<I>ABIC</I>最小化法によるブーゲー密度の推定

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タイトル別名
  • Estimation of Bouguer Reduction Density Using <I>ABIC</I> Minimization Method
  • ABIC最小化法によるブーゲー密度の推定
  • ABIC サイショウカホウ ニ ヨル ブーゲー ミツド ノ スイテイ

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抄録

A new method is proposed for the automatic and simultaneous estimation of Bouguer density and anomalies. This method solves and reduces the significant biases and estimation error of Bouguer density especially when the correlation between Bouguer anomalies and terrain is strong. The Bouguer density is estimated by fitting a smooth surface to observed Bouguer anomalies. This is carried out by an objective trade-off between the minimizations of the sum of the square of the residuals and a penalty to the surface roughness. Roughness of the surface is evaluated by integration of squares of the first and the second order derivatives. Specifically, the object function to be minimized is given as<BR>where ρ is the unknown Bouguer density, f is a surface function estimating the Bouguer anomalies, s is a vector of unknown parameters for the surface function, Fi, i=1, ..., N are observed free-airanomalies, Hi, i=1, ..., N are coefficients for a Bouguer density, xi and yi are observed coordinates, Δ [1] f and Δ [2] f are the first-order and the second-order derivatives of f, and ω1 and ω2 are hyperparameters controlling the trade-off between the residuals and the roughness. Once the suitable trade-off parameters are given, Bouguer density ρ and parameter vector s can be estimated by a standard least square algorithm such as Householder decomposition. Determination of suitable trade-off parameters is done by an objective Bayesian procedure minimizing ABIC (Akaike Bayes Information Criterion) [AKAIKE (1980)] . Analysis of three data sets of gravitational observation demonstrates the utility of the ABIC minimization method. One data set covers a large area (50km×70km) over granitic rocks and metamorphic rocks in Abukuma, next data set covers a middle area (25km×20km) over andesite in Kirishima volcano area, and the other covers a small area (750m×850m) in Oya rock region. Other automatic methods, like the F-H relationship method, determine unreasonable Bouguer densities, while the ABIC minimization method estimates reasonable density values.

収録刊行物

  • 地震　第２輯

    地震　第２輯 43 (3), 327-339, 1990

    公益社団法人 日本地震学会

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