2013年甘肃岷县—漳县M 6.6地震序列精定位研究

采用双差定位法对2013年7月22日甘肃岷县—漳县交界地区M 6.6地震及主震后48小时内388次余震序列进行重新定位,得到350个精定位地震数据。结果表明,余震优势展布以北东向较大倾角的铲状结构为特征,长约12 km,以主震为中心两侧对称分布;震源深度主要集中在4—10 km范围内,但余震震级由10 km左右深度的3—4级向3 km深度之上近地表的2—3级迁移变化;余震分布清晰呈现双层结构,较深层分布在4—10 km深度,而较浅层分布3 km深度之上,2层之间地震分布较少。分析认为,浅层地震可能为本次地震地表破坏较强原因之一。震源深度剖面显示,破裂面向NE倾斜,推测此次地震的发震断裂为临潭—宕昌断裂。     

1974年和1979年江苏省溧阳两次中等强度地震的前兆性空区.

1974年4月22日、1979年7月9日在江苏省溧阳地区先后发生5.8级、6.3级(ML)两次地震.在这两次地震前约23个月,其周围200多公里范围内出现地震空区图象.1974年5.8级地震前16个月,在240公里范围内没有发生小地震;临近震前7个月空区活化,爆发一系列小地震.1979年6.3级地震前15个月,在100公里范围内和240公里范围外发生一些小地震,形成环形空区;临近地震前7个月,约200公里范围内均无小震活动.根据两次主震等震线,主、余震展布和震源机制结果认为,它们是在北东东向压应力和北北西向张应力作用下,发生在同一震源区的不同期共轭地震.两次地震空区图象的形成、发展和消失过程,描绘了区域应力持续作用下,中等均匀程度的地壳不均匀应变的演化过程.      

The Beni Haoua,Algeria, Mw 4.9 earthquake: source parameters,engineering, and seismotectonic implications

A moderate Mw 4.9 earthquake struck the Beni Haoua (Algeria) coastal area on April 25, 2012. The mainshock was largely recorded by the accelerograph network of the Centre National de Recherche Appliquée en Génie Parasismique (CGS). The same day the earthquake occurred, eight mobile short period stations were deployed through the epicentral area. In this study, we use accelerogram and seismogram data recorded by these two networks. We combined the focal mechanism built from the first motion of P waves and from waveform inversion, and the distribution of aftershocks to well constrain the source parameters. The mainshock is located with a shallow focal depth, ～9 km, and the focal mechanism shows a nearly pure left lateral strike slip motion, with total seismic moment of 2.8?×?10¹⁶ N.m (M_w?=?4.9). The aftershocks mainly cluster on a narrow NS strip, starting at the coast up to 3–4 km inland. This cluster, almost vertical, is concentrated between 6 and 10 km depth. The second part of this work concerns the damage distribution and estimated intensity in the epicentral area. The damage distribution is discussed in connection with the observed maximum strong motion. The acceleration response spectrum with 5 % damping of the mainshock and aftershocks give the maximum amplitude in high frequency which directly affects the performance of the high-frequency structures. Finally, we tie this earthquake with the seismotectonic of the region, leading to conclude that it occurred on a N–S transform zone between two major compressional fault zones oriented NE–SW.     

唐山、海城、盐源-宁蒗地震强余震特征

对大地震发生后强余震的震源机制,基于主要地震断层上小余震的时空分布进行了详细研究.近期在中国境内发生的强烈板内地震,如1976年唐山、1975年海城、1976年盐源——宁蒗等地震曾被中国地震台网很好记录.主震刚发生后的小余震以及强余震前后的小余震的震源用 S——P 时间的收敛法进行测定.强余震的断层是依靠这些小余震的震中分布来描绘的.可以看出有三种情况.第一,在主震断层区内,一次强余震发生在较小余震的比较不密集的部位;第二,一次强余震沿断层发生并与主震断层是共轭的;第三,一次强余震在沿平行并离开主震断层的断层上发生.可以认为,地质条件控制着强余震的发生.作为强余震的可能前兆,则有唐山地震的一次强余震,震级为7.1.其发生前,出现一些前震以及在接近主震断层方向上的某些地震台所记录的初动方向有变化.可以设想,这里的应力场在强余震发生前是有所变化的.      

2017年漾濞MS4.8和MS5.1地震序列的微震检测及重定位

基于云南地震台网记录到的2017年漾濞M_S4.8和M_S5.1地震序列的地震目录和波形数据,采用结合波形互相关的双差定位方法得到了M_S5.1主震前7天至主震后30天共258次地震事件更加准确的震源位置,然后利用匹配定位方法获得了更加丰富的地震目录,并对其余震活动的时空演化特征进行了初步分析。双差重定位获得了漾濞地震序列中193次地震的精确位置,水平方向和垂直方向的定位误差均值分别为1.3 km和1.9 km,重定位及震源机制解反演结果显示维西—乔后断裂中南段应为此次地震的发震断层。使用匹配定位方法检测得到了1 625次中小地震事件,事件数量是云南地震台网目录中的6倍,被检测事件主要为主震后早期余震及M_L≤0微震事件。对比2016年云龙M_S5.0地震序列的研究结果后初步分析认为,“震群（多震）型”和“主余型”地震序列的一个主要区别可能是“震群（多震）型”地震序列的余震数量相对更少、余震活动衰减得更快。      

Strong ground motion simulation of the 2003 Bam, Iran, earthquake using the empirical Green’s function method

The 2003 Bam, Iran, earthquake caused catastrophic damage to the city of Bam and neighboring villages. Given its magnitude (M _w ) of 6.5, the damage was remarkably large. Large-amplitude ground motions were recorded at the Bam accelerograph station in the center of Bam city by the Building and Housing Research Center (BHRC) of Iran. We simulated the Bam earthquake acceleration records at three BHRC strong-motion stations—Bam, Abaraq, and Mohammad-Abad—by the empirical Green’s function method. Three aftershocks were used as empirical Green’s functions. The frequency range of the empirical Green’s function simulations was 0.5–10 Hz. The size of the strong motion generation area of the mainshock was estimated to be 11 km in length by 7 km in width. To estimate the parameters of the strong motion generation area, we used 1D and 2D velocity structures across the fault and a combined source model. The empirical Green’s function method using a combination of aftershocks produced a source model that reproduced ground motions with the best fit to the observed waveforms. This may be attributed to the existence of two distinct rupture mechanisms in the strong motion generation area. We found that the rupture starting point for which the simulated waveforms best fit the observed ones was near the center of the strong motion generation area, which reproduced near-source ground motions in a broadband frequency range. The estimated strong motion generation area could explain the observed damaging ground motion at the Bam station. This suggests that estimating the source characteristics of the Bam earthquake is very important in understanding the causes of the earthquake damage.     

A high-resolution aftershock seismicity image of the 2002 Sultandaği-Çay earthquake (Mw = 6.2), Turkey

A moderate-size earthquake (Mw = 6.2) occurred on 3 February 2002 (07:11:28 GMT) in the Sultanda??-Çay region of southwest Turkey. The mainshock was followed by a strong aftershock of Mw = 6.0 just 2 h after the mainshock, at 09:26:49 GMT. A temporary seismic network of 27 vertical component seismometers was installed to monitor aftershock activity. One thousand sixty nine aftershocks (0.2 < ML < 3.3) were recorded during the period from 5 to 10 February 2002. We analyzed the P and S arrival times and P wave first motion data to obtain high-quality hypocenters and focal mechanisms, which revealed fine details of the fault zone. We infer that the mainshock has ruptured a segment of the Sultanda? Fault Zone that is approximately 37 km long and 7 km wide at depth. The average slip over the rupture plane during the mainshock is estimated to be 32 cm. The linear distribution of the aftershocks and the location of the mainshock epicenter suggest that rupture has initiated in the eastern bending of the fault and propagated unilaterally to the west. The majority of fault plane solutions indicate E–W to ESE–WNW striking oblique–normal faulting mechanisms with an average dip angle of 62° N ± 10° . The high-resolution aftershock seismicity image also shows that faulting involved a complex array of synthetic and possibly antithetic structures during the evolution of the aftershock sequence. The steady increase of the b value towards the west implies that the highest moment release of the mainshock occurred to the west of the epicenter. The study clearly shows the activation of the WNW–ESE-trending Sultanda? Fault Zone along the southern margin of the Ak?ehir-Afyon Graben (AAG). The westernmost end of the aftershock activity corresponds to a structurally complex zone distinct from the main rupture. It is characterized by both ENE–WSW- and NNE–SSW-trending oblique-slip normal faulting mechanisms, the latter being associated with the NNE–SSW-trending Karam?k Graben. The intersection of these two grabens, AAG and Karam?k Graben, provides abundant faults available for failure in this region. The occurrence pattern of large events in recent years indicates a possible migration of earthquakes from east to west. Thus, we conclude that this has an important implication for earthquake hazard for the city of Afyon, which lies along the same fault line and only 20 km west of the termination point of the aftershock zone.     

联合强震记录和InSAR/GPS结果的四川九寨沟7.0级地震震源滑动分布反演及其地震学应用

2017年8月8日我国四川九寨沟发生里氏7.0级地震.本研究利用基线校正方法获得距震中100km范围内9个强震台站同震位移,基于Sentinel-1卫星干涉SAR影像对获取了InSAR同震形变场.结合GPS形变数据,本研究进行了震源滑动模型联合反演,结果显示此次地震整体以走滑运动为主,释放地震矩约为7.60×1018 N·m(～MW6.52).通过对比模拟形变场和观测值显示,联合反演结果优于单独基于InSAR形变场的反演结果.静态应力变化计算结果显示断层平均静态应力降为1.07MPa.反演滑动模型沿走向和倾角方向拐角波数值分别为0.99×10-4和1.10×10-4.同震静态库仑应力变化计算结果显示共有83.6%的余震位于库仑应力增加的区域,被主震所触发的余震占总数的77.9%,主震对后续余震具有显著触发作用.强地面运动模拟结果显示模拟结果在烈度分布范围和等级方面与调查烈度符合度很高,模拟结果能够很好地反映断层破裂的方向性效应等特征.本研究计算结果显示九寨沟地震无论是平均静态应力降还是拐角波数均低于同类型地震的平均水平,这可能是造成本次地震强地震动水平相对不高的原因.     

Seismological aspects of the 27 June 2015 Gulf of Aqaba earthquake and its sequence of aftershocks

On 27 June 2015, a moderate earthquake with magnitude Mb 5.2 struck the Gulf of Aqaba near Nuweiba City. This event was instrumentally recorded by the Egyptian National Seismic Network (ENSN) and many other international seismological centres. The event was felt in all the cities on the Gulf of Aqaba, as well as Suez City, Hurghada City, the greater Cairo Metropolitan Area, Israel, Jordan and the north-western part of Saudi Arabia. No casualties were reported, however. Approximately 95 aftershocks with magnitudes ranging from 0.7 to 4.2 were recorded by the ENSN following the mainshock. In the present study, the source characteristics of both the mainshock and the aftershocks were estimated using the near-source waveform data recorded by the very broadband stations of the ENSN, and these were validated by the P-wave polarity data from short period stations. Our analysis reveals that an estimated seismic moment of 0.762?×?10¹⁷ Nm was released, corresponding to a magnitude of Mw 5.2, a focal depth of 14 km, a fault radius of 0.72 km and a rupture area of approximately 1.65 km². Monitoring the sequence of aftershocks reveals that they form a cluster around the mainshock and migrated downwards in focal depth towards the west. We compared the results we obtained with the published results from the international seismological centres. Our results are more realistic and accurate, in particular with respect to the epicenteral location, magnitude and fault plane solution which are in accordance with the hypocentre distribution of the aftershocks.     

2000年姚安地震的震源参数

根据近场小孔径观测台网记录的余震序列资料，研究了2000年1月15日云南姚安MS6.4地震序列的地震物理过程. 用地震标定律关系估算主震的地震矩M0=1.58×1018N·m，矩震级MW=6.0，平均位错=0.63m，断层长度L=16.6km，断层宽度W=5.6km. 余震序列的高精度定位结果和能量分布走向，很好地证实了主震的断层破裂走向为N50°W，震区马尾菁断裂为主震发震构造，断层错动性质以右旋走滑为主. 用横波记录资料及波谱分析方法估算出余震的震源参数: 地震矩范围为1010～1016N·m，震源破裂半径a为80～500m，地震应力降范围为0.01～9.5MPa. 较大应力降(Δσ>1.0MPa)沿主断层线性排列，大应力降(Δσ>2.0MPa)与ML≥3.0级地震相关. 余震能量释放和高应力降的地震多发生在6.0～11km的深度范围，说明在这一深度范围内最大程度地集中了地壳中的应力.     

2015尼泊尔M_S8.1地震中等余震震源机制研究

本研究利用西藏台网记录的波形数据,采用gCAP方法反演了2015年4月25日尼泊尔MS8.1大震5次中等余震(5.0≤MS≤6.5)及西藏定日MS5.9地震震源机制解.结果显示,6次地震包含2个正断、2个走滑及2个逆冲型地震.其中2个正断型地震位于主震的东北方向,即发震断层的上盘,表明该区域受到主震同震位移的影响,表现出应力拉张的变化特征;2个走滑型地震在主震破裂的东南方向上,说明随着破裂往东南方向延伸,余震的走滑分量增强;另外2个逆冲型地震位于5月12日MS7.5强余震区域,与MS7.5地震的滑移状态一致,可能与主震同震位移引起该区域处于应力挤压状态密切相关.这些结果表明,尼泊尔MS8.1主震发生后,由于同震位移的影响,不同区域处于不同的应力状态,从而使中等余震表现出不同的震源类型.     

1989年大同—阳高6.1级地震烈度宏观考察

文中叙述了大同—阳高地震区的烈度划分原则、烈度分布范围、烈度异常情况,给出了宏观地震参数(h=11.2km,震级5.8M_L),指出宏观调查的烈度值与强震仪记录的强余震加速度基本一致。     

2013年芦山地震序列震源机制与震源区构造变形特征分析

基于四川区域地震台网记录的波形资料,利用CAP波形反演方法,同时获取了2013年4月20日芦山M7.0级地震序列中88个M≥3.0级地震的震源机制解、震源矩心深度与矩震级,进而利用应变花（strain rosette）和面应变（areal strain）As值,分析了芦山地震序列震源机制和震源区构造运动与变形特征.获得的主要结果有：（1）芦山M7.0级主震破裂面参数为走向219°/倾角43°/滑动角101°,矩震级为M_W6.55,震源矩心深度15 km.芦山地震余震区沿龙门山断裂带走向长约37 km、垂直断裂带走向宽约16 km.主震两侧余震呈不对称分布,主震南西侧余震区长约27 km、北东侧长约10 km.余震分布在7~22 km深度区间,优势分布深度为9~14 km,序列平均深度约13 km,多数余震分布在主震上部.粗略估计的芦山地震震源体体积为37 km×16 km×16 km.（2）面应变As值统计显示,芦山地震序列以逆冲型地震占绝对优势,所占比例超过93%.序列主要受倾向NW、倾角约45°的近NE-SW向逆冲断层控制;部分余震发生在与上述主发震断层近乎垂直的倾向SE的反冲断层上;龙门山断裂带前山断裂可能参与了部分余震活动.P轴近水平且优势方位单一,呈NW-SE向,与龙门山断裂带南段所处区域构造应力场方向一致,反映芦山地震震源区主要受区域构造应力场控制,芦山地震是近NE-SW向断层在近水平的NW-SE向主压应力挤压作用下发生逆冲运动的结果.序列中6次非逆冲型地震均发生在主震震中附近,且主震震中附近P轴仰角变化明显,表明主震对其震中附近局部区域存在明显的应力扰动.（3）序列整体及不同震级段的应变花均呈NW向挤压白瓣形态,显示芦山地震震源区深部构造呈逆冲运动、NW向纯挤压变形.各震级段的应变花方位与形状一致,具有震级自相似性特征,揭示震源区深部构造运动和变形模式与震级无关.（4）不同深度的应变花形态以NW-NWW向挤压白瓣为优势,显示震源区构造无论是总体还是分段均以NW-NWW向挤压变形为特征.但应变花方位与形状随深度仍具有较明显的变化,可能反映了震源区构造变形在深度方向上存在分段差异.（5）芦山地震震源体尺度较小,且主震未发生在龙门山断裂带南段主干断裂上,南段长期积累的应变能未能得到充分释放,南段仍存在发生强震的危险.     

Seismic Source Parameters from a New Dial-up Seismological Network in Greece

—A regional dial-up PT telemetric network of eight digital short-period seismic stations has been in full operation since the beginning of 1995 in Greece. During the first year of full operation, three destructive earthquake sequences struck different regions of central and northern Greece. The dial-up network managed to successfully record more than 85% of these seismic events including foreshocks, main shocks and aftershocks, and 45 of these events were selected in order to determine their seismic source parameters by spectral analysis. The results show that seismic moment correlates very well with earthquake magnitude, fault radius and fault displacement. The determined scaling relations are in general agreement with those obtained by other studies for Greek earthquakes that used different methodologies. Since digital seismic instrumentation is now expanding in Greece, these first results from spectral analysis of digital short-period data can be considered useful for future seismic hazard studies.     

High-precision relocation of the aftershock sequence of the January 8, 2022, MS6.9 Menyuan earthquake

The 2022 Menyuan M_S6.9 earthquake, which occurred on January 8, is the most destructive earthquake to occur near the Lenglongling (LLL) fault since the 2016 Menyuan M_S6.4 earthquake. We relocated the mainshock and aftershocks with phase arrival time observations for three days after the mainshock from the Qinghai Seismic Network using the double-difference method. The total length and width of the aftershock sequence are approximately 32 km and 5 km, respectively, and the aftershocks are mainly concentrated at a depth of 7–12 km. The relocated sequence can be divided into 18 km west and 13 km east segments with a boundary approximately 5 km east of the mainshock, where aftershocks are sparse. The east and west fault structures revealed by aftershock locations differ significantly. The west fault strikes EW and inclines to the south at a 71º–90º angle, whereas the east fault strikes 133º and has a smaller dip angle. Elastic strain accumulates at conjunctions of faults with different slip rates where it is prone to large earthquakes. Based on surface traces of faults, the distribution of relocated earthquake sequence and surface ruptures, the mainshock was determined to have occurred at the conjunction of the Tuolaishan (TLS) fault and LLL fault, and the west and east segments of the aftershock sequence were on the TLS fault and LLL fault, respectively. Aftershocks migrate in the early and late stages of the earthquake sequence. In the first 1.5 h after the mainshock, aftershocks expand westward from the mainshock. In the late stage, seismicity on the northeast side of the east fault is higher than that in other regions. The migration rate of the west segment of the aftershock sequence is approximately 4.5 km/decade and the afterslip may exist in the source region.     

岫岩-海城Ms5.4地震序列震源机制解

应用 P波初动符号资料 ,求解得到了岫岩 -海城 5.4级地震前、主、余震 2 0个 ML ≥ 4.0的震源机制解。分析表明 ,该地区的主压应力轴 (P)大多为 NEE- SWW向 ,主张应力轴 (T)大多为 NNW- SSE向 ,P、T轴仰角基本上小于 30°,表明力轴以水平者最多。N轴大多较陡。A、B节面的走向分别为 NWW向和 NNE向。岫岩 -海城地震主要为走滑断层类型。余震震源机制解绝大多数与主震相近 ,结果比较稳定 ,表明余震的应力场主要受主震震源应力场的控制     

Rupture process and aftershock focal mechanisms of the 2022 M6.8 Luding earthquake in Sichuan

According to the China Earthquake Networks Center, a strong earthquake of M6.8 occurred in Luding County, Ganzi Tibetan Autonomous Prefecture, Sichuan Province, China (102.08°E, 29.59°N), on September 5, 2022, with a focal depth of 16 km. Rapid determination of the source parameters of the earthquake sequence is vital for post-earthquake rescue, disaster assessment, and scientific research. Near-field seismic observations play a key role in the fast and reliable determination of earthquake source parameters. The numerous broadband seismic stations and strong-motion stations recently deployed by the National Earthquake Intensity Rapid Report and Early Warning project have provided valuable real-time near-field observation data. Using these near-field observations and conventional mid- and far-field seismic waveform records, we obtained the focal mechanism solutions of the mainshock and M ≥ 3.0 aftershocks through the waveform fitting method. We were further able to rapidly invert the rupture process of the mainshock. Based on the evaluation of the focal mechanism solution of the mainshock and the regional tectonic setting, we speculate that the Xianshuihe fault formed the seismogenic structure of the M6.8 strong earthquake. The aftershocks formed three spatially separated clusters with distinctly different focal mechanisms, reflecting the segmented nature of the Xianshuihe fault. As more high-frequency information has been applied in this study, the absolute location of the fault rupture is better constrained by the near-field strong-motion data. The rupture process of the mainshock correlates well with the spatial distribution of aftershocks, i.e., aftershock activities were relatively weak in the maximum slip area, and strong aftershock activities were distributed in the peripheral regions.     

2014年2月12日新疆于田MS7.3级地震主震及余震序列重定位研究

本研究采用基于贝叶斯理论的绝对定位方法对2014年2月12日新疆于田M_S7.3级地震进行绝对定位,得到震中位置为82.56°E、36.04°N、震源深度为12.3 km;采用双差定位法对254个地震序列进行相对定位,得到101个重定位事件.结果显示,主震位于阿尔金断裂带西南端多个分支断裂的交汇处.余震震源主要分布范围在5~10 km深度之间,主震处余震代表的断层面较为陡立,且余震序列呈现出明显的西南向纯单侧扩展模式.沿阿尔金断裂带主震的北东向民丰震区本次地震后显示一个明显的地震丛集,说明本次主震对该震区具有触发作用.     

The 20 April 2013 Lushan,Sichuan, mainshock,and its aftershock sequence: tectonic implications

Using the double-difference relocation algorithm, we relocated the 20 April 2013 Lushan, Sichuan, earthquake (M _S 7.0), and its 4,567 aftershocks recorded during the period between 20 April and May 3, 2013. Our results showed that most aftershocks are relocated between 10 and 20 km depths, but some large aftershocks were relocated around 30 km depth and small events extended upward near the surface. Vertical cross sections illustrate a shovel-shaped fault plane with a variable dip angle from the southwest to northeast along the fault. Furthermore, the dip angle of the fault plane is smaller around the mainshock than that in the surrounding areas along the fault. These results suggest that it may be easy to generate the strong earthquake in the place having a small dip angle of the fault, which is somewhat similar to the genesis of the 2008 Wenchuan earthquake. The Lushan mainshock is underlain by the seismically anomalous layers with low-V_P, low-V_S, and high-Poisson’s ratio anomalies, possibly suggesting that the fluid-filled fractured rock matrices might significantly reduce the effective normal stress on the fault plane to bring the brittle failure. The seismic gap between Lushan and Wenchuan aftershocks is suspected to be vulnerable to future seismic risks at greater depths, if any.     

The 2010 M w 7.2 El Mayor-Cucapah Earthquake Sequence, Baja California, Mexico and Southernmost California, USA: Active Seismotectonics along the Mexican Pacific Margin

The El Mayor-Cucapah earthquake sequence started with a few foreshocks in March 2010, and a second sequence of 15 foreshocks of M?>?2 (up to M4.4) that occurred during the 24?h preceding the mainshock. The foreshocks occurred along a north?Csouth trend near the mainshock epicenter. The M _w 7.2 mainshock on April 4 exhibited complex faulting, possibly starting with a ~M6 normal faulting event, followed ~15?s later by the main event, which included simultaneous normal and right-lateral strike-slip faulting. The aftershock zone extends for 120?km from the south end of the Elsinore fault zone north of the US?CMexico border almost to the northern tip of the Gulf of California. The waveform-relocated aftershocks form two abutting clusters, each about 50?km long, as well as a 10?km north?Csouth aftershock zone just north of the epicenter of the mainshock. Even though the Baja California data are included, the magnitude of completeness and the hypocentral errors increase gradually with distance south of the international border. The spatial distribution of large aftershocks is asymmetric with five M5+ aftershocks located to the south of the mainshock, and only one M5.7 aftershock, but numerous smaller aftershocks to the north. Further, the northwest aftershock cluster exhibits complex faulting on both northwest and northeast planes. Thus, the aftershocks also express a complex pattern of stress release along strike. The overall rate of decay of the aftershocks is similar to the rate of decay of a generic California aftershock sequence. In addition, some triggered seismicity was recorded along the Elsinore and San Jacinto faults to the north, but significant northward migration of aftershocks has not occurred. The synthesis of the El Mayor-Cucapah sequence reveals transtensional regional tectonics, including the westward growth of the Mexicali Valley and the transfer of Pacific?CNorth America plate motion from the Gulf of California in the south into the southernmost San Andreas fault system to the north. We propose that the location of the 2010 El Mayor-Cucapah, as well as the 1992 Landers and 1999 Hector Mine earthquakes, may have been controlled by the bends in the plate boundary.