1.1 横向卡尔曼地震滤波

 $\mathit{\boldsymbol{X}}_k^{\rm{s}} = {\mathit{\boldsymbol{A}}_k}\left( {{\mathit{\boldsymbol{X}}_{k - 1}} + {\mathit{\boldsymbol{X}}_{k + 1}}} \right) + {\mathit{\boldsymbol{W}}_k}$ (1)

 $\mathit{\boldsymbol{X}}_k^{\rm{m}} = {\mathit{\boldsymbol{X}}_k} + {\mathit{\boldsymbol{V}}_k}$ (2)

 ${\mathit{\boldsymbol{P}}_k} = {\rm{ }}{\mathit{\boldsymbol{A}}_k}{\mathit{\boldsymbol{P}}_{k - 1}}\mathit{\boldsymbol{A}}_k^{\rm{T}}k + {\mathit{\boldsymbol{R}}_k}$ (3)

 $\mathit{\boldsymbol{X}}_k^{{\rm{op}}} = \mathit{\boldsymbol{X}}_k^{\rm{s}} + {\mathit{\boldsymbol{g}}_k}(\mathit{\boldsymbol{X}}_k^{\rm{m}} - \mathit{\boldsymbol{X}}_k^{\rm{s}})$ (4)

 ${\mathit{\boldsymbol{g}}_k} = \frac{{{\mathit{\boldsymbol{P}}_k}\mathit{\boldsymbol{A}}_k^{\rm{T}}}}{{{\mathit{\boldsymbol{A}}_k}{\mathit{\boldsymbol{P}}_k}\mathit{\boldsymbol{A}}_k^{\rm{T}} + {\mathit{\boldsymbol{Q}}_k}}}$ (5)

 ${\mathit{\boldsymbol{P}}_k} = {\mathit{\boldsymbol{P}}_k}(1 - {\mathit{\boldsymbol{g}}_k})$ (6)

 ${\mathit{\boldsymbol{R}}_k} = {\rm{std}}(\mathit{\boldsymbol{X}}_k^{\rm{m}} - \mathit{\boldsymbol{X}}_k^{\rm{s}})$ (7)
 ${\mathit{\boldsymbol{Q}}_k} = {\mathit{\boldsymbol{A}}_k}\left[ {{\rm{std}}\left( {{\mathit{\boldsymbol{X}}_k} - {\mathit{\boldsymbol{X}}_{k - 1}}} \right) + {\rm{std}}\left( {{\mathit{\boldsymbol{X}}_{k + 1}} - {\mathit{\boldsymbol{X}}_k}} \right)} \right]$ (8)

1.2 纵向卡尔曼地震滤波

 $\mathit{\boldsymbol{X}}_t^{\rm{s}} = {\mathit{\boldsymbol{A}}_t}\left( {{\mathit{\boldsymbol{X}}_{t - 1}} + {\mathit{\boldsymbol{X}}_{t + 1}}} \right) + {\mathit{\boldsymbol{W}}_t}$ (9)

 $\mathit{\boldsymbol{X}}_t^{\rm{m}} = {\mathit{\boldsymbol{X}}_t} + {\mathit{\boldsymbol{V}}_t}$ (10)

 ${\mathit{\boldsymbol{P}}_t} = {\rm{ }}{\mathit{\boldsymbol{A}}_t}{\mathit{\boldsymbol{P}}_{t - 1}}\mathit{\boldsymbol{A}}_t^{\rm{T}} + {\mathit{\boldsymbol{R}}_t}$ (11)

 $\mathit{\boldsymbol{X}}_t^{{\rm{op}}} = \mathit{\boldsymbol{X}}_t^{\rm{s}} + {\mathit{\boldsymbol{g}}_t}(\mathit{\boldsymbol{X}}_t^{\rm{m}} - \mathit{\boldsymbol{X}}_t^{\rm{s}})$ (12)

 ${\mathit{\boldsymbol{g}}_t} = \frac{{{\mathit{\boldsymbol{P}}_t}\mathit{\boldsymbol{A}}_t^{\rm{T}}}}{{{\mathit{\boldsymbol{A}}_t}{\mathit{\boldsymbol{P}}_t}\mathit{\boldsymbol{A}}_t^{\rm{T}} + {\mathit{\boldsymbol{Q}}_t}}}$ (13)

 ${\mathit{\boldsymbol{P}}_t} = {\mathit{\boldsymbol{P}}_t}(1 - {\mathit{\boldsymbol{g}}_t})$ (14)

 ${\mathit{\boldsymbol{R}}_t} = {\rm{std}}(\mathit{\boldsymbol{X}}_t^{\rm{m}} - \mathit{\boldsymbol{X}}_t^{\rm{s}})$ (15)
 ${\mathit{\boldsymbol{Q}}_t} = {\mathit{\boldsymbol{A}}_t}[{\rm{std}}({\mathit{\boldsymbol{X}}_t} - {\mathit{\boldsymbol{X}}_{t - 1}}) + {\rm{std}}({\mathit{\boldsymbol{X}}_{t + 1}} - {\mathit{\boldsymbol{X}}_t})]$ (16)
1.3 横纵向组合的卡尔曼地震资料滤波

2 方法测试 2.1 模型测试

 图 1 Marmousi2模型(a)及选取的(绿框)测试部分(b)[1]

 图 2 原始合成(a)及加入1∶2高斯随机噪声(b)剖面

 图 3 二维中值滤波1次(a)和100次(b)后剖面对比

 图 4 单一横向卡尔曼滤波100次(a)和200次(b)后剖面对比

 图 5 单一纵向卡尔曼滤波25次(a)和50次(b)后剖面对比

 图 6 横纵向同时滤波50次(a)和100次(b)后剖面对比
2.2 实际资料测试

 图 7 实际原始地震剖面(a)及本文方法滤波后剖面(b)

 图 8 实际原始地震剖面(a)及本文方法滤波后剖面(b) 左：W1井旁道；中：井数据合成道；右左图与中图的相关

 图 9 本文方法滤波前、后目的层曲率属性平面图

 图 10 本文方法滤波前(a)、后(b)频谱对比图
3 结论

(1) 对地震资料做横向卡尔曼滤波，所取得的信噪比和连续性的改善远优于单一纵向滤波；

(2) 经过测试发现，基于卡尔曼滤波原理的地震资料横、纵向以迭代循环滤波次数4∶1的形式进行横纵向组合滤波，在改善地震资料的信噪比和连续性的效果和效率两方面都优于单一横向或纵向及二维中值滤波；

(3) 实际资料测试表明，本文方法能显著提高地震资料信噪比及同相轴的连续性，且不会造成高频成分缺失，可有效确保构造解释精度。