A Fast Approximation Algorithm for Housner's Spectral Intensity
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摘要: Housner谱烈度及修正谱烈度作为基于加速度记录时程直接得到的地震动强度参数，与建筑结构破坏及地震宏观烈度存在较高的相关性，是可靠的地震仪器烈度物理参数指标。然而，相对于地面加速度峰值、地面速度峰值等地震动峰值参数，三分量加速度记录对应的谱烈度计算过程较为复杂，耗时相对较长，影响了利用谱烈度确定地震仪器烈度的时效性。基于对强震动加速度记录的统计分析，本文提出了谱烈度的快速近似算法，仅计算4个方向上的谱烈度值，采用其中3点作圆即可获得水平面内谱烈度迹线的近似最大值，使计算速度提高了45倍，且保持了谱烈度作为地震仪器烈度物理指标的精度。利用在汶川MS 8.0地震等386次MS > 3.0地震中获取的2701组强震动加速度记录，经可靠性检验，结果表明所提出的Housner谱烈度快速近似算法的计算误差在±4.5%以内，可以同时满足地震仪器烈度速报的可靠性和时效性需求。Abstract: As a parameter of ground motion strength derived directly from acceleration records, Housner's spectral intensity and its modified version are highly correlated to building destructure and seismic intensity, and has been adopted as a reliable metric of instrumental seismic intensity. But the algorithm for Housner spectum intensity of a three-component acceleration record was relatively complicated than that of peak ground motion parameter such as peak ground acceleration and peak ground velocity, and this defect of time consuming severely influences the timeliness in instrumental seismic intensity determination. Base on the analyses and ststistics of strong-motion acceleration records, a fast calculating algorithm for spectral intensity is proposed, which obtained the approximate value of the maximum spectral intensity value in the horizontal plane by circle fitting of three points among the spectral intensity values in 4 certain directions. The calculation speed of this algorithm is 45 times higher than that of former algorithms, and the precision accuracy of spectral intensity as a metric of instrumental seismic intensity does not decrease. The reliability testing using 2701 sets of acceleration records in 386 MS > 3.0 earthquakes including Wenchuan MS 8.0 eartuquake indicated that the relative error of this fast calculating algorithm is less than 4.5%, which can satisfied the needs of reliability and timeliness for the rapid report of seismic intensity.
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图 1 谱烈度计算方法（以汶川地震绵竹清平台记录为例）
Figure 1. Calculation method for Housner spectum intensity at station 051MZQ in the Wenchuan earthquake
图 2 谱烈度迹线统计特征
Figure 2. Statistical characteristics for the trace of Housner spectum intensity in the horizontal plane
图 3 加速度记录谱烈度快速算法
Figure 3. Fast calculating algorithm for Housner spectum intensity of a three-component acceleration record
图 4 加速度记录谱烈度快速算法可靠性
Figure 4. Reliability of fast calculating algorithm for Housner spectum intensity
表 1 算法可靠性验证所用强震动记录的数量统计
Table 1. Acceleration records used in reliability veritification of fast calculating algorithm for Housner spectum intensity
震级 PGA/cm·s－2 PGA＜3 3≤PGA＜10 10≤PGA＜30 30≤PGA＜100 100≤PGA＜300 300≤PGA＜500 PGA≥500 MS＝8.0 64 135 132 64 44 6 5 MS＝7.0 20 39 31 21 7 5 3 MS＝6.5 26 31 11 3 2 1 6.0≤MS＜6.5 21 84 76 29 7 5.5≤MS＜6.0 29 103 65 40 8 1 5.0≤MS＜5.5 36 201 89 31 6 4.5≤MS＜5.0 74 270 119 27 3 4.0≤MS＜4.5 96 296 145 30 7 3.0≤MS＜4.0 18 84 43 13 
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