Finite difference calculation of traveltime on non-orthogonal grid

Finite difference methods have been widely employed in solving the eikonal equation so as to calculate traveltime of seismic phase. Most previous studies used regular orthogonal grid. However, much denser grid is required to sample the interfaces that are undulating in depth direction, such as the Moho and the 660 km discontinuity.Here we propose a new finite difference algorithm to solve the eikonal equation on non-orthogonal grid（irregular grid）.To demonstrate its efficiency and accuracy, a test was conducted with a two-layer model. The test result suggests that the similar accuracy of a regular grid with ten times grids could achieve with our new algorithm, but the time cost is only about 0.1 times. A spherical earth model with an undulant660 km discontinuity was constructed to demonstrate the potential application of our new method. In that case, the traveltime curve fluctuation corresponds to topography. Our new algorithm is efficient in solving the first arrival times of waves associated with undulant interfaces.

3D S-wave velocity structure of the Ningdu basin in Jiangxi province inferred from ambient noise tomography with dense array

The Ningdu basin,located in southern Jiangxi province of southwest China,is one of the Mesozoic basin groups which has exploration prospects for geothermal energy.A study on the detailed velocity structure of the Ningdu basin can provide important information for geothermal resource exploration.In this study,we deployed a dense seismic array in the Ningdu basin to investigate the 3D velocity structure and discuss implications for geothermal exploration and geological evolution.Based on the dense seismic array including 35 short-period(5 s-100 Hz)seismometers with an average interstation distance of~5 km,Rayleigh surface wave dispersion curves were extracted from the continuous ambient noise data for surface wave tomographic inversion.Group velocity tomography was conducted and the 3D S-wave velocity structure was inverted by the neighborhood algorithm.The results revealed obvious low-velocity anomalies in the center of the basin,consistent with the low-velocity Cretaceous sedimentary rocks.The basement and basin-controlling fault can also be depicted by the S-wave velocity anomalies.The obvious seismic interface is about 2 km depth in the basin center and decreases to 700 m depth near the basin boundary,suggesting spatial thickness variations of the Cretaceous sediment.The fault features of the S-wave velocity profile coincide with the geological cognition of the western boundary basincontrolling fault,which may provide possible upwelling channels for geothermal fluid.This study suggests that seismic tomography with a dense array is an effective method and can play an important role in the detailed investigations of sedimentary basins.

Donald V.Helmberger,the master mentor:Testimonials from former international students

Don trained many Ph.D.students over the〜5 decades of his career,at least 45 were advised or co-advised according to a Caltech account.A large number were international students including a high percentage of Chinese students.The contributors to this article graduated over a time span of 26 years,and we are now distributed in 6 countries across 14 time zones,yet we represent only a small fraction of his former students and postdocs.

The 2023 M_(w)6.8 Adassil Earthquake(Chichaoua,Morocco)on a steep reverse fault in the deep crust and its geodynamic implications

The Mw 6.8 Adassil earthquake that occurred in the High Atlas on September 8,2023,was a catastrophic event that provided a rare opportunity to study the mechanics of deep crustal seismicity.This research aimed to decipher the rupture characteristics of the Adassil earthquake by analyzing teleseismic waveform data in conjunction with interferometric synthetic aperture radar(InSAR)observations from both ascending and descending orbits.Our analysis revealed a reverse fault mechanism with a centroid depth of approximately 28 km,exceeding the typical range for crustal earthquakes.This result suggests the presence of cooler temperatures in the lower crust,which facilitates the accumulation of tectonic stress.The earthquake exhibited a steep reverse mechanism,dipping at 70°,accompanied by minor strike-slip motion.Within the geotectonic framework of the High Atlas,known for its volcanic legacy and resulting thermal irregularities,we investigated the potential contributions of these factors to the initiation of the Adassil earthquake.Deep seismicity within the lower crust,away from plate boundaries,calls for extensive research to elucidate its implications for regional seismic hazard assessment.Our findings highlight the critical importance of studying and preparing for significant seismic events in similar geological settings,which would provide valuable insights into regional seismic hazard assessments and geodynamic paradigms.

Determination of focal depth by two waveform-based methods:A case study for the 2008 Panzhihua earthquake

With the 2008 Ms6.1 Panzhihua earthquake as a case study, we demonstrate that the focal depth of the main shock can be well constrained with two approaches： （1） using the depth phase sPL and （2） using full waveform inversion of local and teleseismic data. We also show that focal depths can be well constrained using the depth phase sPL with single broadband seismic station. Our study indicates that the main shock is located at a depth of ii kin, much shallower than those from other studies, confirming that the earthquake occurs in upper crust. Aftershocks are located in the depth range of 11 16 kin, which is consistent with a ruptured near vertical fault whose width is about 10 km, as expected for an Ms6.1 earthquake.

Composition of high frequency ambient noise from cross-correlation:A case study using a small aperture array

Long-time cross correlation of ambient noise has been proved as a powerful tool to extract Green＇s function between two receivers. The study of composition of ambient noise is important for a better understanding of this method. Previous studies confirm that ambient noise in the long period （3 s and longer） mostly consists of surface wave, and 0.25-2.5 s noise consists more of body waves. In this paper, we perform cross correlation processing at much higher frequency （30-70 Hz） using ambient noise recorded by a small aperture array. No surface waves emerge from noise correlation function （NCF）, but weak P waves emerge. The absence of surface wave in NCF is not due to high attenuation since surface waves are strong from active source, therefore probably the high ambient noise mostly consists of body wave and lacks surface wave. Origin of such high frequency body waves in ambient noise remains to be studied.

Seismic attenuation in the lower mantle beneath Northeast China constrained from short-period reflected core phases at short epicentral distances

The thermal structure of the lower mantle plays a key role in understanding the dynamic processes of the Earth's evolution and mantle convection.Because intrinsic attenuation in the lower mantle is highly sensitive to temperature,determining of the attenuation of the lower mantle could help us determine its thermal state.We attempted to constrain the attenuation of the lower mantle by measuring the amplitude ratios of p to ScP on the vertical component and s to ScS on the tangential component at short epicentral distances for seismic wave data from deep earthquakes in Northeast China.We calculated the theoretical amplitude ratios of p to ScP and s to ScS by using ray theory and the axial-symmetric spectral element method AxiSEM,as well as by considering the effects of radiation patterns,geometrical spreading,and ScP reflection coefficients.By comparing the observed amplitude ratios with the synthetic results,we constrained the quality factors as Qα≈3,000 and Qβ≈1,300 in the lower mantle beneath Northeast China,which are much larger than those in the preliminary reference Earth model(PREM)model of Qα~800 and Qβ~312.We propose that the lower mantle beneath Northeast China is relatively colder than the average mantle,resulting in weaker intrinsic attenuation and higher velocity.We estimated the temperature of the lower mantle beneath Northeast China as approximately 300–700 K colder than the global average value.

Source model of the 11th July 2004 Zhongba earthquake revealed from the joint inversion of InSAR and seismological data

We use interferometric synthetic aperture radar （InSAR） and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within the seismically active zone of southwestern Tibetan Plateau where the east-west extension of the upper crust is observed. Because of limitations in one pair of InSAR data available, there are trade-offs among centroid depth, rupture area and amount of slip. Available seismic data tightly constrain the focal mechanism and centroid depth of the earthquake but not the horizontal location. Together, two complementary data sets can be used to identify the actual fault plane, better constrain the slip model and event location. We first use regional seismic waveform to estimate point source mechanism, then InSAR data is used to obtain better location. Finally, a joint inversion of teleseismic P-waves and InSAR data is performed to obtain a distributed model. Our preferred point source mechanism indicates a seismic moment of ～2.2×10 18 N·m （～M W 6.2）, a fault plane solution of 171° （342 ° ）/42 ° （48 ° ）/-83 ° （-97 ° ）, corresponding to strike/dip/rake, and a depth of 11 km. The fault plane with strike of 171 ？ and dip of 42° is identified as the ruptured fault with the aid of InSAR data. The preferred source model features compact area of slips between depth of 5–11 km and 10 km along strike with maximum slip amplitude of about 1.5 m.

Stationary phase approximation in the ambient noise method revisited

The method of extracting Green＇s function between stations from cross correlation has proven to be effective theoretically and experimentally. It has been widely applied to surface wave tomography of the crust and upmost mantle. However, there are still controversies about why this method works. Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space, and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green＇s function. His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green＇s function. However, his derivation ignores influence from the two stationary points at infinities, therefore it may fail when attenuation is absent. In order to obtain accurate noise-correlation function due to scatters over the whole space, we compute the total contribution with numerical integration in polar coordinates. Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function, in both amplitude and phase, when the frequency is low with reasonable quality factor Q. Our results argue that the dis- tance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method, and only the station pairs whose distances are above several （〉5） wavelengths can be used.

Crustal S-wave velocity structure of the Yellowstone region using a seismic ambient noise method

The Yellowstone volcano is one of the largest active volcanoes in the world, and its potential hazards demand detailed seismological and geodetic studies. Previous studies with travel time tomography and receiver functions have revealed a low-velocity layer in the crust beneath the Yellowstone volcano, suggesting the presence of a magma chamber at depth. We use ambient seismic noise from regional seismic stations to retrieve short-period surface waves and then study the shallow shear velocity structure of the Yellowstone region by surface wave dispersion analysis. We first obtained a crustal model of the area outside of the Yellowstone volcano and then constructed an absolute shear wave velocity structure in combination with receiver function results for the crust beneath the Yellowstone volcano. The velocity model shows a low-velocity layer with shear velocity at around 1.3 km/s, suggesting that a large-scale magma chamber exists at shallow levels within the crust of the Yellowstone volcanic region.

Effects of sedimentary layer on earthquake source modeling from geodetic inversion

Ground deformation as observed with GPS or InSAR has been broadly inverted in constraining source parameter of earthquakes. However, for earthquakes occurring beneath sedimentary basins, the very slow sub-surface shear velocity （v S , down to 200 m/s） may cause substantial bias to earthquake source inversion if simple crustal models are used. For Bohai basin, Sichuan basin and rock-sites, we test effects of sub-surface shear velocity structure on ground deformation, and find that up to a factor of 2 overestimate of seismic moment could be generated by the basin structures. Therefore, the very slow sub-surface velocity has to be taken into account before accurate source inversion can be applied.

运用26s定点持续脉动源的同步洲际地震台网

地震学的定量研究需要精确的仪器时钟。最近的研究进展表明,可利用背景噪声来检测存在软件/硬件问题的海底地震仪(OBS)或陆上地震仪的台站时钟漂移情况。在稀疏的全球地震台网尺度下,从背景噪声中提取的短周期(<20s)瑞利波信号相对较弱,应用时受到限制。位于几内亚湾的持续稳定的26s固定脉动源,辐射出较强的噪声信号,可以被全球台站记录到,因而可以利用它同步加大距离台站间的时钟漂移情况。本文基于噪声互相关方法,我们尝试运用该26s的脉动信号检测非洲、北美和欧洲等地区地震台站的时钟精度。结果发现TAM,OBN台站的时钟在2002~2009年间相对稳定;CCM台站的时钟在2006~2009年间出现了约1s偏差,并且时钟的漂移量不稳定;KOWA台站的时钟漂移从2012年10月的约150s最大上升至2013年1月的约500s。本文将得到的结果与Stehly等(2007)利用背景噪声方法得到的结果、以及远震P波初至到时残差进行了对比分析。利用本文提出的方法,通过与经精确校正过的陆地台站同步,可校正北大西洋海底地震仪的时钟。

体波接收函数与瑞利波椭圆率联合反演研究

近年来,结合体波接收函数或瑞利波椭圆率,面波频散已被广泛应用于岩石层结构的成像研究中。由于面波频散是其传播路径的总传播效应,因此联合反演方法需依赖于密集的地震台阵或较高的地震活动性,从而获得局部速度结构。但是,接收函数和瑞利波椭圆率均为具有局部敏感性的单台测量方法,并且能自然地相互合并进行联合反演。本文中,我们对利用瑞利波椭圆率和接收函数联合反演的可行性进行了探讨。我们通过正演模拟进行了敏感性检验,发现接收函数对速度跃变的界面较为敏感,但对长波结构显示较弱的敏感性,这几乎与瑞利波椭圆率互补。因此,利用两种单台测量方法进行联合反演为地震台站下方的速度结构提供了更严格的条件约束。本文提出了一种基于快速模拟退火方法的联合反演算法,对岩石层结构的瑞利波椭圆率和接收函数进行反演。该算法在印度克拉通和美国威利斯顿盆地的应用中,在减少反演的非唯一性方面证明了其有效性。但是,通过该联合反演可能无法获得有效的地壳平均速度,表明有必要结合面波频散(或其他类型的观察研究)、接收函数和瑞利波椭圆率来获得更准确的速度结构。

Wave separation for the great Sumatra-Andaman earthquake with regional seismic array

We analyzed the seismic waveforms from the December 26, 2004 Sumatra-Andaman earthquake recorded at broadband seismic stations in western Europe. Previous studies involving of the beam-forming technique and high frequency analysis suggest that the earthquake ruptured with a duration of around 500 s. This very long duration makes P wave overlap with later arrivals such as PP wave, which follows P in about 200 s. Since P waves are crucial for modeling earthquake processes, we propose an iterative method to separate P and PP waveforms. The separated P waveform confirms a second large energy release around 300 s after the initial rupture. The iterative signal separation technique is particularly useful for mixed signals that are not independent and the number of recording stations far exceeds number of mixed signal sources.

Preface to the special issue on Lushan earthquake

On April 20th, 2013, a strong earthquake （Ms7, China Earthquake Network Center） struck Lushan county of Sichuan province and the quake （hereafter referred to as Lushan earthquake） caused substantial loss of life and damage to infrastructure. Just as the 2008 Ms8 Wenchuan earthquake, the Lushan earthquake also occurred on the Longmenshan fault system. After the Lushan earthquake, preliminary studies of the Lushan earthquake and its pos- sible link to the Wenchuan earthquake have been published in special issues rapidly organized in a few journals such as Seismological Research Letters, Chinese Journal of Geo- physics and Science in China.

Preface to the special issue on earthquake geodesy

Geodesy is among the oldest branches of Earth science with historical record of geodesy study by Thales of Miletus more than 2000 years. Originally geodesy was defined as the science of measuring and portraying of the Earth＇s surface, i.e., assuming that the Earth is

Causative fault and seismogenic mechanism of the 2010 Suining M5.0 earthquake from joint modeling of seismic and InSAR data

Although the Sichuan basin is a stable block with low historical seismicity,the Suining M5.0 earthquake on January31,2010 occurred near the center of the basin,causing casualty and substantial damage.Previous studies have shown that the earthquake is very shallow and may occur in the sedimentary cover rocks,but its causative fault has not been identified.Based on local broadband seismic waveform data as well as a pair of ALOS PALSAR ascending orbit data,we explore the seismogenic mechanism via further constraining the source depth and the ruptured fault.The earthquake caused ground uplift in the southeast of the epicenter area,with a maximum line of sight displacement of about 13.6 cm,much larger than the displacement caused by a M5 earthquake at a typical depth of 10 km,which indicates that the earthquake is very shallow.Through joint inversion of seismic waveform and InSAR data,we obtain the moment magnitude of Suining earthquake as MW4.5,with the strike,dip,and rake of its fault plane as 17°,66° and 90°,respectively,and the centroid depth less than 1 km,supporting that the earthquake occurred at the shallow part of a high angle thrust fault dipping to the southeast.It is further confirmed that the earthquake may be triggered by the diffusion of high-pressure fluid migrating from the underside gas reservoir.

2008年汶川地震ScS波是否触发了首个6级余震?

2008年汶川7.8级地震的15 min后,发生了首个6级强余震.由于该余震的发生时刻接近主震的ScS到达时,有学者认为此次地震是由主震的ScS波动态触发的.作为第一个核幔反射震相触发强余震的案例,需要进行细致研究.为了更准确地探讨ScS的触发作用,基于射线理论计算了合成地震图,并分析主震ScS的波形特征.首先,计算主震近距离ScS的到达时,推导该震相的几何扩散因子并估计其振幅,合成理论ScS波形.通过与实际观测波形的对比发现,主震ScS尚未到达时,首个6级强余震已经发生.而且主震ScS波形引起的长周期应力变化不足1 kPa,低于余震触发阈值.此外,青藏高原周边另外两次大地震的余震序列也未发现ScS触发强余震的现象.因此认为大地震的ScS也许难以触发大陆内部强余震,但是否适用于俯冲带地区还需进一步研究.

An Adaptive 2D Planar Projection and Its Application in Geoscience Studies

A linear projection approach is developed to present geoscience research result in planar coordinate system projected from spherical coordinate system. Here, the sphere is intersected by a plane and its surface is projected onto the plane. In order to keep the projected coordinate system orthogonal, and minimize the distortion, one axis of the planar coordinate system is chosen in our projection based on the shape of the region to be projected, and the other axes can be chosen arbitrarily or based on the constraint of the orthogonality. In the new method the projection is self-contained. The forward projection can be fully projected backward without loss of precision. The central area of the sphere will be projected to the planar system without distortion, and the latitudinal length in the rotated spherical system keeps constant during the projecting process. Only the longitudinal length in the rotated spherical system changes with the rotated latitude. The distortion of the projection therefore, overall, is small and suitable for geoscience studies.

Complexities of the Turkey-Syria doublet earthquake sequence

WHAT,WHERE,AND WHEN In the early morning of February 6th,2023,an M7.8 earthquake occurred in southeastern T€urkiye near the northern border of Syria.The event initiated a complex sequence of aftershocks,including an M7.6 earthquake about 9 h later and 90 km to the north(Figures 1A and 1B).The earthquake sequence is also referred to as a strong doublet earthquake sequence.Aftershocks of the two strong earthquakes occurred along two separate branches of the East Anatolia Fault,with lengths of up to 300 km,and some aftershocks occurred in Syria(NEIC/USGS,2023).