重力位三阶梯度张量异常的波数域转换计算及其DEXP定量解释方法

doi:10.11720/wtyht.2023.1597

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摘要

现在的仪器测量技术还不能直接测量重力位三阶梯度张量,本文提供了一种基于重力异常及重力梯度张量数据的重力位三阶梯度张量波数域转换计算方法。为验证计算方法的正确性,文中计算了三维模型重力位三阶梯度张量异常,并将重力位三阶梯度张量波数域转换结果和模型正演结果进行对比,结果表明所采用的波数域转换方法是可行的,并且相对于重力异常数据,基于重力梯度张量数据的波数域转换结果精度更高,其均方根误差不超过1 pMKS。此外,基于Vinton盐丘区实测数据利用波数域转换方法得到该地区的重力三阶梯度张量数据,并将其用于DEXP方法的数据解释中,所得的深度以及边界结果与前人的研究结果相符合。

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	邱峰

关键词 ：重力位三阶梯度张量异常, 波数域, 转换计算, DEXP, 定量解释

Abstract：

Since the current instrumental measurement technology cannot directly measure the third-order gradient tensor of gravitational potential, this study proposed a wavenumber-domain transform calculation method for the third-order gradient tensor of gravitational potential based on the gravity anomaly and gradient tensor data. To verify the correctness of this method, this study computed the third-order gradient tensor anomalies of gravitational potential using a 3D model and compared the wavenumber-domain transform calculation results with the forward modeling results, suggesting that the wavenumber-domain transform calculation method is feasible. Moreover, the wavenumber-domain transform calculation results based on gravitational gradient tensor data were more accurate than those based on gravity anomaly data, yielding a root mean square error not exceeding 1 pMKS. In addition, based on the measured data of the Vinton salt dome area, the third-order gradient tensor data of gravitational potential of this area were obtained using the wavenumber-domain transform calculation method. The obtained data were used for DEXP-based data interpretation, attaining consistent depth and boundary results with the previous research results.

Key words： third-order gradient tensor anomaly of gravitational potential wavenumber domain transform calculation DEXP quantitative interpretation

收稿日期: 2022-10-01 修回日期: 2023-06-05 出版日期: 2023-12-20

P631

基金资助:江西省技术创引导类计划“科技+水利”联合计划(2022KSG01003);江西省技术创引导类计划“科技+水利”联合计划(2023KSG01008)

作者简介: 邱峰(1992-),男,工程师,研究方向为提防隐患探测。Email:1102979410@qq.com

引用本文:

邱峰. 重力位三阶梯度张量异常的波数域转换计算及其DEXP定量解释方法[J]. 物探与化探, 2023, 47(6): 1500-1507.
QIU Feng. Methods for wavenumber-domain transform calculation and DEXP-based quantitative interpretation of third-order gradient tensor anomalies of gravitational potential. Geophysical and Geochemical Exploration, 2023, 47(6): 1500-1507.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2023.1597 或 https://www.wutanyuhuatan.com/CN/Y2023/V47/I6/1500

Fig.1 直立长方体模型几何示意

Fig.2 模型重力位一阶至三阶张量异常空间分布

Fig.3 基于重力异常的重力位三阶梯度张量FFT转换与正演计算各分量之间的差异

模型的RMS误差/pMKS	重力位三阶梯度张量
模型的RMS误差/pMKS	W_xxx	W_xxy	W_xxz	$W x y y$	W_xyz	W_xzz	W_yyy	W_yyz	W_yzz	W_zzz
不去除边界畸变值	7.66	0.17	10.61	0.16	0.04	7.64	7.32	10.11	7.29	14.66
去掉部分边界畸变值	2.54	0.17	0.17	0.16	0.04	2.51	2.43	0.16	2.39	0.23

Table 1 基于重力异常的重力三阶梯度张量异常转换计算结果与理论值间的均方根误差

Fig.4 基于重力梯度张量数据的重力位三阶梯度张量FFT转换与正演计算各分量之间的差异

Table 2 基于重力梯度张量的重力三阶梯度张量异常转换计算结果与理论值间的均方根误差

Fig.5 处理后的Vinton盐丘区重力梯度张量数据
a—T_xx异常;b—T_xy异常;c—T_xz异常;d—T_yy异常;e—T_yz异常;f—T_zz异常

Fig.6 转换得到的Vinton盐丘区重力位三阶梯度张量数据
a—W_xxx;b—W_xxy;c—W_xxz;d—W_xyy;e—W_xyz;f—W_xzz;g—W_yyy;h—W_yyz;i—W_yzz;j—W_zzz

Fig.7 波数域转换所得的重力位三阶张量数据的DEXP变换结果
a—Ω_xxx;b—Ω_xxy;c—Ω_xxz;d—Ω_xyy;e—Ω_xzz;f—Ω_yyy;g—Ω_yyz;h—Ω_yzz;i—Ω_zzz

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