JP4509837B2 - Early earthquake specifications estimation method and system - Google Patents

Early earthquake specifications estimation method and system Download PDF

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JP4509837B2
JP4509837B2 JP2005093906A JP2005093906A JP4509837B2 JP 4509837 B2 JP4509837 B2 JP 4509837B2 JP 2005093906 A JP2005093906 A JP 2005093906A JP 2005093906 A JP2005093906 A JP 2005093906A JP 4509837 B2 JP4509837 B2 JP 4509837B2
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洋光 中村
直泰 岩田
新二 佐藤
俊一 小高
公稔 芦谷
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Railway Technical Research Institute
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Description

本発明は、早期地震諸元推定方法に係り、特に、P波到達から1秒間のデータを用いて地震諸元(震央距離とマグニチュード)を推定する早期地震諸元推定方法及びそのシステムに関するものである。   The present invention relates to an early earthquake specification estimation method, and more particularly to an early earthquake specification estimation method and system for estimating an earthquake specification (epicenter distance and magnitude) using data for 1 second from arrival of a P wave. is there.

震央距離やマグニチュードを推定するために、本願発明者らは、既に、地震波の初動部分の波形形状をパラメータが数個の簡易な関数でフィッティングしてその波形形状を定量化し、得られたパラメータから震央距離とマグニチュードを推定することができる、震央距離及びマグニチュード推定方法を提案している(下記特許文献1,2参照)。
特開2002−277557号公報 特開2005−010041号公報
In order to estimate the epicenter distance and magnitude, the inventors of the present application have already fitted the waveform shape of the initial motion part of the seismic wave with a few simple functions to quantify the waveform shape, and from the obtained parameters can be estimated epicentral distance and magnitude proposes epicentral distance and Magunichu de estimation method (see below Patent documents 1 and 2).
JP 2002-277557 A JP 2005-010041 A

上記した地震諸元推定方法である関数フィッティング法を用いて、本願発明者らは、P波到達から2秒間のデータを使って地震諸元を推定することを提案していたが、直下型の地震などにおいては、さらなる早期の地震諸元推定方法が要望されるに至っている。
本発明は、上記状況に鑑みて、P波到達から1秒間のデータを用いて、さらに早く地震諸元の推定を的確に行うことができる早期地震諸元推定方法及びそのシステムを提供することを目的とする。
Using the function fitting method, which is the above-mentioned earthquake specification estimation method, the inventors of this application have proposed to estimate the earthquake specification using data for 2 seconds from the arrival of the P wave. In earthquakes and the like, an early method for estimating earthquake specifications has been demanded.
In view of the above situation, the present invention provides an early earthquake specification estimation method and system capable of accurately estimating an earthquake specification more quickly using data for 1 second after arrival of a P wave. Objective.

本発明は、上記目的を達成するために、
〔1〕早期地震諸元推定方法において、関数フィッティング法を用いて得られるP波初動振幅の時間変化の程度を表す係数Bの1秒間データ(1秒B)と、P波到達から1秒間の初期微動の最大振幅(1秒Amax )から、震央距離をlogΔ=αlog(1秒B)+βに基づいて、かつ、マグニチュードをM=αlog(1秒Amax )+βlog(1秒B)+γ+k(α、β、γは統計的に決める係数、kは0.5)に基づいて推定することを特徴とする。
In order to achieve the above object, the present invention provides
[1] In the early earthquake specifications estimation method, the 1-second data (1 second B) of the coefficient B representing the degree of temporal change of the P-wave initial motion amplitude obtained by using the function fitting method, and the 1-second data from the arrival of the P-wave From the maximum amplitude of the initial tremor (1 second A max ), the epicenter distance is based on log Δ = α log (1 second B) + β, and the magnitude is M = α log (1 second A max ) + β log (1 second B) + γ + k ( α, β, and γ are statistically determined coefficients, and k is estimated based on 0.5 ).

〕早期地震諸元推定システムにおいて、地震計と、この地震計からの情報により関数フィッティング法により1秒間のP波初動振幅の時間変化の程度を表す係数Bを演算する1秒間係数Bの演算部と、前記1秒間係数Bに基づいて震央距離を推定する震央距離の推定部と、P波到達から1秒の最大振幅(1秒Amax )を求める最大振幅の演算部と、前記最大振幅と前記1秒間係数Bと定数k=0.5とに基づいてマグニチュードを推定するマグニチュード推定部とを具備することを特徴とする。 [ 2 ] In the early earthquake specifications estimation system, the coefficient B for 1 second for calculating the coefficient B representing the degree of time change of the P wave initial motion amplitude for 1 second by the function fitting method based on the information from the seismometer and the seismometer A calculation unit, an epicenter distance estimation unit that estimates the epicenter distance based on the one-second coefficient B, a maximum amplitude calculation unit that obtains a maximum amplitude (1 second A max ) from the arrival of the P wave, and the maximum And a magnitude estimating unit for estimating a magnitude based on the amplitude, the one-second coefficient B, and the constant k = 0.5 .

本発明によれば、P波到達から1秒間のデータを用いて、直下型の地震諸元を素早く的確に推定し、それに伴う事故の被害を最小限に抑えることができる。   According to the present invention, it is possible to quickly and accurately estimate the specifications of a direct type earthquake using data for one second from the arrival of the P wave, and to minimize the damage caused by the accident.

本発明の早期地震諸元推定方法及びそのシステムは、関数フィッティング法を用いて得られるP波初動振幅の時間変化の程度を表す係数Bの1秒間データ(1秒B)と、P波到達から1秒間の初期微動の最大振幅(1秒Amax )から、震央距離をlogΔ=αlog(1秒B)+βに基づいて、かつ、マグニチュードをM=αlog(1秒Amax )+βlog(1秒B)+γ+k(α、β、γは統計的に決める係数、kは0.5)に基づいて推定する。よって、直下型の地震諸元を素早く的確に推定し、それに伴う事故の被害を最小限に抑える。 The early earthquake specification estimation method and system according to the present invention include 1 second data (1 second B) of coefficient B representing the degree of temporal change in P wave initial motion amplitude obtained using the function fitting method, and the arrival of the P wave. From the maximum amplitude (1 second A max ) of the initial tremor for 1 second, the epicenter distance is based on log Δ = α log (1 second B) + β, and the magnitude is M = α log (1 second A max ) + β log (1 second B) ) + Γ + k (α, β, γ are statistically determined coefficients, k is 0.5 ). Therefore, it will quickly and accurately estimate the specifications of the direct type earthquake and minimize the damage caused by the accident.

以下、本発明の実施の形態について詳細に説明する。
図1は本発明の実施例を示す早期地震諸元推定システムを示す図である。
この図において、1は地震計、2は定数kの入力部、3は情報処理装置、4は関数フィッティング法による1秒間のP波初動振幅の時間変化の程度を示す1秒間係数B(1秒B)の演算部、5はその1秒間係数B(1秒B)に基づいた震央距離の推定部、6はP波到達から1秒間の最大振幅Amax (1秒Amax )の検出部、7はそのP波到達から1秒間の最大振幅Amax (1秒Amax )と1秒間係数B(1秒B)と定数kとに基づいたマグニチュードの推定部、8は震央距離とマグニチュードの推定値の送信部、9はその震央距離とマグニチュードの推定値が送信される通信回線である。
Hereinafter, embodiments of the present invention will be described in detail.
FIG. 1 is a diagram showing an early earthquake specification estimating system showing an embodiment of the present invention.
In this figure, 1 is a seismometer, 2 is an input unit for a constant k, 3 is an information processing device, 4 is a 1-second coefficient B (1 second) indicating the degree of temporal change in P-wave initial motion amplitude for 1 second by the function fitting method. B) a calculation unit, 5 is an epicenter distance estimation unit based on the 1-second coefficient B (1 second B), 6 is a detection unit of the maximum amplitude A max (1 second A max ) for 1 second from the arrival of the P wave, 7 is a magnitude estimation unit based on the maximum amplitude A max (1 second A max ), 1 second coefficient B (1 second B) and a constant k from the arrival of the P wave, and 8 is an epicenter distance and magnitude estimation. A value transmission unit 9 is a communication line through which the epicenter distance and the estimated value of the magnitude are transmitted.

この早期地震諸元推定システムでは、まず、1秒間係数B(1秒B)の演算部4において、地震計1から得られる地震情報に基づいて、関数フィッティング法(上記特許文献1参照)を用いて、1秒間のP波初動振幅の時間変化の程度を示す1秒間係数B(1秒B)を演算する。次に、その求められた1秒間係数B(1秒B)に基づいて震央距離の推定部5で震央距離の推定を行う。一方、1秒間の最大振幅Amax (1秒Amax )の検出部6で、P波到達から1秒間の最大振幅Amax (1秒Amax )を求め、前記1秒間係数B(1秒B)と、定数kの入力部2から入力される定数kとに基づいてマグニチュードの推定部7でマグニチュードを推定する。そのようにして得られた震央距離の推定値とマグニチュードの推定値とは送信部8から通信回線9を介して地震情報センター(図示なし)へリアルタイムに送信される。 In this early earthquake specification estimation system, first, the function fitting method (see Patent Document 1 above) is used based on the earthquake information obtained from the seismometer 1 in the calculation unit 4 of the coefficient B (1 second B) for 1 second. Then, a 1-second coefficient B (1 second B) indicating the degree of time change of the P wave initial motion amplitude for 1 second is calculated. Next, the epicenter distance is estimated by the epicenter distance estimation unit 5 based on the obtained one-second coefficient B (1 second B). On the other hand, by the detection unit 6 of the maximum amplitude A max 1 second (1 sec A max), determine the maximum amplitude A max of one second from the P-wave arrival (second A max), said one second coefficient B (1 sec B ) And the constant k input from the constant k input unit 2, the magnitude estimation unit 7 estimates the magnitude. The estimated epicenter distance and magnitude estimated value thus obtained are transmitted from the transmitter 8 to the earthquake information center (not shown) via the communication line 9 in real time.

具体的な震央距離とマグニチュードの推定方法について説明する。
(1)震央距離の推定
関数フィッティング法に基づき、P波到達から1秒間のデータを下記式(1)に適用し、震央距離を推定する。
logΔ=αlog(1秒B)+β …(1)
ここで、α、βは統計的に決める係数である。
A specific epicenter distance and magnitude estimation method will be described.
(1) Estimation of epicenter distance Based on the function fitting method, the data for one second from the arrival of the P wave is applied to the following formula (1) to estimate the epicenter distance.
log Δ = α log (1 second B) + β (1)
Here, α and β are coefficients determined statistically.

(2)マグニチュードの推定
関数フィッティング法に基づき、P波到達から1秒間のデータを使って求めた係数B(1秒B)と1秒間の地震動の最大振幅(1秒Amax )から、マグニチュードを推定する。
M=αlog(1秒Amax )+βlog(1秒B)+γ …(2)
α、β、γは統計的に決める係数である。
(2) Magnitude estimation Based on the function fitting method, the magnitude is calculated from the coefficient B (1 second B) obtained using the data for 1 second from the arrival of the P wave and the maximum amplitude of ground motion (1 second A max ) for 1 second. presume.
M = α log (1 second A max ) + β log (1 second B) + γ (2)
α, β, and γ are statistically determined coefficients.

以下、震央距離とマグニチュードの推定について実際のデータを適用して説明する。
(1)震央距離の推定
従来の早期地震諸元推定方法(上記特許文献1,2)では、図2に概要を示すように、P波初動を下記式(3)にあてはめ、係数A,Bを求め、P波初動の振幅の増加率に対応する係数Bと震央距離の関係から、震央距離を推定する。
In the following, the epicenter distance and magnitude estimation will be described by applying actual data.
(1) Estimation of epicenter distance In the conventional early earthquake specifications estimation method (the above-mentioned patent documents 1 and 2), as shown in FIG. 2, the P wave initial motion is applied to the following equation (3), and coefficients A and B And the epicenter distance is estimated from the relationship between the coefficient B corresponding to the increase rate of the amplitude of the P wave initial motion and the epicenter distance.

y(t)=Bt×exp(−At) …(3)
ただし、tはP波到達時刻を0とする時間、係数A,Bは関数をあてはめることによって得られるパラメータである。
ここでは、P波到達から1秒間と2秒間のデータを使って求めた係数B(それぞれ1秒B、2秒Bと呼ぶ)と実際の震央距離の関係の比較を行い、1秒間のデータによる推定の精度を検証する。
y (t) = Bt × exp (−At) (3)
However, t is a time when the arrival time of the P wave is 0, and coefficients A and B are parameters obtained by fitting a function.
Here, the relationship between the actual epicenter distance is compared with the coefficient B (referred to as 1 second B and 2 seconds B, respectively) obtained using the data for 1 second and 2 seconds from the arrival of the P wave. Verify the accuracy of the estimation.

解析の対象としたデータは、気象庁の95型震度計で得られた強震記録のべ588観測点分である。地震のマグニチュード範囲は、M2.8〜M7.3である。
図3に1秒Bと2秒Bの震央距離との関係を示す。個々のデータについては、1秒B(△で示す)と2秒B(□で示す)に違いが見られるものの、全体の傾向としては、両者とも同様な震央距離と負の相関関係がある。なお、図3において、破線は下記式(4)を示している。
The data to be analyzed is a total of 588 observation points of strong motion records obtained with the Japan Meteorological Agency Type 95 seismometer. The magnitude range of the earthquake is M2.8 to M7.3.
FIG. 3 shows the relationship between the epicenter distance of 1 second B and 2 seconds B. Although there is a difference between 1 second B (indicated by Δ) and 2 seconds B (indicated by □) for individual data, the overall trend has a negative correlation with the epicenter distance. In FIG. 3, the broken line indicates the following formula (4).

次に、2秒Bから震央距離を推定するために作成した推定式を1秒Bに適用して推定した震央距離と実際の震央距離の差から、1秒Bでの推定精度を検証する。
2秒Bを用いた震央距離の推定式は次のように表せる。
logΔ=−0.498・log(2秒B)+1.965 …(4)
ただし、Δは推定震央距離(km)、2秒Bの単位はgal/sである。
Next, the estimation accuracy at 1 second B is verified from the difference between the epicenter distance estimated by applying the estimation formula created to estimate the epicenter distance from 2 seconds B to 1 second B and the actual epicenter distance.
The epicenter distance estimation formula using 2 seconds B can be expressed as follows.
log Δ = −0.498 · log (2 seconds B) +1.965 (4)
However, (DELTA) is an estimated epicenter distance (km) and the unit of 2 second B is gal / s.

そこで、上記式(4)の2秒Bの項に1秒Bの値を代入し、得られた推定震央距離の推定精度を図4に示す。対象とした588データのうちの約75%が、実際の震央距離の倍半分の範囲 (図4横軸の−0.3〜0.3の範囲)内にあり、2秒Bでの震央距離の推定精度とほぼ同等であることが分かる。
(2)マグニチュードの推定
マグニチュードの推定は、P波検測から1秒間の上下動の最大変位振幅 (1秒Amax と呼ぶ)と1秒Bを用いて、下記の統計式を用いて行う。
Accordingly, FIG. 4 shows the estimated accuracy of the estimated epicenter distance obtained by substituting the value of 1 second B into the 2 second B term of the above equation (4). About 75% of the target 588 data is within the range of half the actual epicenter distance (range of -0.3 to 0.3 on the horizontal axis in Fig. 4), and the epicenter distance at 2 seconds B It can be seen that the estimation accuracy is almost the same.
(2) Magnitude estimation Magnitude is estimated using the following statistical formula using the maximum displacement amplitude (referred to as 1 second A max ) and 1 second B of vertical movement for 1 second from P-wave measurement.

M=αlog(1秒Amax )+βlog(1秒B)+γ …(5)
ただし、Mは推定マグニチュード、1秒Amax はP波検測から1秒間の最大上下動変位(cm)、α、β、γは統計的に求める係数である。
図5に、震央距離と1秒Amax の関係をマグニチュードごとに示す。ここで、■はM(マグニチュード)7、▲はM6、◇はM5、▽はM4、□はM3である。
M = α log (1 second A max ) + β log (1 second B) + γ (5)
Where M is the estimated magnitude, 1 second A max is the maximum vertical displacement (cm) for 1 second from the P-wave detection, and α, β, and γ are statistically obtained coefficients.
FIG. 5 shows the relationship between the epicenter distance and 1 second A max for each magnitude. Here, ■ is M (magnitude) 7, ▲ is M6, ◇ is M5, ▽ is M4, and □ is M3.

マグニチュードごとにみると、震央距離が大きくなるにつれて(すなわち1秒Bが小さくなるにつれて)、1秒Amax は、ある程度ばらつきを持って小さくなる傾向がある。加えて、2秒後以降のマグニチュード推定用の統計式を用いた震央距離とAmax の関係〔下記式(6)〕を、図5に破線で示す。
M=0.7387・log(Amax )−1.02・log(B)+7.07 …(6)
ただし、図5において、係数1秒Bと震央距離の関係は上記式(4)を用いて換算している。
Looking at each magnitude, as the epicenter distance increases (that is, as 1 second B decreases), 1 second A max tends to decrease with some variation. In addition, the relationship between the epicenter distance and A max (the following equation (6)) using the statistical formula for magnitude estimation after 2 seconds is shown by a broken line in FIG.
M = 0.7387 · log (A max ) −1.02 · log (B) +7.07 (6)
However, in FIG. 5, the relationship between the coefficient 1 second B and the epicenter distance is converted using the above equation (4).

ここで、地震諸元推定の対象とする地震を、「被害を及ぼす可能性のあるマグニチュードの下限値であるM5.5以上で、1秒B≧1gal/sとすることで網羅できる震央距離30km以内の地震」とした場合の、上記式(6)を用いたマグニチュードの推定精度を図6に示す。上記の対象となるデータは588データ中22データであり、そのすべてのデータにおいてマグニチュードが過小評価されている。   Here, the earthquake that is the target of the earthquake specification estimation is “Earthquake distance 30 km that can be covered by setting M ≧ 5.5, which is the lower limit of the magnitude that may cause damage, and 1 second B ≧ 1 gal / s” FIG. 6 shows the magnitude estimation accuracy using the above equation (6) in the case of “inside earthquake”. The above data is 22 of 588 data, and the magnitude is underestimated in all the data.

これは、もともと上記式(6)に示す推定式が、P波検測から3秒間の上下動の最大変位とマグニチュードの関係から作成されたものであるためであり、データ数を更に増やしたとしてもこの過小評価の傾向は変わらないと考える。
しかし、図5で示したように1秒Amax の距離減衰の傾きは、上記式(6)と同様であることから、より高精度な1秒Amax によるマグニチュードの推定式は、下記のように上記式(6)の推定式に定数を足し合わせることで作成できる。
This is because the estimation formula shown in the above formula (6) was originally created from the relationship between the maximum vertical displacement for 3 seconds and the magnitude from the P-wave detection, and the number of data was further increased. However, the trend of underestimation is not changed.
However, as shown in FIG. 5, since the slope of the distance attenuation at 1 second A max is the same as that in the above equation (6), the magnitude estimation equation for 1 second A max with higher accuracy is as follows. Can be created by adding a constant to the estimation formula of the above formula (6).

M=0.7387・log(Amax )−1.02・log(B)+7.07+k(定数) …(7)
ここで、kは定数である。また、この定数は、図6の誤差の頻度分布からkを0.5とすることで、1秒間のデータによるマグニチュードの推定精度が高まる。
なお、本発明は上記実施例に限定されるものではなく、本発明の趣旨に基づいて種々の変形が可能であり、これらを本発明の範囲から排除するものではない。
M = 0.7387 · log (A max ) −1.02 · log (B) + 7.07 + k (constant) (7)
Here, k is a constant. In addition, with this constant, by setting k to 0.5 from the error frequency distribution in FIG. 6, the accuracy of estimating the magnitude based on the data for 1 second is increased.
In addition, this invention is not limited to the said Example, A various deformation | transformation is possible based on the meaning of this invention, and these are not excluded from the scope of the present invention.

本発明の早期地震諸元推定方法及びそのシステムは、直下型の地震にも対応可能な早期地震諸元推定方法として利用可能である。   The early earthquake specification estimation method and system of the present invention can be used as an early earthquake specification estimation method that can cope with a direct type earthquake.

本発明の実施例を示す早期地震諸元推定システムを示す図である。It is a figure which shows the early earthquake item estimation system which shows the Example of this invention. 関数フィッティング法の概要説明図である。It is an outline explanatory view of a function fitting method. 関数フィッティング法における係数B(1秒B,2秒B)と震央距離の関係を示す図である。It is a figure which shows the relationship between the coefficient B (1 second B, 2 second B) and epicenter distance in a function fitting method. 1秒Bによる震央距離の推定精度を示す図である。It is a figure which shows the estimation accuracy of the epicenter distance by 1 second B. FIG. 震央距離と1秒Amax の関係を示す図である。It is a figure which shows the relationship between epicenter distance and 1 second Amax . 推定式(6)によるマグニチュードの推定精度を示す図である。It is a figure which shows the magnitude | size estimation precision by an estimation formula (6).

1 地震計
2 定数kの入力部
3 情報処理装置
4 1秒間係数Bの演算部
5 1秒間係数Bに基づいた震央距離の推定部
6 P波到達から1秒間の最大振幅Amax の検出部
7 最大振幅Amax と1秒間係数Bと定数kとに基づいたマグニチュードの推定部
8 震央距離とマグニチュードの推定値の送信部
9 通信回線
DESCRIPTION OF SYMBOLS 1 Seismometer 2 Input part of constant k 3 Information processing device 4 Calculation part of coefficient B for 1 second 5 Estimation part of epicenter distance based on coefficient B for 1 second 6 Detection part of maximum amplitude A max for 1 second from arrival of P wave 7 Magnitude estimation unit based on maximum amplitude A max , 1-second coefficient B, and constant k 8 Epicenter distance and magnitude estimation value transmission unit 9 Communication line

Claims (2)

関数フィッティング法を用いて得られるP波初動振幅の時間変化の程度を表す係数Bの1秒間データ(1秒B)と、P波到達から1秒間の初期微動の最大振幅(1秒Amax )から、震央距離をlogΔ=αlog(1秒B)+βに基づいて、かつ、マグニチュードをM=αlog(1秒Amax )+βlog(1秒B)+γ+k(α、β、γは統計的に決める係数、kは0.5)に基づいて推定することを特徴とする早期地震諸元推定方法。 1 second data (1 second B) of coefficient B representing the degree of time change of the P wave initial motion amplitude obtained using the function fitting method, and the maximum amplitude (1 second A max ) of initial fine motion for 1 second from the arrival of the P wave. From the epicenter distance, log Δ = α log (1 second B) + β, and the magnitude M = α log (1 second A max ) + β log (1 second B) + γ + k (α, β, γ are coefficients that are statistically determined. , K is estimated based on 0.5 ). (a)地震計と、
(b)該地震計からの情報により関数フィッティング法により1秒間のP波初動振幅の時間変化の程度を表す係数Bを演算する1秒間係数Bの演算部と、
(c)前記1秒間係数Bに基づいて震央距離を推定する震央距離の推定部と、
(d)P波到達から1秒の最大振幅(1秒Amax )を求める最大振幅の演算部と、
(e)前記最大振幅と前記1秒間係数Bと定数k=0.5とに基づいてマグニチュードを推定するマグニチュード推定部とを具備することを特徴とする早期地震諸元推定システム。
(A) a seismometer;
(B) a calculation unit for a coefficient B for 1 second for calculating a coefficient B representing the degree of temporal change of the P wave initial motion amplitude for 1 second by the function fitting method based on information from the seismometer;
(C) an epicenter distance estimation unit for estimating an epicenter distance based on the one-second coefficient B;
(D) a maximum amplitude calculation unit for obtaining a maximum amplitude (1 second A max ) for 1 second from arrival of the P wave;
(E) Earthquake Early specification estimation system, characterized by comprising a magnitude estimator that estimates the magnitude based on the said maximum amplitude and said number engaging one second B and a constant k = 0.5.
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