考虑地表起伏的不规则区域重力梯度场模型构建方法——以云南地区为例

STUDY ON THE REGIONAL GRAVITY GRADIENT FIELD MODELING IN IRREGULAR AREA WITH CONSIDERATION OF SURFACE FLUCTUATION:A CASE STUDY OF YUNNAN PROVINCE

文中推导并给出了基于非格网分布的起伏面扰动重力或重力异常解算区域扰动重力梯度场模型的数值计算公式。基于澳大利亚West Arnhem Land地区的格网重力数据,以频谱域(二维快速傅里叶变换)解算的扰动重力梯度全张量作为“基准值”,然后利用基于推导公式的最小二乘配置方法(LSC)对相同区域非规则范围的重力数据进行扰动重力梯度模型解算,将结果作为“评估值”。对比“基准值”与“评估值”之差,研究发现:1)基于推导公式的最小二乘配置方法解算得到的扰动重力梯度值与频谱域方法得到扰动梯度“基准值”各分量在空间形变变化上是一致的;2)统计扰动重力梯度各分量的差值ΔδΓ_(xx)^(fft-lsc)、ΔδΓ_(xy)^(fft-lsc)、ΔδΓ_(xz)^(fft-lsc)、ΔδΓ_(yy)^(fft-lsc)、ΔδΓ_(yz)^(fft-lsc)和ΔΓ_(zz)^(fft-lsc)“基准值”与“评估值”差值的标准差分别为5.54E、5.30E、1.85E、6.55E、2.09E和9.67E(1E=1×10^(-9)s^(-2)),远低于国际上实测重力梯度与解算模型差值的研究结果。最后,基于云南地区实测地表差分重力值,文中首次给出了该区域半波长约20km的重力梯度场年际变化模型。文中的思路和方法提高了广泛分布的重力数据(主要为重力异常和扰动重力)的使用效率,可为地球物理学、地质学研究更好地理解和解释重力数据、重力梯度数据及其与场源的关系提供数据基础。

The gravity gradient full tensor can sense the slight changes of the gravity vector in different directions,and because of the large number of components(6 components),it can reflect more information on different sides of the same field source than the gravity vector.On the other hand,the ground gravity survey has accumulated a lot of basic gravity vector data,and using the mathematical relationship between the gravity vector and the full tensor of gravity gradient to build a full tensor gravity gradient field model is helpful to the depth mining of existing gravity data information.Based on the mathematical relation and covariance function relation of disturbance potential,gravity anomaly,gravity disturbance and gravity gradient disturbance,along with the Least Square Configuration(LSC)algorithm,in this paper,the numerical formulas have been derived in detail for modeling the full tensor of regional gravity gradient disturbance field from gravity disturbance or gravity anomaly which distributed on undulating surface with non-grid pattern.The full tensor of gravity gradient derived from the grid distributed gravity anomaly data in West Arnhem Land,Australia by using the spectral domain(two-dimensional fast Fourier transform)method were taken as the“reference value”,Then,the full tensor of gravity gradient,in the same area with irregular regional gravity data distribution,derived form the LSC algorithm based on derived formulas were taken as the“evaluated value”.By comparing the differences between the“reference value”and the“evaluated value”of the gravity gradient,we found that:1)The“evaluated value”obtained by the LSC method is consistent in spatial pattern of variation with the“reference value”derived from the spectral domain method.The vertical component of the gravity gradient disturbance describes the boundary characteristics of the field source more precisely than the vertical component of the gravity anomaly,and other gravity gradient disturbance components provide the information representation of the same field source,which provides inspiration for the in-depth interpretation of the field source.2)Each difference componentΔδΓ_(xx)^(fft-lsc),ΔδΓ_(xy)^(fft-lsc),ΔδΓ_(xz)^(fft-lsc),ΔδΓ_(yy)^(fft-lsc),ΔδΓ_(yz)^(fft-lsc)andΔΓ_(zz)^(fft-lsc)between the“evaluated value”and the“reference value”of the gravity gradient has systematic deviation,which is 5.54E,5.30E,1.85E,6.55E,2.09E and 9.67E respectively.It is much lower than the difference between measured gravity gradient and that from constructed model in previous studies.The results show that the accuracy of the two methods is within the allowable range,but the accuracy of the modeling method based on the Least Square Configuration needs to be further verified by the measured data.Finally,based on the measured surface differential gravity anomaly values in regional area of Yunnan province,the annul gravity gradient field variation model for this region,about 20km in half wavelength,is firstly constructed and presented by using the LSC with the derived formulas in this paper.The different gravity gradient component models show more abundant interannual scale signal variation characteristics,and demonstrate more local signal characteristics from different sensitive directions in Yunnan region during this time period.In addition,in the vicinity of Zhaotong city in northeast Yunnan province,because there is no gravity points available,both the annual difference results of gravity value and the annual change model of gravity gradient show uniform signal characteristics,indicating that the modeling method in this paper does not introduce additional false“anomalies”.In southern Yunnan province,where gravity points are relatively sparse,both the annual difference results of gravity values and the annual change models of gravity gradients are dominated by long-band signals,and no additional signals will be added due to the increase of expansion order of the LSC algorithm,which is also consistent with our intuitive cognition.These provide support for further research on the relationship between crustal material migration,hydrological changes and earthquakes in Yunnan region.The procedure and method proposed in this paper can improve the efficiency of using measured gravity data(mainly gravity anomaly and gravity disturbance).Moreover,it can provide basic data for better understanding and interpretation of gravity data,gravity gradient data and their relationship with different field sources in geophysics and geology.