分析延续:航空磁数据解读工具

Jeffrey B. Thurston, B. Fornberg
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引用次数: 0

摘要

将势场数据扩展到垂直复平面切片为地表下成像提供了解析函数独有的机会。我们首先使用现有的数值方法,利用柯西积分公式进行积分微分。以加拿大安大略省北部的数据为例,说明与使用有限差分计算的导数相比,该方法的调节效果更好。接下来,利用有理复数列展开(帕代近似)对这些量进行分析延续。这种方法可以提供稳定的向下延续,其距离远远大于泰勒级数和频谱方法。合成测试证实,有理近似值忠实地再现了薄片的磁响应。总磁场的符号反转与薄片的原点重合,在这个例子中非常突出。我们还提供了具有有限深度范围的薄片、点源、薄板和接触的合成结果。这些结果也显示了源位置附近的极性翻转。此外,这些结果还为利用近似函数的形状解释源的几何形状提供了模板。其他合成测试说明了一种自动方法,可用于定位间距较近的孤立极点随机组合。我们将我们的方法应用于加拿大绿岩带最近发现的火山成因块状硫化物矿床的矿床规模日光勘测。该矿床的分析延续剖面表明,存在一个深度未知的亚垂直薄片。这一解释与之前几个钻孔划定的硫化物矿体相吻合。该矿床附近的一些已知勘探区也出现在帕代近似区的地图和剖面图上。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytic continuation: A tool for aeromagnetic data interpretation
Extending potential-field data to vertical complex-plane slices provides opportunities, unique to analytic functions, for subsurface imaging. We begin with an existing numerical method for differentiation by integration using Cauchy's integral formula. An example from data over northern Ontario, Canada, illustrates better conditioning compared to derivatives computed using finite differences. Next, these quantities are used for analytic continuation using rational complex-series expansion (Padé approximation). This method provides stable downward continuation to distances that are significantly greater than are achievable by Taylor series and spectral methods. A synthetic test confirms that the rational approximant faithfully reproduces the magnetic response of a thin sheet. A sign reversal of the total field, coincident with the origin of the sheet, features prominently on this example. We also provide synthetic results for sheets with finite depth extent, point sources, thin slabs, and contacts. These also exhibit polarity flips near the source location. Further, these provide a template for interpreting the source geometry using the shape of the approximating function. Additional synthetic tests illustrate an automatic method for locating closely spaced random assemblages of isolated poles. We apply our methods to a deposit-scale heliborne survey over a recently discovered volcanogenic massive sulphide ore deposit in a Canadian greenstone belt. The analytically continued profile over the deposit suggests the presence of a subvertical thin sheet of unknown depth extent. This interpretation coincides with a sulphide ore body that has been previously delimited by several drill holes. Some known prospects near this deposit are also imaged on maps and profiles of the Padé approximant.
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