JP3766513B2 - Seismic motion prediction method and recording medium recording seismic motion prediction program - Google Patents
Seismic motion prediction method and recording medium recording seismic motion prediction program Download PDFInfo
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Description
【０００１】
【発明の属する技術分野】
本発明は、小地震の地震動を利用した大地震の地震動の予測に関するものである。
【０００２】
【従来の技術】
従来、小地震の地震動を利用して大地震の地震動を予測する方法は、半経験的地震動予測方法として行われている。例えば、断層モデルとして図１１を仮定し、また、大地震と小地震との関係として図１２を仮定して、大地震の地震動を予測する。ただし、大地震と小地震のスリップ速度関数に図１３の（Ａ）のハスケルモデルを仮定し、スリップの補正を行う（例えば、入倉孝次郎・村松郁栄（１９８２年）：小地震の震動記録を用いて大地震の震動波形を予測する方法、自然災害資料解析９、ｐｐ．１２４−１３７参照）。
【０００３】
ハスケルモデルを仮定すると、予測した大地震の地震に図１４の（Ａ）のスリップ補正関数が組み込まれる。このスリップ補正関数は、図１４の（Ａ）に示すように、やや長周期領域でスペクトル振幅に落ち込みが生じ、短周期領域でノイズが生じる。
【０００４】
そこで、本願発明者である小嶋は（例えば、小嶋英治（１９９５年）：半経験的地震動予測法の検討−その１０ やや長周期地震動のためのスリップ補正関数（その２）−、日本建築学会、ｐｐ．２８１−２８２参照）、すべての小領域でスリップが同じと仮定すると共に、大地震（又は、小地震）の断層を１質点系の過減衰でモデル化し、指数関数的に減少するスリップ速度関数を図１３の（Ｂ）のように構築し、大地震と小地震とのスリップ補正関数を図１４の（Ｂ）として提案した。
【０００５】
そして、一般に、地震動は、ω-2モデルに添うと言われており、このω-2モデルのスリップ補正関数は、長周期領域で大地震と小地震とのスリップ量の比（断層の大地震と小地震とのスベリ量の比）がＮkであり、短周期領域では１となると言われている。小嶋の提案したスリップ補正関数は、図１４の（Ｂ）からω-2モデルに合致しているので、実際の地震動をよく表していると考えられる。
【０００６】
【発明が解決しようとする課題】
＜イ＞本発明は、従来のモデルを発展させ、観測に合ったモデルを提案することにある。
＜ロ＞本発明は、長周期成分の変動を考慮することにある。
＜ハ＞本発明は、短周期成分の変動を考慮することにある。
【０００７】
【課題を解決するための手段】
本発明は、大地震の断層を小地震の断層とほぼ同じ面積に分割し、小地震の地震動、小領域の距離減衰の補正、及びスリップ補正関数から大地震の地震動を予測する方法において、スリップ補正関数は、時間の経過と共に変動しながら指数関数的に減少するように表現した小領域のスリップ速度を用いて算出され、地震動の周波数成分に変動を持たせることを特徴とする、地震動予測方法にある。又は、本発明は、大地震の断層を小地震の断層とほぼ同じ面積に分割し、小地震の地震動、小領域の距離減衰の補正、及びスリップ補正関数から大地震の地震動を予測するプログラムを記録した記録媒体において、スリップ補正関数は、時間の経過と共に変動しながら指数関数的に減少するように表現した小領域のスリップ速度を用いて算出され、地震動の周波数成分に変動を持たせることを特徴とする、地震動予測のプログラムを記録した記録媒体にある。
【０００８】
【発明の実施の形態】
以下、図面を用いて本発明の実施の形態を説明する。
＜イ＞半経験的地震動予測方法の概要
小嶋は、大地震の断層を小地震の断層と同じ面積に分割し、観測された小地震の地震動、小領域の距離減衰の補正、放射特性の補正、及びスリップ補正関数からなる下記の数１の式のモデルで大地震の地震動を予測した（例えば、前記小嶋の文献（１９９５年）参照）。
【０００９】
【数１】
本発明は、このモデルを利用して、スリップ速度に変動を持たせ、小領域のスリップの初期速度などにおいてバラツキを考慮し、また、スリップの停止を行って、実際の地震動に適合するモデルを得る。
【００１１】
＜ロ＞小領域のスリップの初期速度などにおいてバラツキを考慮する
スリップ速度が時間の経過と共に、指数関数的に減少するモデルで、大地震の振動領域を細分化した小領域の地震動に図１のようなバラツキを持たせる。
【００１２】
このバラツキによって、各小領域の地震動のスリップ補正関数が以下の数２〜数４の式で表せられる。なお、これらの関数は数値計算によりコンピュータで算出する。
【００１３】
【数２】
【数３】
【数４】
このバラツキにより、スリップ補正関数を数値計算によりコンピュータで算出すると、図２のように低い周波数成分にバラツキが発生し、実際の地震動をシミュレートすることができる。
【００１７】
＜ハ＞スリップ速度の変動
各小領域のスリップが指数関数的に減衰し、スリップ速度が変動する場合、例えば、バラツキを持って（各小領域毎に停止時間が異なって）途中で停止する場合を検討する。図３のように、ある小領域においてスリップ速度関数を図４のように途中で停止する。このようにスリップが途中で停止した場合の周波数を横軸とした（周波数成分の）スリップ速度関数は、下記の数５〜数６の式で表すことができる。なお、数５の式の中のlmξ（ｔ）及び数６の式は、スリップ速度が一様でなく、変動を示す関数であり、一例として、停止をした場合を示している。数５の式において、Gｖ（ｔ）は、小領域でスリップ速度関数が一定と仮定した場合であり、数３の式のlmｖ（ｔ）でlmκが１の場合の大地震の断層のスリップ速度関数を表し、また、数３の式Gｈ、Sｈを充分大きく取り、Gω、Sωを充分小さくする。ここで、２Gｈ×Gωは大地震のスリップコーナ周波数で、２Sｈ×Sωは小地震のスリップコーナ周波数である。
【００１８】
【数５】
【数６】
この関数を数値計算によりコンピュータで算出すると、図５のようにスリップ速度関数の低い周波数成分及び高い周波数成分に変動が生じ、実際の地震動に適合させることができる。なお、図５は、ある小領域を対象にしているので、低い周波数成分において、スリップ補正関数の値は、lmＤであるが、他の小領域では、別の値になり、小領域毎に変動が生じている。
【００２１】
＜ニ＞スリップの一時停止
ある小領域のスリップが指数関数的に減衰し、途中で停止し、その後、スリップが再開する場合（一時停止の場合）を検討する。各小領域毎に停止までの時間にバラツキを持たせたり、一時停止から再開するまでの一時停止の時間にバラツキを持たせたり、また、再開するスリップ速度にバラツキを持たせることができる。図３では、スリップ速度関数を図６のように途中で一時停止し、その後、停止した時の速度で、直ちに（例えば、地震動のサンプリング時間Δｔの後に）スリップを再開する場合のスリップ補正関数は、数７の式で表すことができる。なお、停止から再開までの時間をΔｔに取ったことは、コンピュータにる数値計算に際して、最小の時間としてサンプリング時間Δｔとしたからであり、任意の時間とすることができる。
【００２２】
【数７】
この関数を数値計算によりコンピュータで算出すると、図８のようにスリップ速度関数の高い周波数成分に変動が生じ、実際の地震動に適合させることができる。それ故、スリップ補正関数は、図９のように高い周波数成分に変動が生じ、実際の地震動に合致する。
【００２４】
以上のモデルを例えば図１０のようなプログラムの流れ図に従って、コンピュータで数値計算により簡単に算出することができる。先ず、大地震の断層モデルの諸元（マグニチュード、断層の大きさ、断層に位置座標、断層の傾き等）を読み込み（Ｓ１）、次に、小地震の地震諸元（マグニチュード、震源の位置座標等）を読み込み（Ｓ２）、サンプリングした小地震の地震動Sｇ（ｔ）を読み込み（Ｓ３）、大地震の断層を分割した各領域の位置座標などを計算し（Ｓ４）、次に各ステップＳ５〜Ｓ８で数１〜数６（又、数７）の式を計算して、大地震の地震動Gｇ（ｔ）を求める。このようにして、大地震の地震動を小地震の地震動から予測することができる。
【００２５】
【発明の効果】
本発明は、次のような効果を得ることができる。
＜イ＞小領域のスリップの初期速度にバラツキを持たせることにより、実際の地震動のように長周期成分に変動を生じる。
＜ロ＞スリップの停止により、実際の地震動における短周期成分および長周期成分に変動を生じる。
＜ハ＞スリップの一時停止により、実際の地震動における短周期成分に変動を生じる。
【図面の簡単な説明】
【図１】断層を分割した小領域のスリップの初速度にバラツキを持たせた説明図
【図２】初速度にバラツキを持たせた小領域の時間領域のスリップ補正関数の説明図
【図３】指数関数的に減少する時間領域のスリップ速度関数の説明図
【図４】スリップを途中で停止した小領域の時間領域のスリップ速度関数の説明図
【図５】スリップを途中で停止した小領域の周波数領域のスリップ速度関数の説明図
【図６】スリップを一時停止した小領域の時間領域のスリップ速度関数の説明図
【図７】一時停止を表す時間の関数
【図８】スリップを一時停止した小領域の周波数領域のスリップ速度関数の説明図
【図９】スリップを一時停止した小領域の周波数領域のスリップ補正関数の説明図
【図１０】大地震の地震動を予測するプログラムの流れ図
【図１１】地震の断層モデルの説明図
【図１２】大地震と小地震との関係を示す説明図
【図１３】ハスケルと小嶋との大地震（又は小地震）の時間領域のスリップ速度関数の説明図
【図１４】ハスケルと小嶋との周波数成分のスリップ補正関数の説明図[0001]
BACKGROUND OF THE INVENTION
The present invention relates to prediction of ground motion of a large earthquake using ground motion of a small earthquake.
[0002]
[Prior art]
Conventionally, a method for predicting a ground motion of a large earthquake using a ground motion of a small earthquake has been performed as a semi-empirical ground motion prediction method. For example, assuming FIG. 11 as a fault model and assuming FIG. 12 as a relationship between a large earthquake and a small earthquake, the ground motion of a large earthquake is predicted. However, slip correction is performed by assuming the Haskel model shown in Fig. 13 (A) as the slip velocity function for large earthquakes and small earthquakes (for example, Kojiro Irikura and Tokuei Muramatsu (1982)). Method for predicting the seismic waveform of a large earthquake using natural disaster data analysis 9, pp. 124-137).
[0003]
Assuming the Haskell model, the slip correction function shown in FIG. 14A is incorporated in the predicted large earthquake. In this slip correction function, as shown in FIG. 14A, the spectral amplitude drops slightly in the long period region, and noise occurs in the short period region.
[0004]
Therefore, Kojima who is the inventor of the present application (for example, Eiji Kojima (1995): Examination of semi-empirical earthquake motion prediction method-Part 10: Slip correction function for slightly long-period ground motion (Part 2)-, Architectural Institute of Japan, pp. 281-282), assuming that the slip is the same in all small regions, and modeling a large earthquake (or small earthquake) fault with one mass overdamping, exponentially decreasing slip velocity A function was constructed as shown in FIG. 13B, and a slip correction function between a large earthquake and a small earthquake was proposed as FIG. 14B.
[0005]
In general, the ground motion is said to follow the ω- 2 model, and the slip correction function of this ω- 2 model is the ratio of the slip amount between a large earthquake and a small earthquake in a long period region (a large earthquake on a fault). The ratio of the amount of slip to the small earthquake is N k , and is said to be 1 in the short period region. The slip correction function proposed by Kojima agrees with the ω- 2 model from Fig. 14B, and is considered to represent the actual earthquake motion well.
[0006]
[Problems to be solved by the invention]
<A> The present invention is to develop a conventional model and propose a model suitable for observation.
<B> The present invention is to consider fluctuations in long-period components.
<C> The present invention is to consider fluctuations in short-period components.
[0007]
[Means for Solving the Problems]
The present invention divides a tomographic large earthquakes in approximately the same area as the fault of the small earthquakes, ground motion of small earthquakes, a method for predicting the ground motion of large earthquakes from the correction, and slip correction function of the distance attenuation of the small regions, the slip The correction function is calculated using the slip velocity of a small area expressed so as to decrease exponentially while changing with the passage of time. Is in the way . Alternatively, the present invention divides a large earthquake fault into almost the same area as a small earthquake fault, and a program for predicting a large earthquake ground motion from a small earthquake ground motion, a small area distance attenuation correction, and a slip correction function. In the recorded recording medium, the slip correction function is calculated using the slip velocity of a small area expressed so as to decrease exponentially while changing with the passage of time , and the frequency component of the seismic motion should be changed. It is in the recording medium which recorded the program of earthquake motion prediction characterized by these.
[0008]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
<B> Outline of semi-empirical ground motion prediction method Kojima divides a large earthquake fault into the same area as a small earthquake fault, and corrects the observed small earthquake ground motion, small area distance attenuation, and correction of radiation characteristics. And the ground motion of a large earthquake was predicted with a model of the following
[0009]
[Expression 1]
The present invention makes use of this model to vary the slip speed, consider variations in the initial speed of the slip in a small area, etc., and stop the slip to fit a model that matches the actual earthquake motion. obtain.
[0011]
<B> A model in which the slip speed taking into account variations in the initial speed of a small area slip, etc. decreases exponentially with time. Give such a variation.
[0012]
Due to this variation, the slip correction function of the ground motion in each small region can be expressed by the following equations (2) to (4). These functions are calculated by a computer by numerical calculation.
[0013]
[Expression 2]
[Equation 3]
[Expression 4]
Due to this variation, when the slip correction function is calculated by a computer by numerical calculation, variation occurs in low frequency components as shown in FIG. 2, and actual earthquake motion can be simulated.
[0017]
<C> Fluctuation of slip speed When the slip of each small area decays exponentially and the slip speed fluctuates, for example, when stopping in the middle with variation (stop time differs for each small area) To consider. As shown in FIG. 3, the slip speed function is stopped halfway as shown in FIG. 4 in a small area. Thus, the slip speed function (of the frequency component) with the frequency when the slip is stopped in the middle as a horizontal axis can be expressed by the following equations (5) to (6). Note that lm ξ (t) and Equation 6 in Equation 5 are functions in which the slip speed is not uniform and shows fluctuation, and as an example, shows a case of stopping. In the number 5 of the formula, G v (t) is the case where the slip velocity function in a small area is assumed to be constant, the fault by the number 3 in the formula of lm v (t) lm κ is large earthquakes in the case of 1 In addition, the equations G h and S h in Equation 3 are sufficiently large, and G ω and S ω are sufficiently small. Here, 2 G h × G ω is a slip corner frequency of a large earthquake, and 2 S h × S ω is a slip corner frequency of a small earthquake.
[0018]
[Equation 5]
[Formula 6]
When this function is calculated by a computer by numerical calculation, the low frequency component and the high frequency component of the slip speed function change as shown in FIG. 5 and can be adapted to the actual earthquake motion. Since FIG. 5 is intended for a certain small region, the slip correction function value is lm D in a low frequency component, but in other small regions, the value is different, and for each small region, There are fluctuations.
[0021]
<D> Slip temporary stop A case where a slip in a small area attenuates exponentially, stops halfway, and then resumes (in the case of temporary stop) is considered. It is possible to vary the time to stop for each small area, to vary the pause time from suspension to resumption, and to vary the slip speed to resume. In FIG. 3, the slip correction function in the case where the slip speed function is temporarily stopped as shown in FIG. 6 and then the slip is restarted immediately (for example, after the ground motion sampling time Δt) at the speed at which the slip was stopped is as follows. , And can be expressed by the equation (7). The reason why the time from the stop to the restart is Δt is that the sampling time Δt is set as the minimum time in the numerical calculation by the computer, and can be set to an arbitrary time.
[0022]
[Expression 7]
When this function is calculated by a computer by numerical calculation, the high frequency component of the slip speed function varies as shown in FIG. 8, and can be adapted to the actual earthquake motion. Therefore, the slip correction function varies in the high frequency component as shown in FIG. 9, and matches the actual earthquake motion.
[0024]
The above model can be easily calculated by numerical calculation with a computer in accordance with a flow chart of a program as shown in FIG. 10, for example. First, the specifications of the fault model (magnitude, fault size, fault coordinates, fault slope, etc.) of the large earthquake are read (S1). etc.) reads (S2), sampled read the small earthquakes ground motion S g (t) has (S3), and calculates and position coordinates of each area obtained by dividing a tomographic large earthquakes (S4), then the step S5 In S8,
[0025]
【The invention's effect】
The present invention can obtain the following effects.
<I> By varying the initial speed of slip in a small area, the long-period component varies as in actual earthquake motion.
<B> Stopping the slip causes fluctuations in short-period components and long-period components in actual earthquake motion.
<C> Suspension of slip causes fluctuations in short-period components in actual earthquake motion.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram in which the initial speed of a slip in a small area obtained by dividing a fault is varied. FIG. 2 is an explanatory diagram of a time domain slip correction function in which the initial speed is varied. ] Explanatory diagram of the slip speed function in the time domain decreasing exponentially [FIG. 4] Explanatory diagram of the slip speed function in the time domain of the small area where the slip was stopped halfway [FIG. 5] Small area where the slip was stopped midway Fig. 6 is an explanatory diagram of the slip velocity function in the frequency domain of Fig. 6. Fig. 6 is an explanatory diagram of the slip velocity function in the time domain of the small region where the slip is paused. Fig. 7 is a function of time representing the pause. Fig. 9 is an explanatory diagram of the slip velocity function in the frequency region of the small region. Fig. 9 is an explanatory diagram of the slip correction function in the frequency region of the small region where the slip is temporarily stopped. 11] Explanatory diagram of earthquake fault model [Fig. 12] Explanatory diagram showing the relationship between large earthquakes and small earthquakes [Fig. 13] Description of slip velocity function in the time domain of large earthquakes (or small earthquakes) between Haskell and Kojima FIG. 14 is an explanatory diagram of a slip correction function of frequency components between Haskell and Kojima.
Claims (10)
スリップ補正関数は、時間の経過と共に変動しながら指数関数的に減少するように表現した小領域のスリップ速度を用いて算出され、地震動の周波数成分に変動を持たせることを特徴とする、地震動予測方法。 In a method of dividing a large earthquake fault into almost the same area as a small earthquake fault, and predicting the ground motion of a large earthquake from the ground motion of a small earthquake, the correction of distance attenuation in a small area, and the slip correction function ,
The slip correction function is calculated using the slip velocity of a small area expressed so as to decrease exponentially while changing with the passage of time. Prediction method.
該スリップ速度の変動として、各小領域の初期のスリップ速度にバラツキを持たせ、地震動の低い周波数成分に変動を持たせることを特徴とする、地震動予測方法。 The earthquake motion prediction method according to claim 1,
A seismic motion prediction method, characterized in that the initial slip speed of each small region is varied as the slip speed variation, and the low frequency component of the seismic motion is varied.
該スリップ速度の変動として、小領域のスリップが、途中で停止することを特徴とする、地震動予測方法。 The earthquake motion prediction method according to claim 1,
A method for predicting ground motion, wherein a slip in a small area stops halfway as the fluctuation of the slip speed .
小領域の停止したスリップが再開することを特徴とする、地震動予測方法。In the earthquake motion prediction method according to claim 3,
A method for predicting ground motion, characterized by resuming a stopped slip in a small area.
小領域の停止したスリップは、初期速度が停止時のスリップ速度として再開することを特徴とする、地震動予測方法。In the earthquake motion prediction method according to claim 4,
A method for predicting ground motion, wherein an initial speed of a stopped slip in a small area is resumed as a slip speed at the time of stopping.
スリップ補正関数は、時間の経過と共に変動しながら指数関数的に減少するように表現した小領域のスリップ速度を用いて算出され、地震動の周波数成分に変動を持たせることを特徴とする、地震動予測のプログラムを記録した記録媒体。 In a recording medium that records a program that predicts the earthquake motion of a large earthquake from a large earthquake fault divided into almost the same area as a small earthquake fault, small earthquake ground motion, small area distance attenuation correction, and slip correction function ,
The slip correction function is calculated using the slip velocity of a small area expressed so as to decrease exponentially while changing with the passage of time. A recording medium on which a prediction program is recorded.
該スリップ速度の変動として、各小領域の初期の該スリップ速度にバラツキを持たせ、地震動の低い周波数成分に変動を持たせることを特徴とする、地震動予測のプログラムを記録した記録媒体。 In the recording medium which recorded the program of earthquake motion prediction of Claim 6 ,
As the fluctuation of the slip speed, the initial of the slip speed of the small area to have a variation, characterized in that to have a variation in the low frequency components of the ground motion, the recording medium having recorded thereon a program seismic hazard.
該スリップ速度の変動として、小領域のスリップが、途中で停止することを特徴とする、地震動予測のプログラムを記録した記録媒体。 In the recording medium which recorded the program of earthquake motion prediction of Claim 6 ,
A recording medium recording a seismic motion prediction program, characterized in that a slip in a small area stops halfway as the fluctuation of the slip speed .
小領域の停止したスリップが再開することを特徴とする、地震動予測のプログラムを記録した記録媒体。A recording medium recording the earthquake motion prediction program according to claim 8,
A recording medium on which a ground motion prediction program is recorded, characterized in that a slip in a small area is restarted.
小領域の停止したスリップは、初期速度が停止時のスリップ速度として再開することを特徴とする、地震動予測のプログラムを記録した記録媒体。In the recording medium which recorded the earthquake motion prediction program of Claim 9,
A recording medium on which a program for predicting earthquake motion is recorded, in which a slip in a small area is stopped, an initial speed is resumed as a slip speed at the time of stop.
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