The Selection of Fitting Curve in Time-Depth Transformation of Deep-Seated Strata and Crust
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摘要: 对珠江口盆地白云凹陷多口探井的数据分别用多项式和幂函数进行了时深关系拟合, 并对结果进行了分析讨论.对于深度大于钻井控制范围的地层和地壳的时深转换, 常用的三次多项式时深关系式只有三次项系数为负和二次项系数为正时才可用, 但在深部必然产生速度倒转的问题, 因此在理论上就不适用于深部; 二次多项式时深关系式虽然不会导致速度倒转, 但其速度向下匀速增大, 也不符合速度向下减速增大的规律, 常常导致深部速度超高.乘幂在1和2之间的幂函数拟合式D=atb+c有可能同时近似浅部和深部的时深关系, 是相对最优的关系式, 但也不是对每口井都能拟合出可用于全区和全部深度的时深关系.分区和分深度进行幂函数拟合是最理想的办法.针对区域性的时深转换, 可以分区对多口井进行幂函数拟合, 从中择优选用.Abstract: Polynomial and power functions have been used to fit the time-depth relation based on data from wells in the Baiyun sag, Pearl River Mouth basin, northern South China Sea.For the time-depth relation of the strata deeper than the termination depth of the wells, the 3rd-order polynomial function may be applicable only if the coefficient of its 3rd-oder term is negative and the coefficient of its 2nd-order term is positive.This function, however, is not applicable to the depth because it inevitably leads to the velocity inversion at depth.The fitting of 2nd-order polynomial function does not cause the velocity inversion, but the velocity increases linearly towards the depth, violating the natural law that the velocity increment decreases downwards in the Earth's strata and crust.The power function D=atb+c with 1 < b < 2 may approximate the time-depth relation for both shallow and deeper strata and crust without the problems encountered by using 3rd-and 2nd-order polynomial functions.It is not guaranteed, however, that for each well the fitted power function is suitable for the entire region and all the depths.For a regional time-depth conversion, the best practice is to divide the region and fit the power function for multiple wells, and then select the best functions for each sub-regions.
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Key words:
- time-depth transformation /
- deep-seated strata /
- Baiyun sag /
- Pearl River Mouth basin
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图 2 用二次多项式拟合时速关系的可适性图示
V为速度, 向下为正; t为时间, 向右为正; a、b、c均为正数.由于时间和速度都是正值, 其关系曲线只能在右下象限.可见只有(b) 中的粗灰线段才符合速度向深部增高且增量向深部减小的要求, 才能用于拟合时速关系
图 3 白云凹陷内部钻井数据的时深关系和时速关系拟合曲线
D代表深度; V代表速度(m·s-1); poly2代表二次多项式; power代表幂函数.为便于对比, 也表示出PY33-1-1数据的实测和幂函数拟合的时深和时速关系曲线
表 1 PY33-1-1井时深拟合数据
Table 1. Time-depth data fitted to well PY33-1-1
表 2 白云凹陷中心处Tg和莫霍面的时速拟合数据
Table 2. Fitted depths of Tg and Moho at the center of the Baiyun sag
表 3 白云凹陷内部钻井时深拟合数据
Table 3. Time-depth data fitted to the well inside the Baiyun sag
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Huang, C. J., Zhou, D., Chen, C. M., et al., 2005. Deep crustal structure of Baiyun sag, northern South China Sea revealed from deep seismic reflection profile. Chinese Science Bulletin, 50 (11): 1131-1138. doi: 10.1360/04wd0207 Kearey, P., Vine, F. J., 1990. Global tectonics. Blackwell Scientific Publications, London. Wang, Y. T., Chen, L., Wu, D. M., 2006. Velocity data analysis and its application to Zhongjiannan basin in South China Sea. J. Tropical Oceanography, 25 (5): 49-55 (in Chinese with English abstract). 黄春菊, 周蒂, 陈长民, 等, 2005. 深反射地震剖面所揭示的白云凹陷的深部地壳结构. 科学通报, 50 (10): 1024-1031. doi: 10.3321/j.issn:0023-074X.2005.10.014 王衍棠, 陈玲, 吴大明, 2006. 南海中建南盆地速度资料分析与应用. 热带海洋学报, 25 (5): 49-55. https://www.cnki.com.cn/Article/CJFDTOTAL-RDHY200605008.htm -
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