用于区域重力场定量解释的多尺度刻痕分析方法

本文介绍一个把小波多尺度分析、表面刻痕分析以及位场频率域解释理论和反演方法结合起来的数据处理、反演解释和信息提取的方法系统.这一方法系统简称为区域重力场多尺度刻痕分析方法,应用于刻画地壳分层的三维密度结构、地壳变形带分布和构造单元分区.多尺度刻痕分析包含频率域重力场场源分层、重力场小波变换多尺度分解、场源分层深度及密度扰动反演、分层刻痕分析和构造边界定位四个子系统.文中扼要地介绍这四个子系统基本原理、方法技术及应用效果.从地球物理探测到大地构造学发现,是一个多学科综合研究的探索过程.要取得重大研究成果,必须研发和组合来自不同学科的多个新方法技术,使多学科综合研究有宽厚的理论支撑.本文介绍的四个子系统组合的理论支撑分别来自应用数学、地球物理学和信息科学.

An multi-scale scratch analysis method for quantitative interpretation of regional gravity fields

This paper presents a new systematic method of regional gravity data processing that combines theories and approaches of multi-scale wavelet analysis, spectral analysis of potential fields, geophysical data, and information extraction. We call this data processing system as the multi-scale scratch analysis for delineation of crustal structures, deformation belts and division of continental tectonic units. The multi-scale scratch analysis contains four modules, which are spectral analysis for division of density layers, decomposition of the field by using wavelet transformation and multi-scale analysis, depth estimation and density inversion of decomposed gravity anomalies, and scratch analysis. The basic principles, application techniques and examples for each module are explained. As a complicate and sophisticate process, the multi-discipline research on regional geophysics from geophysical investigation to tectonic results requires combination of new methods and techniques coming from different disciplines, to build a wide and thick theoretic base for supporting the multi-discipline research. The multi-scale scratch analysis combines supporting bases coming from applied mathematics, geophysics and information science respectively.We introduce first the scale-depth law of the multi-scale wavelet analysis for regional gravity data processing to compute 3D crustal density structures. The greater the depth of field sources buried, the larger the horizontal scale of ground gravity anomalies, as well as the density disturbance, becomes. So after multi-scale wavelet decomposition of gravity data, small-scale wavelet details indicate density distribution of shallow sources, whereas large-scale wavelet details represent the distribution of deep sources. Letting α be a constant between 0.25 to 0.9, the equation h=αΔ2^n-1,n=1,2,3,… represents the relation between the buried depth h of field sources and the nth-order wavelet details, namely the scale-depth conversion law in the multi-scale wavelet analysis for decomposition of Bouguer gravity data. Tests show that the method usually produces good results if data spacing is within 2.5~10 km. However, gravity data sets with the sampling spacing greater than 10 km can be unsuitable for multi-scale wavelet analysis to get fine crustal density structures. While if the sampling spacing is less than 1 km, the result can be good only for decomposition of the density disturbance of the upper crust. After finishing the multi-scale decomposition of gravity anomalies by discrete wavelet transformation, we can use their power spectra to estimate the depths of the equivalent layers, and use generalized linear inversion to determine the density distributions of different layers.From the physical point of view, crustal deformation belts can be regarded as scratches in the crust produced by dynamic processes that cause trip-like variations of rock densities in some narrow belts. Therefore, the crustal deformation belts with different strengths appear as scratches inscribed by lithospheric geological processes, corresponding to long strip-like density anomaly belts in the crust, which also leave "scratches" in the regional gravity field. Characteristic parameters of local scratches mainly include rapid changing in gravity gradients, strong anisotropy and direction stability of anisotropy. When all these characteristic parameters of the scratch in the regional gravity field are extracted, we can locate the Phanerozoic crustal deformation belts, providing evidence for dividing continental tectonic units. The scratch analysis is based on the local spectral moment computation from the inversed density distribution data sets and produces the ridge coefficient Λ images that delineate scratches in the equivalent layers. When we want to extract information of tectonic boundaries, the narrower the tectonic boundary belts are, the more accurately the boundaries will be located. For this purpose, we may conduct further enhanced processing by modifying the ridge coefficient factor. After applying an image sharpening process, we further define a modified ridge parameter MΛ, which is called the boundary ridge coefficient. This procedure has been tested by some synthetic models and real data sets obtained in the Tibetan Plateau, providing clear evidence for the study of crustal structures and mass movement after comparison with geological mappings.