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Title: Stochastic Approach for Obtaining Seismic Wave Paths in Random Heterogeneous Media
Other Titles: 確率的手法によるランダム不均質媒質中の地震波伝播経路の推定
Authors: MIYAZAWA, Masatoshi  kyouindb  KAKEN_id  orcid (unconfirmed)
Author's alias: 宮澤, 理稔
Keywords: 確率的チューブ
stochastic tube
random heterogeneity
ray tracing
traveltime tomography
Brownian motion
Issue Date: 1-Apr-2007
Publisher: 京都大学防災研究所
Journal title: 京都大学防災研究所年報. B = Disaster Prevention Research Institute Annuals. B
Volume: 50
Issue: B
Start page: 259
End page: 268
Abstract: 三次元ランダム不均質構造において二点を結ぶ地震波伝播経路を求める手法を,方程式を導出し解析的に解いて数値計算例を示すことで提案する。媒質が統計的関数によって特徴付けられるランダム不均質性を有する時,決定論的に地震波伝播経路を求めることが出来ないため,確率的に基準波線の周囲に確率的チューブを定義する。確率的チューブは震源と観測点を結び,基準波線と同じ波の伝播経路から成り,伝播経路として可能性のある多重経路を表現する。確率的チューブを表現するために,確率微分方程式を導出し解析的に解く。こうして求められた確率的チューブは地震波伝播経路の確率密度関数を示す。三次元ランダム不均質媒質中における初動P波に対する確率的チューブの例を,確率演算を伴う数値計算により求めて示す。
A stochastic approach is proposed for obtaining two-point seismic wave paths in a three-dimensional random heterogeneous media, by deriving and solving analytical equations and showing some numerical examples. For cases where the media include random heterogeneities characterized by statistic functions, we cannot deterministically obtain seismic wave paths, but stochastically we define a stochastic tube around a reference ray. The stochastic tube connects a source point and an observation station, consists of wave paths of the same type as the reference ray, and represents the probabilistic multiple paths. We derive and analytically solve a stochastic differential equation to represent the stochastic tube. The stochastic tube, thus obtained, indicates a probability density function of the seismic wave paths. The stochastic tubes for first arrival P-wave paths in three-dimensional random heterogeneous media are numerically calculated to illustrate a few examples using stochastic calculus.
Appears in Collections:No.50 B

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