基于地层沉积反演的深时海平面变化曲线恢复方法

doi:10.13745/j.esf.sf.2022.2.64

摘要/Abstract

摘要：

目前常用的海平面曲线恢复方法主要是基于地层沉积的旋回性分析和同位素测量,受地层不完整性的影响较大,海平面变化恢复不够合理。本文基于全球海平面变化旋回与天文旋回、沉积旋回在时间周期上具有较好的多级旋回对应特征,提出了采用傅里叶变换多级正弦分解函数化海平面变化曲线,然后通过地层沉积反演求取函数化的全球海平面变化参数的方法。利用地层沉积模拟方法,求取了元坝地区长兴期的全球海平面曲线,与同时期的Haq曲线、Fischer方法获得的海平面变化曲线相比,具有更多的海平面变化信息,恢复的海平面变化更合理。傅里叶级数函数化海平面变化曲线不仅推动了海平面变化的定量化和函数化发展,还有利于用地层沉积反演求取海平面变化曲线。这种求取海平面变化的新思路,与传统的海平面变化恢复方法相比定量化程度高,对输入资料要求低,具有较好的适用性和更广的应用前景。

关键词: 地层沉积反演, 天文旋回, 傅里叶变换, 沉积正演模拟, 全球海平面变化

Abstract:

The commonly used sea-level curve recovery methods are mainly based on the cyclic analysis and isotopic measurement of stratigraphic sedimentation. These methods are greatly affected negatively by the incompleteness of stratigraphic data, resulting in unreasonable recovery results. In view of this, a global sea-level curve recovery method based on stratigraphic sedimentary inversion is proposed. Based on the fact that the global sea-level cycle has good corresponding relationships with astronomical and sedimentary cycles as multi-scale, multi-level cycles, this method uses trigonometric Fourier series expansion to transform the sea-level change curve, which can greatly smooth out the sea-level curve in stratigraphic sedimentary inversion. Only seven parameters are needed in the new method to characterize sea-level changes in the Haq sea-level curve, demonstrating its applicability. The global sea-level curve of the Changxing Period in the Yuanba area is obtained by stratigraphic sedimentary simulation, which yields more information on the sea-level change, and the recovered sea-level change is more reasonable compared to the Haq sea-level curve and the sea-level change curve of Fischer for the same period. Thus, Fourier series-functionalized sea-level change curve is useful not only in quantification and functionalization of sea-level change, but also in stratigraphic sedimentary inversion to obtain sea-level change curve. Compared with the traditional sea-level change recovery method, this new idea of measuring sea-level change has higher level of quantification, lower requirements for input data, and better applicability and wider application prospect. The application prospect is also discussed.

Key words: stratigraphic inverse modeling, astronomical cycle, Fourier transform, stratigraphic forward modeling, global sea-level change

中图分类号:

沈禄银, 潘仁芳, 段太忠, 刘彦锋, 李蒙, 廉培庆, 黄渊, 张德民. 基于地层沉积反演的深时海平面变化曲线恢复方法[J]. 地学前缘, 2023, 30(2): 109-121.

SHEN Luyin, PAN Renfang, DUAN Taizhong, LIU Yanfeng, LI Meng, LIAN Peiqing, HUANG Yuan, ZHANG Demin. Deep-time sea-level change curve recovery: A recovery method based on stratigraphic inverse modeling[J]. Earth Science Frontiers, 2023, 30(2): 109-121.

图/表 9

图1 傅里叶级数表达Haq曲线趋势图 a—傅里叶级数n=10时表达的Haq曲线趋势;b—用1个正弦表达Haq曲线的一级旋回趋势;c—用2个正弦表达Haq曲线的一、二级旋回趋势;d—用2个正弦分段表达Haq曲线的一、二级旋回趋势。

Fig.1 Trend of Haq curve expressed by Fourier series

表1 线性函数校正各级旋回的周期

Table 1 Cyclic periods corrected by linear function

k_n<0	k_n=0	k_n>0

图2 全球海平面变化及其沉积模拟理论模型

Fig.2 Global sea-level change and the sedimentary simulation model

图3 元坝气田I号礁带工区位置(据文献[26]修改)

Fig.3 Location of Reef Zone I of the Yuanba gas field. Modified after [26].

图4 沉积模拟输入参数——初始地形高程(左)和地形沉降速率(右)

Fig.4 Input parameters for sedimentary simulation. Left: Initial topography. Right: Topographic subsidence.

表2 反演参数设置及反演结果

Table 2 Inversion parameter setup and inversion results

	反演参数		不确定区间	最优值
海平面变化	基准值(A₀)		[0,100]	44.69
	二级旋回	振幅(A₂)	[40,80]	57.00
		周期(T₂)	[1 000,10 000]	5 346.6
		相位(φ₂)	[-1,1]	-0.37
	三级旋回	振幅(A₃)	[20,60]	33.5
		周期(T₃)	确定	111.9
		相位(φ₃)	确定	-0.5
	四级旋回	振幅(A₄)	[6,40]	16.69
		周期(T₄)	[10,55.95]	27.75
		相位(φ₄)	[-1,1]	0.48
	五级旋回	振幅(A₅)	[1,20]	6.28
		周期(T₅)	确定	10
		相位(φ₅)	[-1,1]	0.026
搬运	扩散系数(PDX)		[5 000,20 000]	11 785
搬运	对流系数(KDX)		[1,500]	316.1
产率	水深相关产率幅度(Aprod)		[2,6]	3.47
产率	动能产率系数(kE)		[0.5,1.5]	0.78

图5 反演系统及各个参数的收敛过程

Fig. 5 Convergence process of the inversion system and parameters

图6 观测数据及地层沉积反演结果对比

Fig.6 Comparison of observational data and sediment inversion simulation results

图7 长兴期不同海平面变化曲线对比 A— Haq全球海平面变化曲线(据文献[20]);B—地层沉积反演方法得到的海平面曲线;C— Fischer方法得到的海平面曲线(据文献[30])。

Fig.7 Comparison of sea-level change curves of the Changxing Period obtained by different recovery methods. A: Haq’s global sea-level change curve (adapted from [28]). B: Global sea-level curve obtained by stratigraphic inverse modeling method. C: Sea-level curve obtained by Fischer method (adapted from [30]).

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