JP3676285B2 - Earthquake motion prediction calculation method and earthquake motion prediction calculation system - Google Patents

Description

（ｂ）地殻地盤のラメの定数λがランダム変数である場合
【数２】

（Ｃ）地殻地盤のラメの定数μがランダム変数である場合
【数３】

【数４】

ここに、ρ₁、λ₁、μ₁、δn（ｎ＝ρ，λ，μ）は、密度ρ、ラメの定数λ、μの平均値からの変動とρ、λ、μの不均質性相関長さを表す。ε₀は摂動パラメータである。従って、δnとε₀が不均質の変動の長さと程度を表すパラメータとなる。また、λ₀ 、μ₀、ρ₀は確定系地盤（ランダムでない地殻地盤）のラメの定数と密度を、ｋp、ｋsは次式で示され確定系地盤のＰ波とＳ波の波数である。
【数５】

【００３１】
（３）層境界の波動の振幅ηを計算（ステップＳ３）
また。図９は、本発明で使用する地盤モデルを示す図であり、震源のある層が第ｌ（エル）層であると仮定すると、ｊ≠ｌ（エル）において、第ｌ（エル）層よりも上の層で、波動の振幅ベクトルηはＰ波及びＳ波の場合、次のように表される。
【数６】

また、第ｌ層よりも下の層では、次式の様に示される。
【数７】

【００３２】
（４）点震源による観測点での応答変位ｕと歪みＥを計算（ステップＳ４）
点震源による、第ｊ層の変位成分は、円筒座標系を用いると次式のように示される。
【数８】

【数９】

グリーン関数の歪みは、円筒座標系で表すと次式のように示される。
【数１０】

ここに、Ｊｎは、ｎ次のベッセル関数を示す。
【００３３】
（５）パラメータの入力（ステップＳ５）
震源モデルを求めるためのパラメータを入力する。入力するパラメータとしては、以下のものがある。
・断層の幅Ｗ、長さＬ、傾斜角δ、滑り角λ、走向方向θ、せん断剛性μ、平均滑り量Δｕ、応力降下量、破壊時間Ｔ、ライズタイムτ
【００３４】
（６）空間的・時間的にランダム性を有する滑り関数ｆ(m)とｇ(m)を計算（ステップＳ６）
空間的（小断層の長さＬ方向）なランダム性を有する滑り分布関数ｆ(m)は、図１１に示す変動破壊時間ΔＴ_jによって次式のように表現される。
【数１１】

であり、Ｎ₁はランダム数の個数を示し、ΔＴ_j及びｆ_jは平均値が、
【数１２】

変動係数が、
【数１３】

の、ランダム数である。
また、（９）式のＢは次式で示されるｂｏｘｃａｒ関数である。
【数１４】

また、図１２に示す変動ライズタイムΔτ_kに起因する滑り時間関数ｇ(m)は、次式のように表現される。
【数１５】

であり、Ｎ2はランダム数の個数を示し、Δτ_k及びｇ_kは平均値が、
【数１６】

変動係数が、
【数１７】

のランダム数である。
また、（１３）式のＨはステップ関数である。
【００３５】
（７）小断層の滑り量Δｕ(m)を計算（ステップＳ７）
小断層での不均質な破壊による滑り量は、ｆ(m)とｇ(m)によって、次式のように示される。
【数１８】

【００３６】
（８）小断層の地震モーメントテンソルＭ(m)ｐｑを計算（ステップＳ８）
また、ｍ番目の小断層に関する地震モーメントテンソルは、次式で示される。
【数１９】

ここに、Ｒ(m)pq、Ｍ0(m)は、それぞれｍ番目の小断層に関する放射パターン、要素地震モーメントを表す。
【００３７】
（９）小断層による観測点での地震動ｕ(m)を計算（ステップＳ９）
また、図１３に示すように、断層面を分割した場合に、小断層Σ(m)による地盤媒質の変位応答は、次式で示される。
【数２０】

ここに、Ｅ_npは時刻ｔ＝０で小断層の中心点ξ(m)にｐ方向に単位力が作用した時の観測点Ｘのｎ方向の歪みのpq成分であり、（８）式で示される。また、＊は重畳積分を表す。
【００３８】
（１０）断層全体による観測点での地震動ｕを計算（ステップＳ１０）
そして、断層全体から放射される地震動は、各小断層による地震動を総和することにより得られ、次式で示される。
【数２１】

ここに、ｔ_rは、小断層の中心位置ξ(m)での滑り開始時間である。
【００３９】
［地震動の予測計算の例］
以上、本発明による地震動予測計算方法の計算手順について説明したが、このような地盤モデルと震源モデルを使用して計算を行うことにより、精度よく地震動の予測計算を行うことができる。
図１４は、設定した断層破壊モデルによる南関東地震（Ｍ７．９）の予測計算結果を示す図であり、震源５１により断層面５２で破壊が起こり、横浜地区にある制震高層ビルを観測点５３した場合の予測計算例を示している。
また、図１５は、兵庫県南部地震（１９９５年１月１７日）における計算値と、観測データを比較した例を示している。
【００４０】
［地震動予測計算システムの構成例］
以上、本発明による地震動の予測計算方法について説明したが、この予測計算方法を使用した地震動の予測計算システムの構成例について説明する。
【００４１】
図１６は地震動予測計算システムの構成例を示す図であり、本発明に直接関係する部分についてのみ示したものである。図１６において、１００は地震動予測計算システム、１０１はネットワークと地震動予測計算システムを接続する通信用インタフェース、１０２は地震動予測計算システム全体を統括制御する制御部、１０３はデータベース、１１０は処理プログラム部を示している。
【００４２】
また、処理プログラム部１１０には、以下の処理部が含まれている。
・データ入力処理部１１１は、地盤モデルや震源モデルを生成するために必要なパラメータや、予測計算を行う際に必要な計算条件データを入力するための処理部である。入力されるデータとしては、例えば、「震源と観測点に位置関係：震源深さｄ、震央距離ｒ」、「地盤定数：Ｐ波速度Ｖｐ、Ｓ波速度Ｖｓ、密度ρ、減衰定数ｈ、不均質相関性長さδ、摂動パラメータε₀、「断層の幅Ｗ、長さＬ、傾斜角δ、滑り角λ、走向方向θ、せん断剛性μ、平均滑り量Δｕ、応力降下量、破壊時間Ｔ、ライズタイムτ」などがある。これらの入力されたデータはデータベース１０３に記録される。
・震源関数作成処理部１１２は、断層面１を複数の小断層２に分割し、各小断層２ごとに時間的、空間的なランダム性を考慮した震源関数を生成する処理を行う。
・グリーン関数作成処理部１１３は、小断層２ごとにグリーン関数（各小断層２に単位の点震源を与えたときの、観測点７での応答）を求める処理部である。・地震動計算処理部１１４は、小断層２に配した震源関数とグリーン関数の重畳積分を行い、小断層による観測点７における地震動を計算する。そして、断層破壊過程に応じた時間差を考慮して、小断層２における観測点７での地震動の総和をとり、断層全体による地震動を求める処理を行う。
・表示処理部１１５は、地震動の予測計算の計算結果を、ＣＲＴや液晶表示装置などに出力表示する。
【００４３】
なお、この処理プログラム部１１０は専用のハードウエアにより実現されるものであってもよく、またこの処理プログラム部はメモリおよびＣＰＵ（中央処理装置）等の汎用の情報処理装置により構成され、この処理部の機能を実現するためのプログラム（図示せず）をメモリのロードして実行することによりその機能を実現させるものであってもよい。また、この地震動予測計算システム１００には、周辺機器として入力装置、表示装置等（いずれも表示せず）が接続されているものとする。ここで、入力装置としては、キーボード、マウス等の入力デバイスのことをいう。表示装置とは、ＣＲＴ（Cathode Ray Tube）や液晶表示装置等のことをいう。
【００４４】
またさらに、地震動予測計算システム１００の機能を実現するためのプログラムをコンピュータ読み取り可能な記録媒体に記録して、この記録媒体に記録されたプログラムを地震動予測計算システム内のコンピュータシステムに読み込ませ、実行することにより地震動の予測計算を行ってもよい。なお、ここでいう「コンピュータシステム」とは、ＯＳや周辺機器等のハードウェアを含むものとする。
【００４５】
また、「コンピュータシステム」は、ＷＷＷシステムを利用している場合であれば、ホームページ提供環境（あるいは表示環境）を含むものとする。
また、「コンピュータ読み取り可能な記録媒体」とは、フレキシブルディスク、光磁気ディスク、ＲＯＭ、ＣＤ−ＲＯＭ等の可般媒体、コンピュータシステムに内蔵されるハードディスク等の記憶装置のことをいう。さらに「コンピュータ読み取り可能な記録媒体」とは、インターネット等のネットワークや電話回線等の通信回線を介してプログラムを送信する場合の通信線のように、短時間の間、動的にプログラムを保持するもの(伝送媒体ないしは伝送波)、その場合のサーバやクライアントとなるコンピュータシステム内部の揮発性メモリのように、一定時間プログラムを保持しているものも含むものとする。また上記プログラムは、前述した機能の一部を実現するためのものであっても良く、さらに前述した機能をコンピュータシステムにすでに記録されているプログラムとの組み合わせで実現できるもの、いわゆる差分ファイル（差分プログラム）であっても良い。
【００４６】
以上、本発明の実施の形態について説明したが、本発明は、上述の図示例にのみ限定されるものではなく、本発明の要旨を逸脱しない範囲内において種々変更を加え得ることは勿論である。
【００４７】
[震源モデルについての補足説明］
本発明で用いる震源モデルについて、参考のためにさらに補足して説明しておく、なお、上述した「地震動予測計算の計算手順」の項と説明が重複する部分がある。
【００４８】
（１）震源モデルについて
・震源の破壊過程では、断層面上のある点から破壊が始まり、それが広がって行く現象が見られる。断層面上には、破壊強度の異なる部分が不均質に分布しており、特に強度の大きい部分はアスペリティと呼ばれている。この不均質なアスペリティ分布により、断層の破壊過程は非常に複雑になると考えられる。震源をモデル化する上で、このような断層の不均質性を反映した震源関数を用いることは、実現象を再現するのに不可欠である。特に、構造物の振動特性に係わる比較的短周期領域の地震動の構成には、この断層の不均質な破壊特性が影響する。
断層破壊の動特性のモデル化に関する既往の研究の内、Ｂｕｒｒｉｄｇｅ ａｎｄ Ｋｎｏｐｐｏｆｆは、図１７の上段に示す「板バネでつながれたマスが摩擦面上でコイルバネで線形結合されたモデル」を提案している。また、Ｂｅｎ−Ｍｅｎａｈｅｍは、図１７の下段に示す「連続媒体の膜構造（ｍｅｍｂｒａｎｅ）モデル」を示している。
本発明では、Ｂｅｎ−Ｍｅｎａｈｅｍが示した「連続媒体の膜構造（ｍｅｍｂｒａｎｅ）モデル」を基本に、断層破壊の不均質性を反映させた震源関数を使用している。
【００４９】
（２）Ｂｅｎ−Ｍｅｎａｈｅｍの震源関数
Ｂｅｎ−Ｍｅｎａｈｅｍの示した「膜構造（ｍｅｍｂｒａｎｅ）モデル」の運動方程式は、次式のように表される。
【数２２】

ここに、Ｄは膜構造上の点における変位、βは基準Ｓ波速度、ｂ₀は剛性に関する量（次元：［／長さ］）、ξは座標上の位置、ｔは時間、ｑ₀は有効応力降下に関する量、Ｖ_rは破壊伝搬速度、νは初期速度に関する量を表し、Ｈは次式で表されるステップ関数を、δはクロネッカのデルタ関数を表す。
【数２３】

（２０）式の変位Ｄの解は、次式のように示される。
【数２４】

である。
（２２）式に、時間領域から振動数領域へのフーリエ変換を施すと、
【数２５】

と示される。ここに、ωは角振動数、ｉは虚数単位である。
【００５０】
また、断層の滑り量Δｕ＝Ｄとすると、断層の滑りによる観測点での変位は、次式で表される。
【数２６】

ここに、Ｍ_pqは地震モーメントテンソルであり、次式で示される。
【数２７】

Ｍ₀は、地震モーメントである。
【００５１】
（３）震源関数へのＦｌｕｃｔｕａｔｉｏｎ（変動）の導入
次に、図１８に示す断層面（長さＬ、幅Ｗ）を面積Σｅ＝ＬｅｘＷｅを持つＮ個の小断層面Σ(m)（ｍ＝１，２，・・・・，Ｎ）に分割し、それぞれの小断層に（２０）式で示したｍｅｍｂｒａｎｅモデルを配する。
この場合、ｍ番目の小断層に関する地震モーメントテンソルは、次式で示される。
【数２８】

ここに、Ｒ(m)pq、Δｕ(m)（ξ，ｔ）、Ｍ0(m)（t）は、それぞれｍ番目の小断層に関するラディエーションパターン、滑り量、要素地震モーメントを表す。ここで、断層での不均質なアスペリティの破壊を反映するため、Δｕ(m)（ξ，ｔ）を次式のように、Ｆｌｕｃｔｕａｔｉｏｎ（変動）を持つ断層滑りの振幅とライズタイムによって表現する。
【数２９】

空間的なランダム性を小断層内の長さＬ方向のみ考慮すると、（２７）式より、（２６）式の要素地震モーメントＭ0(m)（t）は、次式のように示される。
【数３０】

ｆ(m)（ζ）は、 図１９に示す変動破壊時間ΔＴ_jによって次式のように表現される。
【数３１】

ここに、
【数３２】

であり、Ｎ₁はランダム数の個数を示し、ΔＴ_j及びｆ_jは平均値が
【数３３】

変動係数が、
【数３４】

の、一様乱数分布に基づくランダム数である。
【００５２】
また、（２９）式のＢは、次式で示されるboxcar関数である。
【数３５】

（２７）式中のg(m)（t）は、変動ライズタイムΔτ_kに起因する滑り時間関数であり、次式のように表現する。
【数３６】

【数３７】

【００５３】
また、τ(m)は、小断層面Σ(m)におけるＮ₂個の平均的なサイズのアスペリティ破壊に関わる全体のライズタイムである。
また、断層の滑り振幅に関わる重み関数ｇ_kも、ｇ_kの平均値（１／Ｎ₂）、変動係数σ_gをもつ一様乱数分布のランダム数である。図２０に小断層破壊の時間的ランダム性に関する概念を示す。
【００５４】
また、（２７）式の小断層での滑りΔｕ(m)（ζ，t）は、滑り振幅関数ｆ(m)（ζ）と滑り時間関数ｇ(m)（t）を用いて、図２１のように示される。小断層内で破壊フロントが進行するに従い、滑りが生じ始め、ライズタイムΔτ_kと破壊時間ΔＴ_j及びそれらの振幅の変動により、不均質な滑りが形成される。
（２９）式、（３４）式より、（２８）式で示した要素地震モーメントは、フーリエ変換することにより、次式のように示される。
【数３８】

Ｍ0(m)は、空間的、時間的なランダム変動関数によって、小断層から高振動数成分の地震動を放射するメカニズムを表現している。
ここで、
【数３９】

【００５５】
とした場合、
【００５６】
以下の関数値、
【数４０】

【００５７】
を、図２２及び図２３に示す。
【００５８】
Ｍ0(m)の時間に関する微分は、Ａkiの長方形断層（Haskellモデル）におけるマグニチュードと地震モーメントのスケーリング則で示された震源スペクトル（ωの−２乗モデル）と同様の形状をしている。高振動数側のスペクトル成分は、主に破壊時間ΔＴとライズタイムΔτに依存するため、ΔＴとΔτの変動係数が大きくなるにつれ、高振動数成分が増大し、時刻歴波形の振幅が大きくなっている。また、Ｍ0(m)の時間に関する微分の関数は、ΔＴとΔτに依存する２つのコーナーの振動数を持っており、図２３（ａ）に示したケースでは、０．０４Ｈｚと０．２６Ｈｚになる。
【００５９】
また、各小断層におけるＭ0(m)の時間に関する微分の関数を、断層全体で総和すると、そのフーリエスペクトルＳ0（ω）と時刻歴波形Ｓ0（ｔ）は、次式のようになる。
【数４１】

【数４２】

【００６０】
全断層の長さをＬ＝１００ｋｍ、幅をＷ＝５０ｋｍとし、前述の小断層（σ_{Δ T}＝σ_f＝σ_Δτ＝σ_g＝０．３、ΔＬ(m)＝４ｋｍ、ΔＷ(m)＝３．３ｋｍ）で格子状に２５×１５＝３７５に分割した場合のとを図２２（ｂ）と図２３（ｂ）に示す。小断層を総和した全断層のスペクトルにおいても（ωの−２乗モデル）になっている。
【００６１】
以上から、本発明で使用する震源モデルは、地震モーメント、ライズタイム、滑り量、破壊時間などのパラメータを介して、マグニチュードと地震モーメントのスケーリング則を満足している。また、空間的、時間的なfluctuationを導入することにより、断層での不均質なアスペリティの破壊現象を表現し、高振動数成分の補充や断層を等間隔に分割したことによる不自然な振動数成分の抑制を図っている。
【００６２】
【発明の効果】
以上説明したように、本発明の地震動予測計算方法においては、震源モデルとして、断層面を複数の小断層に分割し、各小断層ごとに時間的、空間的なランダム性を持つ震源関数を求め、また地盤モデルを層地盤とランダム地盤から構成し、各小断層ごとにグリーン関数を求める。そして、各小断層の震源関数とグリーン関数を基に、各小断層による観測点での地震動を求め、断層の破壊過程に応じた時間差を考慮してそれらの総和をとり、層全体による観測点での地震動を計算するようにする。
これにより、不均質な断層破壊過程を考慮し、また層地盤の最下層をランダム媒質とした複雑な地盤構造による散乱、反射、透過、屈折、増幅などの影響を十分に考慮した地震動の予測計算ができ、高精度の地震動の予測計算が行えるようになる。またさらに、この震源モデルにより、地震動の高振動数成分の発生や断層破壊の方向性を考慮した地震動の予測計算が可能となる。
【００６３】
また、本発明の地震動予測計算システムにおいては、地盤モデルと震源モデルの設定に必要なパラメータ及び予測計算に必要なデータを入力し、この入力データを基に、震源モデルとして断層面を複数の小断層に分割し、各小断層ごとに時間的、空間的なランダム性を持つ震源関数を求め、また地盤モデルを層地盤とランダム地盤から構成し、各小断層ごとにグリーン関数を求める。そして、各小断層の震源関数とグリーン関数を基に、各小断層による観測点での地震動を求め、断層の破壊過程に応じた時間差を考慮してそれらの総和をとり、層全体による観測点での地震動を計算するようにする。そして、その予測計算結果を出力表示する。
これにより、不均質な断層破壊過程を考慮し、また最下層の地殻地盤をランダム媒質とし、その上に層地盤を想定した地盤構造により、波動の散乱、反射、透過、屈折、増幅などの影響を十分に考慮した地震動の予測計算ができ、高精度の地震動の予測計算が行えるようになる。またさらに、この震源モデルにより、地震動の高振動数成分の発生や断層破壊の方向性を考慮した地震動の予測計算が可能となる。そして、例えば、断層パラメータと地盤データ、震源深さ、震央距離などのデータを入力し、建設敷地で想定される設計用地震動を高精度で計算できるようになる。
【図面の簡単な説明】
【図１】 本発明による地震動予測計算方法の概念を説明するための図である。
【図２】 地盤中の地震動の伝播について説明するための図である。
【図３】 地震動予測のための震源モデルと地盤モデルについて説明するための図である。
【図４】 地震動予測モデルの概念図である。
【図５】 断層の発生について説明するための図である。
【図６】 断層のモデル化について説明するための図である。
【図７】 地盤のモデル化について説明するための図である。
【図８】 本発明による地震動予測計算の計算手順を示す図である。
【図９】 本発明で使用する地盤モデルを示す図である。
【図１０】 層全体の波動の透過係数、反射係数を示す図である。
【図１１】 小断層破壊過程の空間的ランダム性を示す図である。
【図１２】 小断層破壊の時間的ランダム性を示す図である。
【図１３】 断層面の分割の例を示す図である。
【図１４】 南関東地震（Ｍ７．９）の予測結果を示す図である。
【図１５】 兵庫県南部地震（１９９５年１月１７日）における計算値と、観測データを比較した例を示す図である。
【図１６】 地震動予測計算システムの構成例を示す図である。
【図１７】 震源のモデル化について説明するための図である。
【図１８】 断層面の分割の例を示す図である。
【図１９】 小断層破壊過程の空間的ランダム性を示す図である。
【図２０】 小断層破壊の時間的ランダム性を示す図である。
【図２１】 小断層における滑り関数について説明するための図である。
【図２２】 断層の時刻歴波形を示す図である。
【図２３】 震源関数を示す図である。
【符号の説明】
１ 断層面
２ 小断層
３ 震源
４ 点震源
５ 層地盤
６ ランダム地殻地盤
７ 観測点
１１ 震源
１２ 断層
２０ 断層面
２１ 震源モデル
２２ 地盤モデル
２３ 平行層地盤
２４ ランダム地殻地盤
１００ 地震動予測計算システム
１０１ 通信用インタフェース
１０２ 制御部
１０３ データベース
１１０ 処理プログラム部
１１１ データ入力処理部
１１２ 震源関数作成処理部
１１３ グリーン関数作成処理部
１１４ 地震動計算処理部
１１５ 表示処理部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an earthquake motion prediction calculation method and an earthquake motion prediction calculation system, and more particularly to an earthquake motion prediction calculation in which a seismic source model and a ground model used for prediction calculation are given randomness, and a prediction calculation is performed using a model closer to an actual situation. The present invention relates to a method and an earthquake motion prediction calculation system.
[0002]
[Prior art]
Earthquake motion reaches the surface of the earth due to the destruction of faults originating from the earthquake and the influence of propagation paths in the ground. For this reason, it is necessary to use a hypocenter model that simulates the fault rupture process and a ground model that simulates the ground structure in order to create earthquake motions by numerical calculation.
[0003]
Conventional methods for creating ground motion using seismic source models and ground models do not fully consider the effects of heterogeneous fault rupture processes and scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures. The earthquake motion with a period of about 0.1 to 10 seconds required for the design of structures such as civil engineering could not be calculated accurately.
[0004]
[Problems to be solved by the invention]
The present invention has been made in view of the above problems, and a seismic motion prediction calculation method capable of accurately performing seismic motion prediction calculation using a hypocenter model and a ground model as models closer to the actual situation, and The purpose is to provide a seismic motion prediction calculation system.
[0005]
[Means for Solving the Problems]
  The present invention has been made to solve the above-described problems, and is a method for calculating ground motion prediction using a ground model and a hypocenter model. The seismic source model divides a fault plane into a plurality of small faults, Each fault has temporal and spatial randomnessThat is, a slip distribution function having spatial randomness and a slip time function having temporal randomness are generated, and a slip for each small fault is obtained based on the slip distribution function and the slip time function. Based on the slip for each fault, find the seismic moment tensor for each small faultSource function generation procedure to determine the source function, and the ground model is composed of layered ground, random crust ground with randomness given by ground density, inhomogeneous correlation length of ground lame constant and perturbation parameter setting input In addition, the procedure for obtaining the Green function, which is the displacement response at the observation point when a unit source is given for each small fault, and the earthquake motion at the observation point at each small fault based on the source function and the Green function. Taking into account the time difference according to the failure process of the fault, taking the total sum of the ground motion at the observation point in each small fault, and calculating the ground motion at the observation point reflecting the failure process of the entire fault It is characterized by including
  This makes it possible to estimate the ground motion in consideration of inhomogeneous fault rupture processes and the effects of scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures with the lowest layer of the ground as a random medium. It is possible to predict earthquake motion with high accuracy. Furthermore, this seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture.
[0006]
  In addition, the earthquake motion prediction calculation method of the present invention is a ground motion prediction calculation method using a ground model and a hypocenter model, and includes parameters necessary for setting the ground model and the hypocenter model and data necessary for setting conditions for the prediction calculation. As a data input procedure for input and a hypocenter model, the fault plane is divided into multiple small faults, and each small fault has temporal and spatial randomness.That is, a slip distribution function having spatial randomness and a slip time function having temporal randomness are generated, and a slip for each small fault is obtained based on the slip distribution function and the slip time function. Based on the slip for each fault, find the seismic moment tensor for each small faultSource function generation procedure for determining the source function, ground model as layer ground,Randomness was given by setting the ground density, the inhomogeneous correlation length of the lame constant and the perturbation parameters.Displacement response at the observation point when it is composed of random crustal ground and a unit source is given for each small faultIsBased on the Green function generation procedure to obtain the Green function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault based on the Green function and the hypocenter function, and the time difference according to the failure process of the fault Considering the sum of the ground motions at the observation points in each small fault, the failure process of the entire faultReflectedIt includes a ground motion calculation procedure for the entire fault for obtaining ground motion at an observation point, and an output display procedure for the calculation result.
  This makes it possible to estimate the ground motion in consideration of inhomogeneous fault rupture processes and the effects of scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures with the lowest layer of the ground as a random medium. It is possible to predict earthquake motion with high accuracy. Furthermore, this seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture.
[0009]
  The seismic motion prediction calculation system according to the present invention is a seismic motion prediction calculation system using a ground model and a hypocenter model, wherein the fault plane is divided into a plurality of small faults, and each small fault is temporally , Spatial randomnessThat is, a slip distribution function having spatial randomness and a slip time function having temporal randomness are generated, and a slip for each small fault is obtained based on the slip distribution function and the slip time function. Based on the slip for each fault, find the seismic moment tensor for each small faultA means for obtaining a hypocenter function, and a ground model are composed of a layer ground and a ground density, a random crust ground to which randomness is given by setting input of a heterogeneous correlation length of a lame constant and a perturbation parameter, and Means for obtaining a Green function that is a displacement response at an observation point when a unit hypocenter is given for each small fault, and means for obtaining ground motion at an observation point in each small fault based on the source function and the Green function; Taking into account the time difference according to the failure process of the fault, and taking the sum of the ground motion at the observation point in each of the small faults and calculating the ground motion at the observation point reflecting the failure process of the entire fault. Features.
  This makes it possible to estimate the ground motion in consideration of inhomogeneous fault rupture processes and the effects of scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures with the lowest layer of the ground as a random medium. It is possible to predict earthquake motion with high accuracy. Furthermore, this seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture. For example, data such as fault parameters, ground data, epicenter depth, epicenter distance, and the like can be input, and the design seismic motion assumed at the construction site can be calculated with high accuracy.
[0010]
  The earthquake motion prediction calculation system of the present invention is a ground motion prediction calculation system using a ground model and a hypocenter model, and includes parameters necessary for setting the ground model and the hypocenter model and data necessary for setting conditions for the prediction calculation. As a data input means for input and an epicenter model, the fault plane is divided into multiple small faults, and each small fault has temporal and spatial randomness.That is, a slip distribution function having spatial randomness and a slip time function having temporal randomness are generated, and a slip for each small fault is obtained based on the slip distribution function and the slip time function. Based on the slip for each fault, find the seismic moment tensor for each small faultSource function generation means for determining the source function, and the ground model as layer groundRandomness was given by setting the ground density, the inhomogeneous correlation length of the lame constant and the perturbation parameters.Displacement response at the observation point when it is composed of random crustal ground and a unit source is given for each small faultIsA green function generating means for obtaining a green function, a ground motion calculating means for calculating a ground motion at an observation point by each small fault based on the green function and the source function, and a time difference corresponding to the failure process of the fault Considering the sum of the ground motions at the observation points in each small fault, the failure process of the entire faultReflectedIt is characterized by comprising ground motion calculation means for the entire fault for obtaining ground motion at the observation point, and output display means for the calculation results.
  This makes it possible to estimate the ground motion in consideration of inhomogeneous fault rupture processes and the effects of scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures with the lowest layer of the ground as a random medium. It is possible to predict earthquake motion with high accuracy. For example, data such as fault parameters, ground data, epicenter depth, epicenter distance, and the like can be input, and the design seismic motion assumed at the construction site can be calculated with high accuracy.
[0013]
  In addition, the computer-readable recording medium of the present invention is necessary for the computer in the earthquake motion prediction calculation system using the ground model and the hypocenter model, necessary for setting the parameters necessary for setting the ground model and the hypocenter model, and the conditions for the prediction calculation. As a data input procedure for inputting data and a hypocenter model, the fault plane is divided into multiple small faults, and each small fault has temporal and spatial randomness.That is, a slip distribution function having spatial randomness and a slip time function having temporal randomness are generated, and a slip for each small fault is obtained based on the slip distribution function and the slip time function. Based on the slip for each fault, find the seismic moment tensor for each small faultSource function generation procedure for determining the source function, ground model as layer ground,Randomness was given by setting the ground density, the inhomogeneous correlation length of the lame constant and the perturbation parameters.Displacement response at the observation point when it is composed of random crustal ground and a unit source is given for each small faultIsBased on the Green function generation procedure to obtain the Green function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault based on the Green function and the hypocenter function, and the time difference according to the failure process of the fault Taking into account the sum total of the ground motion at the observation points in each small fault,ReflectedA computer-readable recording medium recording a program for executing a ground motion calculation procedure for an entire fault for obtaining ground motion at an observation point and an output display procedure for the calculation result.
[0014]
  In addition, the computer program of the present invention is necessary for the computer in the ground motion prediction calculation system using the ground model, the hypocenter model, and the seismic source model to set the parameters necessary for setting the ground model and the hypocenter model and the conditions for the prediction calculation. Data input procedure for inputting simple data, and as a hypocenter model, the fault plane is divided into multiple small faults, and temporal and spatial randomness is provided for each small fault.And generating a slip distribution function having spatial randomness and a slip time function having temporal randomness, obtaining a slip for each small fault based on the slip distribution function and the slip time function, Based on the slip for each fault, find the seismic moment tensor for each small faultSource function generation procedure to determine the source function and the ground modelRandomness was given by setting the ground density, the inhomogeneous correlation length of the lame constant and the perturbation parameters.Displacement response at the observation point when it is composed of random crustal ground and a unit source is given for each small faultIsBased on the Green function generation procedure to obtain the Green function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault based on the Green function and the hypocenter function, and the time difference according to the failure process of the fault Considering the sum of the ground motions at the observation points in each small fault, the failure process of the entire faultReflectedIt is a program for executing a ground motion calculation procedure for an entire fault for obtaining ground motion at an observation point and a procedure for outputting the calculation result.
[0015]
[Action]
FIG. 1 is a diagram for explaining the concept of the earthquake motion prediction calculation method according to the present invention. In the present invention, a seismic source model that can express inhomogeneous fault rupture and a ground model that can express scattering, reflection, transmission, refraction, amplification, and the like of seismic motion propagating in the ground are used. The fault rupture originates from the epicenter 3, and the slip spreads over the fault surface 1 one after another and reaches the entire fault. At this time, the slip distribution of the fault has heterogeneity.
[0016]
The epicenter model used in the present invention has the following characteristics.
The fault surface 1 is divided into a plurality of small faults 2, and each small fault 2 is given a seismic source function considering temporal and spatial randomness. Further, as the fault rupture progresses, the fault rupture process is expressed by adding a time difference to a slip function having a rise time corresponding to each small fault 2. This seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture.
[0017]
In addition, in the process of propagation of ground motion from the epicenter to the ground surface, it is affected by the ground structure and the ground medium. In particular, in the lithosphere (the layer that combines the crust and the top of the mantle), the phenomenon of scattering of ground motion is prominent.
[0018]
The ground model used in the present invention has the following characteristics.
The ground model used in the present invention includes a layered ground structure (layered ground 5) and a random ground medium (random ground crust 6). A layered ground structure can express phenomena such as reflection, transmission, refraction, and amplification of seismic motion, and a random ground medium can evaluate scattering attenuation due to a heterogeneous ground structure with high accuracy.
[0019]
Moreover, the calculation procedure of the ground motion used in the present invention is according to the following procedure.
(1) Calculate the Green function using the ground model (response at the observation point 7 when a unit point source 4 is given to each small fault).
(2) Calculate the ground motion at the observation point 7 by the small fault 2 by superimposing the source function and the Green function arranged on the small fault 2.
(3) In accordance with the fault rupture process, the sum of the ground motions at the observation point 7 on the small fault 2 is obtained in consideration of the time difference.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[0021]
[Outline of the hypocenter model and ground model used for the ground motion prediction of the present invention]
(1) Propagation of ground motion in the ground
First, propagation of ground motion in the ground will be described.
FIG. 2 is a diagram for explaining the propagation of ground motion in the ground. An earthquake occurs at the epicenter 11, a slip occurs on the fault 12, and a fault breaks down and a ground motion occurs. The ground motion propagates in the ground, and propagates in the hard ground and soft ground like the arrowed line a and the arrowed line b. In addition, seismic motion reaches the ground surface by being scattered, reflected, transmitted, refracted, amplified, etc. by the formation.
[0022]
(2) Source model and ground model for earthquake motion prediction
FIG. 3 is a diagram for explaining a hypocenter model and a ground model for earthquake motion prediction. In order to accurately predict earthquake motion, it is necessary to appropriately set the hypocenter model 21 and the ground model 22 in the fault 20. is there. As shown in the conceptual diagram of the ground motion prediction model in FIG. 4, the ground model 22 is a model composed of a parallel ground ground 23 close to the ground surface and a random crust ground 24 composed of a heterogeneous medium. Is used.
[0023]
(3) Fault generation
FIG. 5 is a diagram for explaining the generation of a fault. First, a crack occurs in the random crust ground 31, and the ground slips left and right or up and down with the fault plane 32 as a boundary.
[0024]
(4) Fault modeling
FIG. 6 is a diagram for explaining fault modeling. As shown in FIG. 6A, in the present invention, the fault plane is divided into mesh-shaped small faults, and slips and seismic motions are generated in each small fault. Adopt a model that generates. Further, as shown in FIG. 6B, it is assumed that the slip amount in each small fault occurs randomly.
[0025]
(5) Ground modeling
FIG. 7 is a diagram for explaining the modeling of the ground. In the present invention, the ground model is divided into the random crust ground shown in FIG. 7A and the parallel on the random crust ground shown in FIG. 7B. Consists of layered ground.
・ Random crustal ground is a deep part of the ground including the epicenter, and embodies the phenomenon of seismic wave scattering by an inhomogeneous medium.
・ Parallel layer ground is the portion of the ground close to the ground surface, and the reflection, transmission, refraction, amplification, etc. of seismic waves are realized by the stratum boundary of the stratum for each age.
[0026]
(6) Outline of earthquake motion prediction calculation
Returning to FIG. FIG. 1 is a diagram for explaining the concept of the seismic motion prediction calculation method according to the present invention, and performs seismic motion prediction calculation according to the following procedure.
The fault plane 1 is divided into mesh-like small faults 2, and a hypocenter 3 is generated on the fault plane 1, and a hypocenter function having spatial and temporal randomness is given to each small fault 2. Further, as the fault rupture progresses, a time difference is given to the hypocenter function of each small fault 2.
On the other hand, the green function between the point source 4 on the small fault 2 on the fault plane 1 and the observation point (or building construction site) 7 is obtained.
・ Observe the ground motion at the observation point 7 by the small fault 2 using the source function and the Green function of each small fault 2.
・ For each small fault, the ground motion at observation point 7 is obtained and summed up, and the ground motion at observation point 7 due to the destruction process of the entire entire layer is obtained.
[0027]
[Calculation procedure for earthquake motion prediction calculation]
Next, a prediction calculation algorithm and calculation procedure used in the earthquake motion prediction calculation method of the present invention will be described. FIG. 8 is a diagram showing a calculation procedure of the earthquake motion prediction calculation according to the present invention,
Steps S1 to S4 are steps for obtaining a green function from the ground model.
Steps S5 to S8 are steps for calculating a source function from the source model.
Steps S9 and S10 are steps for obtaining earthquake motion from the Green function and the epicenter function obtained in the above step.
[0028]
Hereinafter, the calculation procedure will be described based on the flow of FIG.
(1) Parameter input (step S1)
Enter the ground model parameters necessary to obtain the Green function. Input parameters include the following.
・ Position relation between epicenter and observation point: epicenter depth d, epicenter distance r
・ Ground constants: P wave velocity Vp, S wave velocity Vs, density ρ, damping constant h, heterogeneous correlation length δn (n = ρ, λ, μ), perturbation parameter ε₀
[0029]
(2) Calculation of effective wave number (step S2)
・ The multiple scattering phenomenon of waves propagating in the ground is thought to be due to the heterogeneous structure in the ground medium. In the present invention, the effective ground wave number of the random ground medium using the perturbation method is used to evaluate the ground attenuation depending on the periodicity due to the scattering of the waves. This effective wave number is expressed by the following equation by using density ρ and lame constants λ and μ as random variables.
[0030]
(A) The density ρ of the crust ground is a random variable
[Expression 1]

(B) When the lame constant λ of the crust ground is a random variable
[Expression 2]

(C) When the lame constant μ of the crust ground is a random variable
[Equation 3]

[Expression 4]

Where ρ₁, Λ₁, Μ₁, Δn (n = ρ, λ, μ) represents the density ρ, the lame constant λ, the variation from the average value of μ, and the heterogeneous correlation length of ρ, λ, μ. ε₀Is a perturbation parameter. Therefore, δn and ε₀Is a parameter that represents the length and extent of inhomogeneous variation. Λ₀ , Μ₀, Ρ₀Is the lame constant and density of the deterministic ground (non-random crust ground), and kp and ks are the wave numbers of the P wave and S wave of the deterministic ground expressed by the following equations.
[Equation 5]

[0031]
(3) Calculate the amplitude η of the wave at the layer boundary (step S3)
Also. FIG. 9 is a diagram showing a ground model used in the present invention. Assuming that a layer having an epicenter is the lth layer, the j layer is more than the lth layer at j ≠ l. In the upper layer, the amplitude vector η of the wave is expressed as follows in the case of the P wave and the S wave.
[Formula 6]

In the layer below the l-th layer, the following equation is shown.
[Expression 7]

[0032]
(4) Calculate the response displacement u and strain E at the observation point by the point source (step S4)
The displacement component of the j-th layer due to the point source is expressed as follows using a cylindrical coordinate system.
[Equation 8]

[Equation 9]

The distortion of the Green function is expressed by the following equation when expressed in the cylindrical coordinate system.
[Expression 10]

Here, Jn represents an nth-order Bessel function.
[0033]
(5) Parameter input (step S5)
Enter parameters to determine the hypocenter model. Input parameters include the following.
Fault width W, length L, inclination angle δ, slip angle λ, strike direction θ, shear stiffness μ, average slip amount Δu, stress drop, failure time T, rise time τ
[0034]
(6) Calculate slip functions f (m) and g (m) having spatial and temporal randomness (step S6)
The slip distribution function f (m) having spatial (small fault length L direction) randomness is represented by the fluctuation failure time ΔT shown in FIG._jIs expressed as follows.
## EQU11 ##

And N₁Indicates the number of random numbers, and ΔT_jAnd f_jIs the mean,
[Expression 12]

The coefficient of variation is
[Formula 13]

Is a random number.
Further, B in the equation (9) is a boxcar function expressed by the following equation.
[Expression 14]

Further, the fluctuation rise time Δτ shown in FIG._kThe slip time function g (m) resulting from is expressed as:
[Expression 15]

N2 represents the number of random numbers and Δτ_kAnd g_kIs the mean,
[Expression 16]

The coefficient of variation is
[Expression 17]

Is a random number.
Further, H in the equation (13) is a step function.
[0035]
(7) Calculate slip amount Δu (m) of small fault (step S7)
The amount of slip due to inhomogeneous failure at a small fault is expressed by f (m) and g (m) as follows:
[Expression 18]

[0036]
(8) Calculate the small moment earthquake moment tensor M (m) pq (step S8)
The seismic moment tensor for the mth small fault is expressed by the following equation.
[Equation 19]

Here, R (m) pq and M0 (m) represent the radiation pattern and the elemental seismic moment for the mth small fault, respectively.
[0037]
(9) Calculate ground motion u (m) at observation point due to small fault (step S9)
As shown in FIG. 13, when the fault plane is divided, the displacement response of the ground medium due to the small fault Σ (m) is expressed by the following equation.
[Expression 20]

Where E_npIs a pq component of strain in the n direction of the observation point X when a unit force is applied in the p direction to the center point ξ (m) of the small fault at time t = 0, and is expressed by equation (8). * Represents a superposition integral.
[0038]
(10) Calculate ground motion u at the observation point by the entire fault (step S10)
The ground motion radiated from the entire fault is obtained by summing the ground motion from each small fault, and is expressed by the following equation.
[Expression 21]

Where t_rIs the slip start time at the center position ξ (m) of the small fault.
[0039]
[Example of earthquake motion prediction calculation]
As described above, the calculation procedure of the earthquake motion prediction calculation method according to the present invention has been described. However, by calculating using such a ground model and a hypocenter model, the prediction calculation of the earthquake motion can be performed with high accuracy.
FIG. 14 is a diagram showing the prediction calculation result of the Minami Kanto earthquake (M7.9) by the set fault destruction model, where the fault 51 occurred on the fault surface 52 by the epicenter 51, and the seismic control skyscraper in the Yokohama area was observed. 53 shows an example of prediction calculation in the case of 53.
FIG. 15 shows an example in which the calculated values in the Hyogoken-Nanbu Earthquake (January 17, 1995) and observation data are compared.
[0040]
[Configuration example of earthquake motion prediction calculation system]
The earthquake motion prediction calculation method according to the present invention has been described above, and a configuration example of a earthquake motion prediction calculation system using this prediction calculation method will be described.
[0041]
FIG. 16 is a diagram showing a configuration example of the seismic motion prediction calculation system, and shows only the portion directly related to the present invention. In FIG. 16, 100 is an earthquake motion prediction calculation system, 101 is a communication interface for connecting the network and the earthquake motion prediction calculation system, 102 is a control unit that controls the entire earthquake motion prediction calculation system, 103 is a database, 110 is a processing program unit. Show.
[0042]
The processing program unit 110 includes the following processing units.
The data input processing unit 111 is a processing unit for inputting parameters necessary for generating a ground model and a hypocenter model and calculation condition data necessary for performing prediction calculation. Examples of input data include “position relation between epicenter and observation point: epicenter depth d, epicenter distance r”, “ground constants: P wave velocity Vp, S wave velocity Vs, density ρ, damping constant h, Homogeneous correlation length δ, perturbation parameter ε₀, “Fault width W, length L, inclination angle δ, slip angle λ, strike direction θ, shear stiffness μ, average slip amount Δu, stress drop amount, failure time T, rise time τ”, and the like. These input data are recorded in the database 103.
The epicenter function creation processing unit 112 divides the fault plane 1 into a plurality of small faults 2 and performs a process of generating a hypocenter function that takes into account temporal and spatial randomness for each small fault 2.
The green function creation processing unit 113 is a processing unit that obtains a green function for each small fault 2 (response at the observation point 7 when a unit point source is given to each small fault 2). The seismic motion calculation processing unit 114 performs superposition integration of the seismic source function arranged on the small fault 2 and the Green function, and calculates the ground motion at the observation point 7 due to the small fault. Then, in consideration of the time difference according to the fault rupture process, the sum total of the ground motions at the observation points 7 in the small fault 2 is taken, and the ground motion due to the entire fault is obtained.
The display processing unit 115 outputs and displays the calculation result of the earthquake motion prediction calculation on a CRT or a liquid crystal display device.
[0043]
The processing program unit 110 may be realized by dedicated hardware, and the processing program unit is configured by a general-purpose information processing device such as a memory and a CPU (central processing unit). A program (not shown) for realizing the function of each unit may be implemented by loading a memory and executing the program. In addition, it is assumed that an input device, a display device, and the like (none of them are displayed) are connected to the seismic motion prediction calculation system 100 as peripheral devices. Here, the input device refers to an input device such as a keyboard and a mouse. The display device refers to a CRT (Cathode Ray Tube), a liquid crystal display device, or the like.
[0044]
Furthermore, a program for realizing the functions of the earthquake motion prediction calculation system 100 is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into a computer system in the earthquake motion prediction calculation system and executed. The earthquake motion prediction calculation may be performed. Here, the “computer system” includes an OS and hardware such as peripheral devices.
[0045]
Further, the “computer system” includes a homepage providing environment (or display environment) if the WWW system is used.
The “computer-readable recording medium” refers to a storage device such as a flexible disk, a magneto-optical disk, a general medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Furthermore, the “computer-readable recording medium” dynamically holds a program for a short time, like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. In this case, it is intended to include those that hold a program for a certain period of time, such as a volatile memory inside a computer system that becomes a server or client in that case (transmission medium or transmission wave). The program may be for realizing a part of the functions described above, and further, a program that can realize the functions described above in combination with a program already recorded in the computer system, a so-called difference file (difference). Program).
[0046]
While the embodiments of the present invention have been described above, the present invention is not limited to the above-described illustrated examples, and various modifications can be made without departing from the scope of the present invention. .
[0047]
[Supplementary explanation about the epicenter model]
The hypocenter model used in the present invention will be further supplemented and described for reference, and there is a part that overlaps with the above-mentioned section “Calculation procedure of earthquake motion prediction calculation”.
[0048]
(1) About the epicenter model
・ In the process of the epicenter destruction, there is a phenomenon that the destruction starts from a certain point on the fault surface and spreads. On the fault plane, the parts with different fracture strengths are distributed inhomogeneously, and the part with particularly high strength is called asperity. Due to this heterogeneous asperity distribution, the failure process of the fault is considered to be very complicated. In modeling the epicenter, the use of a seismic source function that reflects such inhomogeneity of the fault is indispensable to reproduce the actual phenomenon. In particular, the non-homogeneous fracture characteristics of this fault affect the structure of ground motion in a relatively short period related to the vibration characteristics of the structure.
Among previous studies on modeling the dynamics of fault ruptures, Burridge and Knoppoff proposed the “model in which masses connected by leaf springs are linearly coupled by coil springs on the friction surface” shown in the upper part of FIG. Yes. Ben-Menahem indicates a “film structure (continuous medium membrane model)” shown in the lower part of FIG. 17.
In the present invention, the seismic source function reflecting the inhomogeneity of the fault rupture is used based on the “membrane model of the continuous medium” presented by Ben-Menheim.
[0049]
(2) Ben-Menheim epicenter function
The equation of motion of the “membrane structure model” shown by Ben-Menheim is expressed as the following equation.
[Expression 22]

Where D is the displacement at a point on the membrane structure, β is the reference S wave velocity, b₀Is a quantity related to rigidity (dimension: [/ length]), ξ is a coordinate position, t is time, q₀Is the amount related to the effective stress drop, V_rIs a fracture propagation velocity, ν is a quantity related to the initial velocity, H is a step function expressed by the following equation, and δ is a Kronecker delta function.
[Expression 23]

The solution of the displacement D in the equation (20) is expressed as the following equation.
[Expression 24]

It is.
When the Fourier transform from the time domain to the frequency domain is performed on the equation (22),
[Expression 25]

It is indicated. Here, ω is an angular frequency, and i is an imaginary unit.
[0050]
If the fault slip amount Δu = D, the displacement at the observation point due to the fault slip is expressed by the following equation.
[Equation 26]

Where M_pqIs the seismic moment tensor and is given by
[Expression 27]

M₀Is the seismic moment.
[0051]
(3) Introduction of Fluctuation into the source function
Next, the tomographic plane (length L, width W) shown in FIG. 18 is divided into N small tomographic planes Σ (m) (m = 1, 2,..., N) having an area Σe = LexWe. Then, the membrane model shown by the equation (20) is arranged on each small fault.
In this case, the seismic moment tensor for the mth small fault is expressed by the following equation.
[Expression 28]

Here, R (m) pq, Δu (m) (ξ, t), and M0 (m) (t) represent the radiation pattern, slip amount, and elemental seismic moment for the mth small fault, respectively. Here, in order to reflect the inhomogeneous destruction of asperities in the fault, Δu (m) (ξ, t) is expressed by the amplitude and rise time of the fault slip having Fluctuation (variation) as in the following equation.
[Expression 29]

When considering spatial randomness only in the direction of the length L in the small fault, the element seismic moment M0 (m) (t) of the equation (26) is expressed by the following equation from the equation (27).
[30]

f (m) (ζ) is the variable fracture time ΔT shown in FIG._jIs expressed as follows.
[31]

here,
[Expression 32]

And N₁Indicates the number of random numbers, and ΔT_jAnd f_jIs the average value
[Expression 33]

The coefficient of variation is
[Expression 34]

This is a random number based on a uniform random number distribution.
[0052]
Further, B in the equation (29) is a boxcar function expressed by the following equation.
[Expression 35]

In equation (27), g (m) (t) is the variable rise time Δτ_kThis is a slip time function caused by the following expression.
[Expression 36]

[Expression 37]

[0053]
Also, τ (m) is N in the small fault plane Σ (m)₂This is the overall rise time involved in asperity destruction of an average size.
The weight function g related to the slip amplitude of the fault_kG_kAverage value (1 / N₂), Coefficient of variation σ_gIs a random number with a uniform random number distribution. FIG. 20 shows a concept related to temporal randomness of small fault destruction.
[0054]
Further, the slip Δu (m) (ζ, t) at the small fault in the equation (27) is obtained by using the slip amplitude function f (m) (ζ) and the slip time function g (m) (t) as shown in FIG. As shown. As the fracture front progresses within a small fault, slipping begins to occur and rise time Δτ_kAnd destruction time ΔT_jAnd due to their amplitude variations, inhomogeneous slip is formed.
From the formulas (29) and (34), the elemental seismic moment shown in the formula (28) is expressed by the following formula by Fourier transform.
[Formula 38]

M0 (m) expresses a mechanism that radiates high-frequency seismic motion from a small fault by a spatial and temporal random variation function.
here,
[39]

[0055]
If
[0056]
The following function values,
[Formula 40]

[0057]
Is shown in FIG. 22 and FIG.
[0058]
The derivative of M0 (m) with respect to time has the same shape as the epicenter spectrum (ω-square model) indicated by the magnitude and seismic moment scaling law of Aki's rectangular fault (Haskell model). Since the spectral components on the high frequency side mainly depend on the destruction time ΔT and the rise time Δτ, as the coefficient of variation of ΔT and Δτ increases, the high frequency component increases and the amplitude of the time history waveform increases. ing. Further, the derivative function of M0 (m) with respect to time has two corner frequencies depending on ΔT and Δτ, and in the case shown in FIG. 23A, it is 0.04 Hz and 0.26 Hz. Become.
[0059]
Further, when the differential functions relating to the time of M0 (m) in each small fault are summed up in the entire fault, the Fourier spectrum S0 (ω) and the time history waveform S0 (t) are as follows.
[Expression 41]

[Expression 42]

[0060]
The length of all faults is L = 100 km and the width is W = 50 km._{Δ T}= Σ_f= Σ_Δτ= Σ_g= 0.3, ΔL (m) = 4 km, ΔW (m) = 3.3 km) and FIG. 22B and FIG. . The spectrum of all faults summing up small faults is also the (ω-square model).
[0061]
From the above, the hypocenter model used in the present invention satisfies the magnitude and seismic moment scaling laws through parameters such as seismic moment, rise time, slippage, and failure time. In addition, by introducing spatial and temporal fluctuation, the phenomenon of inhomogeneous asperity destruction in the fault is expressed, and the unnatural frequency due to the supplementation of high frequency components and the division of the fault at equal intervals. The suppression of the component is aimed at.
[0062]
【The invention's effect】
As described above, in the earthquake motion prediction calculation method of the present invention, the fault plane is divided into a plurality of small faults as the hypocenter model, and a source function having temporal and spatial randomness is obtained for each small fault. Also, the ground model is composed of layered ground and random ground, and the green function is obtained for each small fault. Based on the seismic source function and green function of each small fault, the ground motion at the observation point of each small fault is obtained, and the sum of them is taken into account according to the time difference according to the failure process of the fault. Try to calculate the earthquake motion at.
This makes it possible to estimate the ground motion in consideration of inhomogeneous fault rupture processes and the effects of scattering, reflection, transmission, refraction, amplification, etc. due to complex ground structures with the lowest layer of the ground as a random medium. It is possible to predict earthquake motion with high accuracy. Furthermore, this seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture.
[0063]
In the earthquake motion prediction calculation system of the present invention, parameters necessary for setting the ground model and the hypocenter model and data necessary for the prediction calculation are input, and based on this input data, a plurality of small fault planes are generated as the hypocenter model. Divide the fault into faults, find the source function with temporal and spatial randomness for each small fault, and construct the ground model from layered ground and random ground, and obtain the green function for each small fault. Based on the seismic source function and green function of each small fault, the ground motion at the observation point by each small fault is obtained, and the sum of them is taken in consideration of the time difference according to the failure process of the fault. Try to calculate the earthquake motion at. Then, the prediction calculation result is output and displayed.
In this way, considering the heterogeneous fault rupture process, the bottom layer's crust ground is a random medium, and the ground structure assuming the layer ground above it is the influence of wave scattering, reflection, transmission, refraction, amplification, etc. The earthquake motion prediction calculation with sufficient consideration can be made, and the highly accurate earthquake motion prediction calculation can be performed. Furthermore, this seismic source model makes it possible to calculate the ground motion prediction considering the occurrence of high frequency components of ground motion and the direction of fault rupture. For example, data such as fault parameters, ground data, epicenter depth, epicenter distance, and the like can be input, and the design seismic motion assumed at the construction site can be calculated with high accuracy.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining the concept of a ground motion prediction calculation method according to the present invention.
FIG. 2 is a diagram for explaining propagation of seismic motion in the ground.
FIG. 3 is a diagram for explaining a hypocenter model and a ground model for earthquake motion prediction.
FIG. 4 is a conceptual diagram of a seismic motion prediction model.
FIG. 5 is a diagram for explaining generation of a fault.
FIG. 6 is a diagram for explaining fault modeling;
FIG. 7 is a diagram for explaining ground modeling.
FIG. 8 is a diagram showing a calculation procedure of earthquake motion prediction calculation according to the present invention.
FIG. 9 is a diagram showing a ground model used in the present invention.
FIG. 10 is a diagram showing a transmission coefficient and a reflection coefficient of waves of the entire layer.
FIG. 11 is a diagram showing spatial randomness of a small fault destruction process.
FIG. 12 is a diagram showing temporal randomness of small fault destruction.
FIG. 13 is a diagram illustrating an example of dividing a tomographic plane.
FIG. 14 is a diagram showing a prediction result of the South Kanto earthquake (M7.9).
FIG. 15 is a diagram showing an example in which the calculated values in the Hyogoken-Nanbu Earthquake (January 17, 1995) and observation data are compared.
FIG. 16 is a diagram illustrating a configuration example of an earthquake motion prediction calculation system.
FIG. 17 is a diagram for explaining hypocenter modeling;
FIG. 18 is a diagram illustrating an example of division of a tomographic plane.
FIG. 19 is a diagram showing spatial randomness of a small fault destruction process.
FIG. 20 is a diagram showing temporal randomness of small fault destruction.
FIG. 21 is a diagram for explaining a slip function in a small fault.
FIG. 22 is a diagram showing a time history waveform of a fault.
FIG. 23 is a diagram showing a hypocenter function.
[Explanation of symbols]
1 Fault plane
2 Small fault
3 epicenters
4 point epicenters
5 layers ground
6 Random crust ground
7 observation points
11 epicenter
12 Fault
20 Fault plane
21 Epicenter model
22 Ground model
23 Parallel layer ground
24 Random crust ground
100 Earthquake motion prediction calculation system
101 Communication interface
102 Control unit
103 Database
110 Processing program part
111 Data input processor
112 Source function creation processing part
113 Green function creation processing part
114 Earthquake motion calculation processing section
115 Display processing unit

Claims (6)

A ground motion prediction calculation method using a ground model and a hypocenter model,
As source model, dividing the fault plane into a plurality of small faults, time for each minor fault, Chi lifting spatial randomness, and slip distribution function having a spatial randomness, temporal randomness And generating a slip time function, obtaining a slip for each small fault based on the slip distribution function and the slip time function, and determining a seismic moment tensor for each small fault based on the slip for each small fault The procedure for
The ground model is composed of layered ground, random crust ground given randomness by input of ground density, inhomogeneous correlation length of ground lame constant and perturbation parameters, and unit for each small fault The procedure for obtaining the Green function, which is the displacement response at the observation point when an epicenter is given,
Based on the seismic source function and Green's function, taking into account the ground motion at the observation point at each small fault and the time difference according to the failure process of the fault, And a method for calculating ground motion at an observation point reflecting the failure process of the entire fault. A ground motion prediction calculation method using a ground model and a hypocenter model,
A data input procedure for inputting the parameters necessary for setting the ground model and the hypocenter model and the data necessary for setting the conditions for the prediction calculation,
As source model, dividing the fault plane into a plurality of small faults, time for each minor fault, Chi lifting spatial randomness, and slip distribution function having a spatial randomness, temporal randomness And generating a slip time function, obtaining a slip for each small fault based on the slip distribution function and the slip time function, and determining a seismic moment tensor for each small fault based on the slip for each small fault A source function generation procedure for
The ground model is composed of layered ground, random crust ground given randomness by input of ground density, inhomogeneous correlation length of ground lame constant and perturbation parameter, and unit of each small fault Green function generation procedure to obtain the Green function which is the displacement response at the observation point when the hypocenter is given,
Based on the Green function and the hypocenter function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault,
Considering the time difference according to the failure process of the fault, taking the total of the ground motion at the observation point in each small fault, and calculating the ground motion by the whole fault to obtain the ground motion at the observation point reflecting the failure process of the whole fault,
And an output display procedure of the calculation result. A seismic hazard computing system using a ground model and source model, as source model, dividing the fault plane into a plurality of small faults, time for each minor fault, Chi lifting spatial randomness, spatial Generating a slip distribution function having random randomness and a slip time function having temporal randomness, obtaining a slip for each small fault based on the slip distribution function and the slip time function, Based on the above, a means to determine the seismic moment tensor for each small fault and to determine the source function,
The ground model is composed of layered ground and ground density, random crustal ground given randomness by setting the heterogeneous correlation length of ground lame constants and perturbation parameters, and unit earthquake source for each small fault Means for obtaining a Green function that is a displacement response at the observation point when
Based on the source function and the Green function, means for obtaining the ground motion at the observation point in each small fault;
Taking into account the time difference according to the failure process of the fault, and taking the sum of the ground motion at the observation point in each small fault and calculating the ground motion at the observation point reflecting the failure process of the entire fault. Characteristic earthquake motion prediction calculation system. A ground motion prediction calculation system using a ground model and a hypocenter model,
A data input means for inputting parameters necessary for setting the ground model and the hypocenter model and data necessary for setting the conditions for the prediction calculation;
As source model, dividing the fault plane into a plurality of small faults, time for each minor fault, Chi lifting spatial randomness, and slip distribution function having a spatial randomness, temporal randomness generating a sliding time function with the sliding seek slide down per minor fault based on the distribution function and sliding function of time, based on the slip of each of the minor fault, the epicenter seeking seismic moment tensor for each minor fault A source function generation means for obtaining a function;
The ground model is composed of layered ground, ground density, inhomogeneous correlation length of ground lame constants, and random crustal ground given randomness by setting perturbation parameters. A green function generating means for obtaining a green function which is a displacement response at the observation point when
Based on the Green function and the epicenter function, the ground motion calculation means by the small fault for calculating the ground motion at the observation point by each small fault,
Considering the time difference according to the failure process of the fault, taking the sum total of the ground motion at the observation point in each small fault, the ground motion calculation means by the whole fault to obtain the ground motion at the observation point reflecting the failure process of the whole fault,
An earthquake motion prediction calculation system comprising: an output display means for the calculation result. In the computer in the ground motion prediction calculation system using the ground model and the hypocenter model,
A data input procedure for inputting the parameters necessary for setting the ground model and the hypocenter model and the data necessary for setting the conditions for the prediction calculation,
As source model, dividing the fault plane into a plurality of small faults, time for each minor fault, Chi lifting spatial randomness, and slip distribution function having a spatial randomness, temporal randomness And generating a slip time function, obtaining a slip for each small fault based on the slip distribution function and the slip time function, and determining a seismic moment tensor for each small fault based on the slip for each small fault A source function generation procedure for
The ground model is composed of layered ground, random crust ground given randomness by input of ground density, inhomogeneous correlation length of ground lame constant and perturbation parameter, and unit of each small fault Green function generation procedure to obtain the Green function which is the displacement response at the observation point when the hypocenter is given,
Based on the Green function and the hypocenter function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault,
Considering the time difference according to the failure process of the fault, taking the sum of the ground motion at the observation point in each small fault, calculating the ground motion by the whole fault to obtain the ground motion at the observation point reflecting the failure process of the whole fault,
A computer-readable recording medium storing a program for executing the calculation result output display procedure. In the computer in the ground motion prediction calculation system using the ground model and the hypocenter model,
A data input procedure for inputting the parameters necessary for setting the ground model and the hypocenter model and the data necessary for setting the conditions for the prediction calculation,
As a hypocenter model, the fault plane is divided into a plurality of small faults, and each small fault has temporal and spatial randomness, and has a slip distribution function with spatial randomness and temporal randomness. A slip time function is generated, a slip for each small fault is obtained based on the slip distribution function and the slip time function, and a seismic moment tensor is obtained for each small fault based on the slip for each small fault, and the source function is obtained. A source function generation procedure to be obtained;
The ground model is composed of layered ground, ground density, inhomogeneous correlation length of ground lame constants, and random crustal ground given randomness by setting perturbation parameters. Green function generation procedure to obtain the Green function that is the displacement response at the observation point when
Based on the Green function and the hypocenter function, the ground motion calculation procedure by the small fault that calculates the ground motion at the observation point by each small fault,
Considering the time difference according to the failure process of the fault, taking the total of the ground motion at the observation point in each small fault, and calculating the ground motion by the whole fault to obtain the ground motion at the observation point reflecting the failure process of the whole fault,
A program for executing the calculation result output display procedure.

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