Study on the Long-period Ground Motion Predicting Model for Interface and Intraslab Earthquakes in Subduction Zone
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摘要: 对海域地震区划中涉及的我国海域有影响的俯冲带地震动参数预测模型研究进展与阶段性成果进行介绍，基于资料、回归方法等，对地震动参数预测模型建立过程进行说明。依托可靠的强震加速度记录与宽频带速度记录，采用使结果更稳定的分步回归方法，考虑俯冲带深大地震断层尺度与震源深度影响选取新的预测模型。针对我国海域实际地震环境，新的预测模型重点关注了对俯冲带长周期地震动的估计。Abstract: The progress and periodical result for establishing ground motion predicting model for subduction earthquakes of China sea area is introduced. The developing procedures are briefly summarized through ground motion data, attenuation model and regression strategy. The study is based on reliable strong motion acceleration records and broad-band velocity data, using a more robust step-regression approach, and with a model considering both rupture scale and focal depth of subduction earthquakes. Special attention is fixed on the long-period spectral predicting base on the realistic earthquake situation for China sea area.
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Key words:
- Sea area /
- Seismic hazard map /
- Ground motion predicting model /
- Response spectral /
- Long-period
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引言
地震动参数预测模型（常称为衰减关系）的建立是地震动参数区划图编制的关键技术环节之一。我国陆域地震区划图编制已经历数代，逐渐完善发展。然而，对于广袤的海域，地震动参数区划仍需开展进一步研究工作。
目前，国内外多位研究者利用强震记录、数值模拟结果建立了全球性或区域性俯冲带地震动预测模型，如Atkinson等（2003）利用全世界范围内俯冲带强震记录建立了地震动预测模型（板缘、板内），并通过实际记录对比分析了该模型在Cascadia区域（华盛顿、北加拿大区域）与其他区域的适用性；Arango等（2012）对比了世界范围内多组俯冲带地震动预测模型在智利、中美洲俯冲带区域的适用性，并探讨了区域性差异及其在地震危险性分析中的影响；胡进军等(2013，2014)和郝彦春（2015）利用强震资料及数值模拟结果研究了俯冲带地震动衰减特性、局部场地效应等，并探讨了潜在地震对我国海域开发和建设的影响；Zhao等（2006，2016）利用日本、台湾等地俯冲带强震记录，采用H/V进行场地分类，建立了板内、板缘地震地震动预测模型。但以上研究针对的反应谱频段多限于周期为5～6 s，对长周期地震动的估计存在一定不足。
陆域地震动参数区划主要针对面大量广的民用建筑与一般性重大工程，而海域几乎不涉及民居，其中岛礁建筑、跨海大桥等长周期结构较多。我国海域地震环境存在特殊性，大部分海域远离俯冲带，除短周期地震动参数主要受陆域或近海海域高震级潜在震源区控制外，长周期地震动参数受远场俯冲带深大地震的影响不容忽视。考虑以上原因，本文进行俯冲带地震动参数预测模型建立时，重点关注了对反应谱长周期段的估计。
1. 总体思路
近年来，我国强震动观测数据虽得到快速积累，但仍缺乏海域强震资料。因此，根据实际情况，广泛收集与我国海域相似区域（日本东部俯冲带、琉球-冲绳俯冲带）地震记录，即从日本强震台网（K-net和Kik-net）收集了该区域基岩强震加速度资料，从国际地震学与地球内部物理学联合会（IASPEI）全球数字地震台网收集了该区域宽频带速度测震记录。建立地震动参数预测模型时，综合强震记录近场高频优势与测震记录远场低频优势，可较好地估计反应谱长周期段。
考虑与陆域区划和我国实际工程设计的衔接，建立俯冲带地震动参数预测模型时，使用阻尼比为5%的基岩水平向加速度反应谱（周期至10.0 s），地震震级采用面波震级，考虑断层尺度和震源深度的影响，距离参数采用断层距Rrup（场点至断层破裂面的最短距离）。
2. 地震资料与分类
2.1 俯冲带强震资料
除搜集琉球-冲绳俯冲带地震记录外，为弥补高震级地震的缺失，挑选具有较多高质量记录且地震活动性较高的日本东部俯冲带地震记录。为保证数据的可靠性，选用近年强震记录，数据获取时间为2000年1月1日至2020年7月1日。获取强震记录后，对其进行基线校正和截止频率0.025 Hz的高通滤波，并计算阻尼比为5%的加速度反应谱。采用人工检查的方式剔除信噪比较低或有明显错误的记录。加速度记录主要用于反应谱周期至1.0 s的短周期段预测模型的确定。
从全球CMT地震目录获取强震资料地震参数，包括震级、断层性质、震源深度等信息。采用面波震级作为统一震级标度，对于没有面波震级却有矩震级的地震，采用刘瑞丰（2015）震级转换公式计算面波震级。采用断层距作为距离参数，对于可在K-net、Kik-net网站查询到的有限断层模型地震，直接计算断层距；对于无法查询到有限断层模型的地震（大部分地震震级较低），采用震源距（场点至震源的距离）作为断层距，当距离较远时（大多数情况），二者差别较小。
采用Vs30（地表以下30 m内折算平均剪切波速）作为场地分类参考依据，采用Vs30超过500 m/s的记录作为基岩场地记录。
2.2 俯冲带测震资料
将宽频带数字测震记录作为速度记录，主要来自于IASPEI全球数字地震台网。该台网台站布设历史较长，记录器中速度平台型宽频带高增益BH信道具有较多记录，能够提供高质量的俯冲带远场记录，适用于长周期地震动研究。
挑选冲绳俯冲带与日本东部俯冲带宽频带速度记录，剔除井下或具有一定高程的记录，主要关注自由地表。获取记录后，与强震资料处理程序相同，完成基线校正和截止频率0.025 Hz的高通滤波，对其进行微分得到加速度时程。测震记录具有高增益特性，常存在近场限幅的情况。为保证资料的可靠性，采用人工检查的方式对信噪比较低、限幅或显著有误的记录进行剔除，然后计算阻尼比为5%的加速度反应谱。该部分速度记录主要用于确定反应谱周期超过1.0 s的长周期段预测模型。
震级与距离参数与强震资料的处理相同，对于场地分类，由于台站放置在基岩或基座上，可不考虑土层的影响。
2.3 板缘与板内地震分类
通过震源深度与震源机制确定板缘、板内地震分类，具体规则如下：
（1）对于震源深度为20～30 km浅壳地震，震源机制为逆断层，考虑俯冲带上缘与地壳之间无明显界限，将这部分地震归为板缘地震。
（2）对于震源深度为30～50 km的地震，归为板缘地震。考虑震源深度为50～70 km处，中深源和深源地震不存在明显界限，一般认为板缘地震震源机制为逆断层，因此，将震源深度为50～70 km且震源机制为逆或走滑断层的地震归为板缘地震。
（3）对于震源深度为50～70 km且震源机制为正断层的地震，归为板内地震。将震源深度超过70 km的地震也归为板内地震。
为完成预测模型的回归，选择面波震级Ms≥5.0、Rrup≤500 km的水平向地震记录进入板缘地震回归数据集；考虑板内地震震源深度较深，适当扩大距离范围，因此选取面波震级Ms≥5.0、Rrup≤600 km的水平向地震记录进入板内地震回归数据集。为增加统计样本量，同一台站2条水平向地震记录视为独立记录，强震资料、测震资料地震目录如表1～4所示，地震震中分布如图1所示。
表 1 强震资料地震目录（板缘地震）Table 1. Catalog of strong earthquakes records (Interface earthquakes)发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-10-03T04:13:30.490 40.282 143.124 5.7 33 2001-08-13T20:11:23.400 41.046 142.308 6.3 38 2001-10-02T08:19:49.460 37.739 141.775 5.2 43 2002-11-03T03:37:42.070 38.886 141.977 6.1 39 2003-09-25T19:50:06.360 41.815 143.910 8.1 27 2003-09-25T21:08:00.030 41.774 143.593 7.4 33 2003-09-29T02:36:53.140 42.450 144.380 6.3 25 2003-10-08T09:06:55.340 42.648 144.570 6.6 32 2003-12-29T01:30:54.700 42.423 144.613 5.9 33 2004-04-11T18:06:12.480 42.918 144.836 5.7 42 2004-09-01T02:49:28.610 36.959 141.607 5.1 35 2005-01-18T14:09:06.220 42.946 144.866 5.7 42 2005-03-11T18:47:36.690 43.085 144.674 5.0 54 2005-07-09T23:37:11.140 33.422 140.825 5.4 55 2005-08-16T02:46:28.400 38.276 142.039 6.8 36 2005-10-19T11:44:42.790 36.405 140.839 6.5 32 2005-12-02T13:13:09.520 38.089 142.122 6.3 29 2007-11-26T13:51:39.800 37.392 141.586 5.9 42 2008-05-07T16:45:18.700 36.164 141.526 6.8 27 2008-07-19T02:39:28.700 37.552 142.214 7.0 22 2008-09-11T00:20:50.920 41.892 143.754 7.0 25 2009-06-05T03:30:33.060 41.824 143.445 6.4 29 2010-03-14T08:08:03.960 37.745 141.590 6.5 32 2010-07-04T21:55:51.980 39.697 142.369 6.3 27 2011-03-09T02:45:20.330 38.435 142.842 7.3 32 2011-03-11T05:46:24.120 38.297 142.373 9.0 29 2011-03-11T06:15:40.280 36.281 141.111 6.8 43 2011-03-25T11:36:24.490 38.772 141.880 6.2 39 2011-04-07T14:32:43.290 38.276 141.588 7.1 42 2011-04-21T13:37:03.340 35.579 140.305 6.2 43 2011-07-10T00:57:10.800 38.034 143.264 7.0 23 2011-07-23T04:34:24.180 38.898 141.815 6.4 41 2011-07-24T18:51:25.070 37.730 141.390 6.3 40 2011-07-30T18:53:50.720 36.942 140.955 6.5 38 2011-08-19T05:36:33.040 37.671 141.652 6.3 47 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-11-24T10:25:34.030 41.898 142.639 6.2 38 2012-06-17T20:32:20.590 38.919 141.831 6.4 36 2012-12-07T08:18:23.130 37.890 143.949 7.3 31 2015-02-16T23:06:28.270 39.8558 142.8808 6.7 23 2015-05-12T21:12:58.890 38.9056 142.0317 6.8 35 2016-01-14T03:25:33.640 41.9723 142.7810 6.7 46 2018-01-24T10:51:19.090 41.1034 142.4323 6.3 31 2018-09-05T18:07:59.150 42.6861 141.9294 6.6 35 表 2 宽频带资料地震目录（板缘地震）Table 2. Catalog of broad-band records (Interface earthquakes)发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-06-10T18:23:29.320 23.843 121.225 6.2 33 2000-07-04T22:19:44.160 20.240 122.163 5.2 33 2000-07-16T03:21:45.530 20.253 122.043 6.3 33 2000-09-10T08:54:45.960 24.008 121.526 5.6 35 2000-10-03T04:13:30.490 40.282 143.124 5.7 33 2001-06-14T02:35:25.810 24.513 122.033 5.6 32 2001-08-13T20:11:23.400 41.046 142.308 6.3 38 2001-08-17T22:25:49.010 25.748 126.190 5.6 33 2002-03-26T03:45:48.700 23.346 124.090 6.6 33 2002-03-31T06:52:50.490 24.279 122.179 7.4 33 2002-05-13T19:57:22.900 19.132 121.238 5.3 33 2002-07-11T07:36:26.060 24.075 122.288 5.6 44 2002-11-03T03:37:42.070 38.886 141.977 6.1 39 2003-06-09T01:52:51.010 24.413 122.020 5.5 48 2003-06-10T08:40:30.830 23.520 121.628 5.7 45 2003-09-25T19:50:06.360 41.815 143.910 8.1 27 2003-09-25T21:08:00.030 41.774 143.593 7.4 33 2003-09-29T02:36:53.140 42.450 144.380 6.3 25 2003-10-08T09:06:55.340 42.648 144.570 6.6 32 2005-01-18T14:09:06.220 42.946 144.866 5.7 42 2005-08-16T02:46:28.400 38.276 142.039 6.8 36 2005-09-06T01:16:02.350 24.084 122.191 6.1 32 2005-10-19T11:44:42.790 36.405 140.839 6.5 32 2006-07-28T07:40:11.840 24.183 122.526 5.9 33 2007-01-25T10:59:17.650 22.564 121.926 6.0 36 2007-04-20T19:37:58.230 27.471 128.379 5.3 42 2007-09-06T17:51:26.190 24.340 122.219 6.2 53 2008-06-01T01:57:23.690 20.124 121.350 6.3 31 2008-07-08T07:42:10.730 27.532 128.334 6.0 43 2008-09-11T00:20:50.920 41.892 143.754 6.7 25 2009-06-05T03:30:33.060 41.824 143.445 6.4 29 2009-10-30T07:03:39.120 29.218 129.782 6.8 34 2009-12-19T13:02:15.570 23.796 121.605 6.4 43 2010-03-14T08:08:03.960 37.745 141.590 6.5 32 2010-07-04T21:55:51.980 39.697 142.369 6.3 27 2010-10-04T13:28:38.860 24.270 125.154 6.3 32 2011-03-09T02:45:20.330 38.435 142.842 7.3 32 2011-03-11T05:46:24.120 38.297 142.373 9.0 29 2011-03-11T06:15:40.280 36.281 141.111 6.8 43 2011-03-11T15:13:14.680 35.994 141.808 6.3 21 2011-03-25T11:36:24.490 38.772 141.880 6.2 39 2011-04-07T14:32:43.290 38.276 141.588 7.1 42 2011-04-21T13:37:03.340 35.579 140.305 6.2 43 2011-07-10T00:57:10.800 38.034 143.264 7.0 23 2011-07-23T04:34:24.180 38.898 141.815 6.4 41 2011-07-24T18:51:25.070 37.730 141.390 6.3 40 2011-07-30T18:53:50.720 36.942 140.955 6.5 38 2011-08-19T05:36:33.040 37.671 141.652 6.2 47 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-11-24T10:25:34.030 41.898 142.639 6.2 38 2012-06-09T21:00:18.070 24.572 122.248 5.9 70 2012-06-17T20:32:20.590 38.919 141.831 6.4 36 2012-12-07T08:18:23.130 37.890 143.949 7.3 31 2013-06-07T16:38:02.900 24.098 122.671 5.8 33 2013-10-25T17:10:19.710 37.1557 144.6611 7.1 35 2014-10-22T00:15:17.440 27.4158 128.5533 5.8 43 2015-02-13T20:06:32.330 22.6374 121.4270 6.2 30 2015-02-16T23:06:28.270 39.8558 142.8808 6.7 23 2015-05-12T21:12:58.890 38.9056 142.0317 6.8 35 2016-01-14T03:25:33.640 41.9723 142.7810 7.0 46 2016-12-26T01:23:37.880 19.1524 121.1743 5.2 34 2018-01-24T10:51:19.090 41.1034 142.4323 6.3 31 2018-09-05T18:07:59.150 42.6861 141.9294 6.6 35 2018-10-23T04:34:58.630 24.1153 122.6027 5.8 30 2018-10-23T16:04:04.240 23.9912 122.6791 5.7 31 2018-11-05T14:46:58.690 29.2376 130.5301 5.0 36 表 3 强震资料地震目录（板内地震）Table 3. Catalog of strong earthquakes records (Intraslab earthquakes)发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-06-03T08:54:49.200 35.552 140.464 5.6 62 2001-12-02T13:01:53.670 39.402 141.089 6.5 124 2002-04-03T23:42:12.810 41.543 141.851 5.3 71 2002-10-14T14:12:43.750 41.174 142.249 5.9 61 2003-05-26T09:24:33.400 38.849 141.568 6.9 68 2003-09-20T03:54:50.780 34.998 140.172 5.3 52 2007-04-18T15:07:31.600 42.658 141.861 5.0 120 2007-07-01T04:12:07.750 43.663 144.734 5.8 130 2008-07-23T15:26:19.950 39.802 141.464 6.8 108 2008-09-22T07:31:59.170 41.578 140.450 5.2 149 2009-02-28T00:35:56.700 42.610 142.104 5.0 105 2009-08-12T22:48:51.420 32.821 140.395 6.6 53 2010-03-13T12:46:26.380 37.594 141.299 5.2 77 2013-02-02T14:17:35.130 42.770 143.092 6.9 107 2013-11-03T05:25:15.340 35.9713 140.1213 5.1 77 2014-06-14T17:31:41.560 39.4384 140.9876 5.0 92 2015-07-09T18:32:51.220 40.3631 141.4646 5.0 81 2019-04-27T17:24:45.654 42.4547 142.8191 5.4 111 表 4 测震资料地震目录（板内地震）Table 4. Catalog of broad-band records (Intraslab earthquakes)发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-01-28T16:39:24.280 26.076 124.496 5.8 194 2000-06-03T08:54:49.200 35.552 140.464 5.6 62 2001-12-02T13:01:53.670 39.402 141.089 6.5 124 2003-05-26T09:24:33.400 38.849 141.568 6.9 68 2004-10-15T04:08:50.240 24.530 122.694 6.7 94 2005-10-15T15:51:08.130 25.309 123.351 6.4 192 2008-07-23T15:26:19.950 39.802 141.464 6.8 108 2008-09-09T07:43:13.320 24.666 122.570 5.0 102 2009-03-26T19:19:59.560 27.415 126.702 5.9 160 2009-08-12T22:48:51.420 32.821 140.395 6.6 53 2010-01-15T11:08:38.370 26.746 126.285 5.7 139 2011-11-08T02:59:08.510 27.324 125.621 6.9 225 2013-02-02T14:17:35.130 42.770 143.092 6.9 107 2013-09-06T11:33:53.520 20.1721 122.3193 6.0 175 2014-03-02T20:11:23.430 27.4312 127.3674 6.5 119 2014-12-10T21:03:39.260 25.5403 122.4503 6.1 256 2014-12-31T07:54:36.890 24.6707 122.5575 5.2 104 2016-03-14T07:03:17.710 29.8888 128.9567 5.5 211 2016-05-31T05:23:47.310 25.5615 122.5458 6.4 246 2017-04-30T01:57:22.160 21.2987 121.8285 5.2 106 2017-08-16T12:51:25.870 28.6737 127.9007 5.7 198 2019-02-17T20:36:56.890 20.6674 122.1168 5.0 169 板缘地震使用资料震级-断层距分布关系如图2所示，由图2可知，震级为6级以下时，由于断层距较远，导致加速度幅值过小或信噪比较低，多条中小震级地震记录被剔除，对回归产生一定影响。板内地震使用资料震级-断层距分布关系如图3所示，由图3可知，板内地震震级上限为7级，对高震级结果的约束性相对较弱。总体来看，宽频带资料较好地弥补了强震记录在远场的缺失，有利于长周期预测模型的建立。
图 2 板缘地震记录震级-断层距分布关系图Figure 2. Distribution of magnitude-distance of interface earthquakes
图 3 板内地震记录震级-断层距分布关系图Figure 3. Distribution of magnitude-distance of intraslab earthquakes3. 模型与回归方法
借鉴《中国地震动参数区划图》（GB 18306—2015）分段线性模型（高孟潭，2015）建立板缘地震动预测模型，对于板内地震，增加震源深度相关项，回归模型可统一写为：
$$ \left\{ \begin{array}{l}M<6.5{\text{时}},\\ \mathrm{lg}Y(M,R,T)={A}_{1}(T)+{B}_{1}(T)M-C(T)\mathrm{lg}(R+D{{\rm{e}}}^{EM})+\\ F\cdot h+\varepsilon \\ M\geqslant 6.5{\text{时}},\\ \mathrm{lg}Y(M,R,T)={A}_{2}(T)+{B}_{2}(T)M-C(T)\mathrm{lg}(R+D{{\rm{e}}}^{EM})+\\ F\cdot h+\varepsilon \end{array} \right.$$ (1) 式中，Y为反应谱值；M为面波震级；R为断层距；T为反应谱周期，当震源深度<70 km时，h=0，当震源深度为70～120 km时，h=震源深度－70 km，当震源深度>120 km时，h=50 km；ε为具有标准差σ的随机量，均值为0；其余参数由回归拟合得到。由于板缘地震震源深度<70 km，震源深度项对于板缘地震不起作用；对于板内地震，震源深度项可在一定程度上反映震级量规函数对震源深度的补偿，由于对深源地震的研究较少，人为设定线性关系在120 km震源深度处不再增长。
沿用与五代图相配套的分段回归方法（肖亮等，2010）进行预测模型回归，对每个周期点反应谱值进行回归，并对整体谱型进行适当光滑，得到完整的反应谱预测模型。由于俯冲带地震一般远离大陆，近场记录天然性较少，对直接回归近场饱和因子
$D{{\rm{e}}^{EM}}$ 造成较大困难。考虑$D{{\rm{e}}^{EM}}$ 主要反映断层破裂尺度信息，仅对近场区域有影响，因此，直接借用陆域回归结果，即D=0.956，E=0.462，其余参数由回归确定。4. 回归结果
对于阻尼比为5%的基岩水平向加速度反应谱，选取10.0 s范围内基本等对数间隔的30个点。强震记录用于短周期段（1.0 s前）的回归，宽频带速度记录用于长周期段（3.0 s后）的回归，对于1.5～3.0 s周期段，采用强震资料与宽频带速度资料混用的方式进行衔接，最终得到周期至10.0 s的长周期反应谱预测模型。板缘地震和板内地震预测模型相关参数分别如表5、6所示，相应的反应谱曲线（由下至上Ms=5、6、7、8级）如图4所示，周期6.0 s反应谱值随断层距的衰减曲线如图5所示（由下至上Ms=5、6、7、8级）。
表 5 板缘地震基岩水平向加速度反应谱预测模型相关参数Table 5. Coefficients of horizontal rock spectral acceleration prediction model for interface earthquakes周期/s A1 B1 A2 B2 C D E σ 0.01 1.812 0.555 2.339 0.474 1.935 0.956 0.462 0.377 0.04 1.746 0.573 2.445 0.465 1.929 0.956 0.462 0.378 0.05 1.960 0.581 2.856 0.443 1.990 0.956 0.462 0.376 0.07 2.342 0.559 3.277 0.416 2.018 0.956 0.462 0.381 0.10 2.432 0.562 3.303 0.428 2.044 0.956 0.462 0.374 0.12 2.455 0.558 3.232 0.438 2.045 0.956 0.462 0.365 0.16 2.569 0.526 2.871 0.480 2.025 0.956 0.462 0.358 0.20 2.549 0.508 2.596 0.501 1.993 0.956 0.462 0.353 0.24 2.412 0.510 2.480 0.500 1.946 0.956 0.462 0.339 0.26 2.361 0.497 2.307 0.505 1.897 0.956 0.462 0.334 0.30 2.316 0.495 2.134 0.523 1.897 0.956 0.462 0.329 0.34 1.980 0.515 1.966 0.518 1.817 0.956 0.462 0.326 0.40 1.684 0.539 1.735 0.532 1.781 0.956 0.462 0.325 0.50 1.344 0.571 1.535 0.542 1.757 0.956 0.462 0.325 0.60 1.105 0.588 1.206 0.572 1.738 0.956 0.462 0.342 0.80 0.592 0.643 0.878 0.600 1.731 0.956 0.462 0.348 1.00 −0.036 0.719 0.537 0.630 1.730 0.956 0.462 0.335 1.20 −0.325 0.744 0.182 0.666 1.734 0.956 0.462 0.334 1.50 −0.850 0.809 0.027 0.674 1.730 0.956 0.462 0.325 1.70 −1.000 0.819 −0.107 0.682 1.720 0.956 0.462 0.324 2.00 −1.410 0.860 −0.419 0.708 1.700 0.956 0.462 0.320 2.40 −1.610 0.860 −0.904 0.752 1.672 0.956 0.462 0.319 3.00 −1.891 0.873 −1.328 0.786 1.639 0.956 0.462 0.317 4.00 −2.091 0.858 −1.994 0.845 1.605 0.956 0.462 0.316 5.00 −2.484 0.885 −2.484 0.885 1.573 0.956 0.462 0.295 6.00 −2.903 0.917 −2.903 0.917 1.537 0.956 0.462 0.304 7.00 −3.273 0.945 −3.273 0.945 1.502 0.956 0.462 0.312 8.00 −3.546 0.963 −3.546 0.963 1.463 0.956 0.462 0.311 9.00 −3.800 0.977 −3.800 0.977 1.425 0.956 0.462 0.319 10.00 −4.099 1.000 −4.099 1.000 1.389 0.956 0.462 0.328 表 6 板内地震基岩水平向加速度反应谱预测模型的参数Table 6. Coefficients of horizontal rock spectral acceleration prediction model for intraslab earthquakes周期/s A1 B1 A2 B2 C D E F σ 0.01 3.541 0.516 3.639 0.501 2.442 0.956 0.462 0.008 0.377 0.04 3.652 0.506 3.678 0.502 2.440 0.956 0.462 0.008 0.377 0.05 3.679 0.525 3.881 0.494 2.471 0.956 0.462 0.008 0.378 0.07 3.825 0.528 4.094 0.486 2.488 0.956 0.462 0.008 0.376 0.10 3.927 0.537 4.220 0.491 2.507 0.956 0.462 0.008 0.381 0.12 4.005 0.529 4.249 0.491 2.517 0.956 0.462 0.008 0.374 0.16 3.834 0.549 3.898 0.540 2.516 0.956 0.462 0.008 0.365 0.20 3.678 0.562 3.707 0.558 2.506 0.956 0.462 0.008 0.358 0.24 3.514 0.574 3.546 0.569 2.483 0.956 0.462 0.008 0.353 0.26 3.447 0.567 3.460 0.566 2.451 0.956 0.462 0.008 0.339 0.30 3.299 0.573 3.341 0.567 2.415 0.956 0.462 0.008 0.334 0.34 3.334 0.565 3.341 0.563 2.426 0.956 0.462 0.007 0.329 0.40 3.236 0.571 3.347 0.553 2.431 0.956 0.462 0.006 0.326 0.50 3.262 0.563 3.388 0.544 2.462 0.956 0.462 0.004 0.325 0.60 3.122 0.574 3.126 0.573 2.476 0.956 0.462 0.004 0.325 0.80 2.778 0.637 3.348 0.549 2.560 0.956 0.462 0.004 0.342 1.00 2.431 0.667 3.170 0.553 2.550 0.956 0.462 0.004 0.348 1.20 2.298 0.671 3.063 0.553 2.547 0.956 0.462 0.004 0.335 1.50 2.105 0.671 2.792 0.564 2.524 0.956 0.462 0.004 0.334 1.70 1.682 0.718 2.705 0.561 2.501 0.956 0.462 0.004 0.325 2.00 1.384 0.743 2.561 0.562 2.480 0.956 0.462 0.004 0.324 2.40 1.174 0.741 2.130 0.594 2.451 0.956 0.462 0.004 0.320 3.00 0.459 0.746 1.353 0.609 2.217 0.956 0.462 0.004 0.319 4.00 0.219 0.675 0.219 0.675 2.039 0.956 0.462 0.004 0.317 5.00 −0.159 0.693 −0.159 0.693 2.005 0.956 0.462 0.004 0.316 6.00 −0.727 0.740 −0.727 0.740 1.973 0.956 0.462 0.004 0.295 7.00 −0.941 0.742 −0.941 0.742 1.937 0.956 0.462 0.004 0.304 8.00 −1.129 0.729 −1.129 0.729 1.863 0.956 0.462 0.004 0.312 9.00 −1.319 0.738 −1.319 0.738 1.863 0.956 0.462 0.004 0.311 10.00 −1.512 0.741 −1.512 0.741 1.825 0.956 0.462 0.004 0.319 
图 4 基岩水平向加速度反应谱曲线Figure 4. Spectral acceleration curves for horizontal rock ground motion5. 讨论
为观察回归结果的可靠性，给出板缘、板内地震关键周期点（周期6.0 s）反应谱回归残差随震级、断层距的变化关系，如图6、7所示。由图6，7可知，随着断层距和震级的变化，回归残差在零值附近水平分布，无明显趋势，说明回归结果真实可靠，且本模型中离散标准差可视为不随断层距和震级变化的常数。
为进行合理分析，选择目前国际上常用的俯冲带衰减关系与本文结果进行比较，包括Abrahamson等（2016）采用全球俯冲带强震记录统计结果和Zhao等（2006）采用日本俯冲带强震记录统计结果。震级6.5级、断层距50 km（板缘地震，震源深度30 km），震级7.5级、断层距200 km（板缘地震，震源深度50 km），震级6.5级、断层距100 km（板内地震，震源深度70 km），震级7.5级、断层距200 km（板内地震，震源深度70 km）处反应谱的对比如图8所示。由图8可知，在震源深度较浅的板缘地震情况下，对于近场高频部分，本文预测模型得到的结果较高，具有一定保守性，对弈中远场部分，本文预测模型得到的结果居中；在外推较深的板内地震情况下，3组预测模型得到的结果较接近，对于远场部分，本文预测模型得到的长周期略低。总体来看，3组预测模型反应谱曲线基本相当，在主要震级-断层距段结果较接近，可在一定程度上验证本文预测模型的可靠性。靠性。Abrahamson等（2016）的研究使用全球资料，Zhao等（2006）的研究可用周期截至5.0 s，考虑区域性衰减特性与长周期可用性等，本文预测模型更适用于我国海域及长周期地震动的估计，适用震级为5.0～8.0级，断层距为0～600 km。
图 8 基岩水平向加速度反应谱曲线对比结果Figure 8. Comparison of spectral acceleration curves for horizontal rock ground motion致谢 本文使用日本K-net、Kik-net地震台网、IASPEI全球地震台网地震资料，研究和成文过程中得到李小军教授、周正华教授及审稿专家的热心指导与建议，在此一并表示感谢！
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图 2 板缘地震记录震级-断层距分布关系图
Figure 2. Distribution of magnitude-distance of interface earthquakes
图 3 板内地震记录震级-断层距分布关系图
Figure 3. Distribution of magnitude-distance of intraslab earthquakes
图 4 基岩水平向加速度反应谱曲线
Figure 4. Spectral acceleration curves for horizontal rock ground motion
图 8 基岩水平向加速度反应谱曲线对比结果
Figure 8. Comparison of spectral acceleration curves for horizontal rock ground motion
表 1 强震资料地震目录（板缘地震）
Table 1. Catalog of strong earthquakes records (Interface earthquakes)
发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-10-03T04:13:30.490 40.282 143.124 5.7 33 2001-08-13T20:11:23.400 41.046 142.308 6.3 38 2001-10-02T08:19:49.460 37.739 141.775 5.2 43 2002-11-03T03:37:42.070 38.886 141.977 6.1 39 2003-09-25T19:50:06.360 41.815 143.910 8.1 27 2003-09-25T21:08:00.030 41.774 143.593 7.4 33 2003-09-29T02:36:53.140 42.450 144.380 6.3 25 2003-10-08T09:06:55.340 42.648 144.570 6.6 32 2003-12-29T01:30:54.700 42.423 144.613 5.9 33 2004-04-11T18:06:12.480 42.918 144.836 5.7 42 2004-09-01T02:49:28.610 36.959 141.607 5.1 35 2005-01-18T14:09:06.220 42.946 144.866 5.7 42 2005-03-11T18:47:36.690 43.085 144.674 5.0 54 2005-07-09T23:37:11.140 33.422 140.825 5.4 55 2005-08-16T02:46:28.400 38.276 142.039 6.8 36 2005-10-19T11:44:42.790 36.405 140.839 6.5 32 2005-12-02T13:13:09.520 38.089 142.122 6.3 29 2007-11-26T13:51:39.800 37.392 141.586 5.9 42 2008-05-07T16:45:18.700 36.164 141.526 6.8 27 2008-07-19T02:39:28.700 37.552 142.214 7.0 22 2008-09-11T00:20:50.920 41.892 143.754 7.0 25 2009-06-05T03:30:33.060 41.824 143.445 6.4 29 2010-03-14T08:08:03.960 37.745 141.590 6.5 32 2010-07-04T21:55:51.980 39.697 142.369 6.3 27 2011-03-09T02:45:20.330 38.435 142.842 7.3 32 2011-03-11T05:46:24.120 38.297 142.373 9.0 29 2011-03-11T06:15:40.280 36.281 141.111 6.8 43 2011-03-25T11:36:24.490 38.772 141.880 6.2 39 2011-04-07T14:32:43.290 38.276 141.588 7.1 42 2011-04-21T13:37:03.340 35.579 140.305 6.2 43 2011-07-10T00:57:10.800 38.034 143.264 7.0 23 2011-07-23T04:34:24.180 38.898 141.815 6.4 41 2011-07-24T18:51:25.070 37.730 141.390 6.3 40 2011-07-30T18:53:50.720 36.942 140.955 6.5 38 2011-08-19T05:36:33.040 37.671 141.652 6.3 47 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-11-24T10:25:34.030 41.898 142.639 6.2 38 2012-06-17T20:32:20.590 38.919 141.831 6.4 36 2012-12-07T08:18:23.130 37.890 143.949 7.3 31 2015-02-16T23:06:28.270 39.8558 142.8808 6.7 23 2015-05-12T21:12:58.890 38.9056 142.0317 6.8 35 2016-01-14T03:25:33.640 41.9723 142.7810 6.7 46 2018-01-24T10:51:19.090 41.1034 142.4323 6.3 31 2018-09-05T18:07:59.150 42.6861 141.9294 6.6 35 
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表 2 宽频带资料地震目录（板缘地震）
Table 2. Catalog of broad-band records (Interface earthquakes)
发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-06-10T18:23:29.320 23.843 121.225 6.2 33 2000-07-04T22:19:44.160 20.240 122.163 5.2 33 2000-07-16T03:21:45.530 20.253 122.043 6.3 33 2000-09-10T08:54:45.960 24.008 121.526 5.6 35 2000-10-03T04:13:30.490 40.282 143.124 5.7 33 2001-06-14T02:35:25.810 24.513 122.033 5.6 32 2001-08-13T20:11:23.400 41.046 142.308 6.3 38 2001-08-17T22:25:49.010 25.748 126.190 5.6 33 2002-03-26T03:45:48.700 23.346 124.090 6.6 33 2002-03-31T06:52:50.490 24.279 122.179 7.4 33 2002-05-13T19:57:22.900 19.132 121.238 5.3 33 2002-07-11T07:36:26.060 24.075 122.288 5.6 44 2002-11-03T03:37:42.070 38.886 141.977 6.1 39 2003-06-09T01:52:51.010 24.413 122.020 5.5 48 2003-06-10T08:40:30.830 23.520 121.628 5.7 45 2003-09-25T19:50:06.360 41.815 143.910 8.1 27 2003-09-25T21:08:00.030 41.774 143.593 7.4 33 2003-09-29T02:36:53.140 42.450 144.380 6.3 25 2003-10-08T09:06:55.340 42.648 144.570 6.6 32 2005-01-18T14:09:06.220 42.946 144.866 5.7 42 2005-08-16T02:46:28.400 38.276 142.039 6.8 36 2005-09-06T01:16:02.350 24.084 122.191 6.1 32 2005-10-19T11:44:42.790 36.405 140.839 6.5 32 2006-07-28T07:40:11.840 24.183 122.526 5.9 33 2007-01-25T10:59:17.650 22.564 121.926 6.0 36 2007-04-20T19:37:58.230 27.471 128.379 5.3 42 2007-09-06T17:51:26.190 24.340 122.219 6.2 53 2008-06-01T01:57:23.690 20.124 121.350 6.3 31 2008-07-08T07:42:10.730 27.532 128.334 6.0 43 2008-09-11T00:20:50.920 41.892 143.754 6.7 25 2009-06-05T03:30:33.060 41.824 143.445 6.4 29 2009-10-30T07:03:39.120 29.218 129.782 6.8 34 2009-12-19T13:02:15.570 23.796 121.605 6.4 43 2010-03-14T08:08:03.960 37.745 141.590 6.5 32 2010-07-04T21:55:51.980 39.697 142.369 6.3 27 2010-10-04T13:28:38.860 24.270 125.154 6.3 32 2011-03-09T02:45:20.330 38.435 142.842 7.3 32 2011-03-11T05:46:24.120 38.297 142.373 9.0 29 2011-03-11T06:15:40.280 36.281 141.111 6.8 43 2011-03-11T15:13:14.680 35.994 141.808 6.3 21 2011-03-25T11:36:24.490 38.772 141.880 6.2 39 2011-04-07T14:32:43.290 38.276 141.588 7.1 42 2011-04-21T13:37:03.340 35.579 140.305 6.2 43 2011-07-10T00:57:10.800 38.034 143.264 7.0 23 2011-07-23T04:34:24.180 38.898 141.815 6.4 41 2011-07-24T18:51:25.070 37.730 141.390 6.3 40 2011-07-30T18:53:50.720 36.942 140.955 6.5 38 2011-08-19T05:36:33.040 37.671 141.652 6.2 47 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-09-16T19:26:40.260 40.273 142.779 6.7 30 2011-11-24T10:25:34.030 41.898 142.639 6.2 38 2012-06-09T21:00:18.070 24.572 122.248 5.9 70 2012-06-17T20:32:20.590 38.919 141.831 6.4 36 2012-12-07T08:18:23.130 37.890 143.949 7.3 31 2013-06-07T16:38:02.900 24.098 122.671 5.8 33 2013-10-25T17:10:19.710 37.1557 144.6611 7.1 35 2014-10-22T00:15:17.440 27.4158 128.5533 5.8 43 2015-02-13T20:06:32.330 22.6374 121.4270 6.2 30 2015-02-16T23:06:28.270 39.8558 142.8808 6.7 23 2015-05-12T21:12:58.890 38.9056 142.0317 6.8 35 2016-01-14T03:25:33.640 41.9723 142.7810 7.0 46 2016-12-26T01:23:37.880 19.1524 121.1743 5.2 34 2018-01-24T10:51:19.090 41.1034 142.4323 6.3 31 2018-09-05T18:07:59.150 42.6861 141.9294 6.6 35 2018-10-23T04:34:58.630 24.1153 122.6027 5.8 30 2018-10-23T16:04:04.240 23.9912 122.6791 5.7 31 2018-11-05T14:46:58.690 29.2376 130.5301 5.0 36
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表 3 强震资料地震目录（板内地震）
Table 3. Catalog of strong earthquakes records (Intraslab earthquakes)
发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-06-03T08:54:49.200 35.552 140.464 5.6 62 2001-12-02T13:01:53.670 39.402 141.089 6.5 124 2002-04-03T23:42:12.810 41.543 141.851 5.3 71 2002-10-14T14:12:43.750 41.174 142.249 5.9 61 2003-05-26T09:24:33.400 38.849 141.568 6.9 68 2003-09-20T03:54:50.780 34.998 140.172 5.3 52 2007-04-18T15:07:31.600 42.658 141.861 5.0 120 2007-07-01T04:12:07.750 43.663 144.734 5.8 130 2008-07-23T15:26:19.950 39.802 141.464 6.8 108 2008-09-22T07:31:59.170 41.578 140.450 5.2 149 2009-02-28T00:35:56.700 42.610 142.104 5.0 105 2009-08-12T22:48:51.420 32.821 140.395 6.6 53 2010-03-13T12:46:26.380 37.594 141.299 5.2 77 2013-02-02T14:17:35.130 42.770 143.092 6.9 107 2013-11-03T05:25:15.340 35.9713 140.1213 5.1 77 2014-06-14T17:31:41.560 39.4384 140.9876 5.0 92 2015-07-09T18:32:51.220 40.3631 141.4646 5.0 81 2019-04-27T17:24:45.654 42.4547 142.8191 5.4 111
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表 4 测震资料地震目录（板内地震）
Table 4. Catalog of broad-band records (Intraslab earthquakes)
发震时刻 震中纬度N/° 震中经度E/° Ms/级 震源深度/km 2000-01-28T16:39:24.280 26.076 124.496 5.8 194 2000-06-03T08:54:49.200 35.552 140.464 5.6 62 2001-12-02T13:01:53.670 39.402 141.089 6.5 124 2003-05-26T09:24:33.400 38.849 141.568 6.9 68 2004-10-15T04:08:50.240 24.530 122.694 6.7 94 2005-10-15T15:51:08.130 25.309 123.351 6.4 192 2008-07-23T15:26:19.950 39.802 141.464 6.8 108 2008-09-09T07:43:13.320 24.666 122.570 5.0 102 2009-03-26T19:19:59.560 27.415 126.702 5.9 160 2009-08-12T22:48:51.420 32.821 140.395 6.6 53 2010-01-15T11:08:38.370 26.746 126.285 5.7 139 2011-11-08T02:59:08.510 27.324 125.621 6.9 225 2013-02-02T14:17:35.130 42.770 143.092 6.9 107 2013-09-06T11:33:53.520 20.1721 122.3193 6.0 175 2014-03-02T20:11:23.430 27.4312 127.3674 6.5 119 2014-12-10T21:03:39.260 25.5403 122.4503 6.1 256 2014-12-31T07:54:36.890 24.6707 122.5575 5.2 104 2016-03-14T07:03:17.710 29.8888 128.9567 5.5 211 2016-05-31T05:23:47.310 25.5615 122.5458 6.4 246 2017-04-30T01:57:22.160 21.2987 121.8285 5.2 106 2017-08-16T12:51:25.870 28.6737 127.9007 5.7 198 2019-02-17T20:36:56.890 20.6674 122.1168 5.0 169
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表 5 板缘地震基岩水平向加速度反应谱预测模型相关参数
Table 5. Coefficients of horizontal rock spectral acceleration prediction model for interface earthquakes
周期/s A1 B1 A2 B2 C D E σ 0.01 1.812 0.555 2.339 0.474 1.935 0.956 0.462 0.377 0.04 1.746 0.573 2.445 0.465 1.929 0.956 0.462 0.378 0.05 1.960 0.581 2.856 0.443 1.990 0.956 0.462 0.376 0.07 2.342 0.559 3.277 0.416 2.018 0.956 0.462 0.381 0.10 2.432 0.562 3.303 0.428 2.044 0.956 0.462 0.374 0.12 2.455 0.558 3.232 0.438 2.045 0.956 0.462 0.365 0.16 2.569 0.526 2.871 0.480 2.025 0.956 0.462 0.358 0.20 2.549 0.508 2.596 0.501 1.993 0.956 0.462 0.353 0.24 2.412 0.510 2.480 0.500 1.946 0.956 0.462 0.339 0.26 2.361 0.497 2.307 0.505 1.897 0.956 0.462 0.334 0.30 2.316 0.495 2.134 0.523 1.897 0.956 0.462 0.329 0.34 1.980 0.515 1.966 0.518 1.817 0.956 0.462 0.326 0.40 1.684 0.539 1.735 0.532 1.781 0.956 0.462 0.325 0.50 1.344 0.571 1.535 0.542 1.757 0.956 0.462 0.325 0.60 1.105 0.588 1.206 0.572 1.738 0.956 0.462 0.342 0.80 0.592 0.643 0.878 0.600 1.731 0.956 0.462 0.348 1.00 −0.036 0.719 0.537 0.630 1.730 0.956 0.462 0.335 1.20 −0.325 0.744 0.182 0.666 1.734 0.956 0.462 0.334 1.50 −0.850 0.809 0.027 0.674 1.730 0.956 0.462 0.325 1.70 −1.000 0.819 −0.107 0.682 1.720 0.956 0.462 0.324 2.00 −1.410 0.860 −0.419 0.708 1.700 0.956 0.462 0.320 2.40 −1.610 0.860 −0.904 0.752 1.672 0.956 0.462 0.319 3.00 −1.891 0.873 −1.328 0.786 1.639 0.956 0.462 0.317 4.00 −2.091 0.858 −1.994 0.845 1.605 0.956 0.462 0.316 5.00 −2.484 0.885 −2.484 0.885 1.573 0.956 0.462 0.295 6.00 −2.903 0.917 −2.903 0.917 1.537 0.956 0.462 0.304 7.00 −3.273 0.945 −3.273 0.945 1.502 0.956 0.462 0.312 8.00 −3.546 0.963 −3.546 0.963 1.463 0.956 0.462 0.311 9.00 −3.800 0.977 −3.800 0.977 1.425 0.956 0.462 0.319 10.00 −4.099 1.000 −4.099 1.000 1.389 0.956 0.462 0.328
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表 6 板内地震基岩水平向加速度反应谱预测模型的参数
Table 6. Coefficients of horizontal rock spectral acceleration prediction model for intraslab earthquakes
周期/s A1 B1 A2 B2 C D E F σ 0.01 3.541 0.516 3.639 0.501 2.442 0.956 0.462 0.008 0.377 0.04 3.652 0.506 3.678 0.502 2.440 0.956 0.462 0.008 0.377 0.05 3.679 0.525 3.881 0.494 2.471 0.956 0.462 0.008 0.378 0.07 3.825 0.528 4.094 0.486 2.488 0.956 0.462 0.008 0.376 0.10 3.927 0.537 4.220 0.491 2.507 0.956 0.462 0.008 0.381 0.12 4.005 0.529 4.249 0.491 2.517 0.956 0.462 0.008 0.374 0.16 3.834 0.549 3.898 0.540 2.516 0.956 0.462 0.008 0.365 0.20 3.678 0.562 3.707 0.558 2.506 0.956 0.462 0.008 0.358 0.24 3.514 0.574 3.546 0.569 2.483 0.956 0.462 0.008 0.353 0.26 3.447 0.567 3.460 0.566 2.451 0.956 0.462 0.008 0.339 0.30 3.299 0.573 3.341 0.567 2.415 0.956 0.462 0.008 0.334 0.34 3.334 0.565 3.341 0.563 2.426 0.956 0.462 0.007 0.329 0.40 3.236 0.571 3.347 0.553 2.431 0.956 0.462 0.006 0.326 0.50 3.262 0.563 3.388 0.544 2.462 0.956 0.462 0.004 0.325 0.60 3.122 0.574 3.126 0.573 2.476 0.956 0.462 0.004 0.325 0.80 2.778 0.637 3.348 0.549 2.560 0.956 0.462 0.004 0.342 1.00 2.431 0.667 3.170 0.553 2.550 0.956 0.462 0.004 0.348 1.20 2.298 0.671 3.063 0.553 2.547 0.956 0.462 0.004 0.335 1.50 2.105 0.671 2.792 0.564 2.524 0.956 0.462 0.004 0.334 1.70 1.682 0.718 2.705 0.561 2.501 0.956 0.462 0.004 0.325 2.00 1.384 0.743 2.561 0.562 2.480 0.956 0.462 0.004 0.324 2.40 1.174 0.741 2.130 0.594 2.451 0.956 0.462 0.004 0.320 3.00 0.459 0.746 1.353 0.609 2.217 0.956 0.462 0.004 0.319 4.00 0.219 0.675 0.219 0.675 2.039 0.956 0.462 0.004 0.317 5.00 −0.159 0.693 −0.159 0.693 2.005 0.956 0.462 0.004 0.316 6.00 −0.727 0.740 −0.727 0.740 1.973 0.956 0.462 0.004 0.295 7.00 −0.941 0.742 −0.941 0.742 1.937 0.956 0.462 0.004 0.304 8.00 −1.129 0.729 −1.129 0.729 1.863 0.956 0.462 0.004 0.312 9.00 −1.319 0.738 −1.319 0.738 1.863 0.956 0.462 0.004 0.311 10.00 −1.512 0.741 −1.512 0.741 1.825 0.956 0.462 0.004 0.319
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1. 党浩天，王自法，赵登科，位栋梁，王祥琪，WANG Jianming，李兆焱. 基于Stacking模型融合策略的日本俯冲带板缘地震动预测. 世界地震工程. 2024(01): 80-95 . 
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