Double-difference tomography of P- and S-wave velocity structure beneath the western part of Java,Indonesia

West Java in the western part of the Sunda Arc has a relatively high seismicity due to subduction activity and faults. In this study, double-difference tomography was used to obtain the 3D velocity tomograms of P and S waves beneath the western part of Java. To infer the geometry of the structure beneath the study area, precise earthquake hypocenter determination was first performed before tomographic imaging. For this, earthquake waveform data were extracted from the regional Meteorological, Climatological, Geophysical Agency (BMKG) network of Indonesia from South Sumatra to Central Java. The P and S arrival times for about 1,000 events in the period April 2009 to July 2016 were selected, the key features being events of magnitude > 3, azimuthal gap < 210° and number of phases > 8. A nonlinear method using the oct-tree sampling algorithm from the NonLinLoc program was employed to determine the earthquake hypocenters. The hypocenter locations were then relocated using double-difference tomography (tomoDD). A significant reduction of travel-time (root mean square basis) and a better clustering of earthquakes were achieved which correlated well with the geological structure in West Java. Double-difference tomography was found to give a clear velocity structure, especially beneath the volcanic arc area, i.e., under Mt Anak Krakatau, Mt Salak and the mountains complex in the southern part of West Java. Low velocity anomalies for the P and S waves as well as the v_P/v_S ratio below the volcanoes indicated possible partial melting of the upper mantle which ascended from the subducted slab beneath the volcanic arc.     

Tomography and the Herglotz-Wiechert inverse formulation

In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (seeHerglotz, 1907;Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.     

Potential and limits of double-difference tomographic methods

Double-difference tomographic methods use directly accurate time delays computed between similar signals. Such methods are designed to image very heterogeneous media, such as volcanoes or fault zones. In seismological applications, similar signals are recorded at a given station from earthquakes sharing similar and close-by sources. In seismic exploration experiments, similar signals are often recorded at neighbouring receivers. After a brief presentation of the tomographic algorithm used, a seismological application is summarized. The potential and limits of double-difference tomographic methods are explored using various numerical experiments. They show that two effects are competing in double-difference tomography: (i) the degradation of the stability of the inversion due to the geometrical proximity of the rays used in the differentiation and (ii) the decrease in modelling error, which allows improving the stability of the inversion and using smaller quantities of a priori information when data are sufficiently accurate. The best resolution is obtained for an optimal value of the inter-source or inter-receiver distance. For optimal values of these distances and a priori information, tomography using traveltime differences provides significantly better resolved results than using traveltimes.     

Crustal Structure Along the Lawrencepur-Astor Profile in the Northwest Himalayas

During the Pamir Himalayan project in the year 1975 seismic refraction and wide-angle reflection data were recorded along a 270 km long Lawrencepur-Astor (Sango Sar) profile in the northwest Himalayas. The profile starts in the Indus plains and crosses the Main Central Thrust (MCT), the Hazara Syntaxis, the Main Mantle Thrust (MMT) and ends to the east of Nanga Parbat. The seismic data, as published by Guerra et al. (1983), are reinterpreted using the travel-time ray inversion method of Zelt and Smith (1992) and the results of inversion are constrained in terms of parameter resolution and uncertainty estimation. The present model shows that the High Himalayan Crystallines (HHC, velocity 5.4 km s⁻¹) overlie the Indian basement (velocity 5.8–6.0 km s⁻¹). The crust consists of four layers of velocity 5.8–6.0, 6.2, 6.4 and 6.8 km s⁻¹ followed by the upper mantle velocity of 8.2 km s⁻¹ at a depth of about 60 km.     

Seismic phase picking in China Seismic Array using a deep convolutional neuron network*

Seismic phase picking is the preliminary work of earthquake location and body-wave travel time tomography. Manual picking is considered as the most accurate way to access the arrival times but time consuming. Many automatic picking methods were proposed in the past decades, but their precisions are not as high as human experts especially for events with low ratio of signal to noise and later arrivals. As the increasing deployment of large seismic array, the existing methods can not meet the requirements of quick and accurate phase picking. In this study, we applied a phase picking algorithm developed on the base of deep convolutional neuron network (PickNet) to pick seismic phase arrivals in ChinArray-Phase III. The comparison of picking error of PickNet and the traditional method shows that PickNet is capable of picking more precise phases and can be applied in a large dense array. The raw picked travel-time data shows a large variation deviated from the traveltime curves. The absolute location residual is a key criteria for travel-time data selection. Besides, we proposed a flowchart to determine the accurate location of the single-station earthquake via dense seismic array and phase arrival picked by PickNet. This research expands the phase arrival dataset and improves the location accuracy of single-station earthquake.     

Velocity and Attenuation Structure of the Tibetan Lithosphere Under the Hi-CLIMB Array From the Modeling of Pn Attributes

Using seismic data from regional earthquakes in Tibet recorded by the Hi-CLIMB experiment, Pn attributes are used to constrain the velocity gradient and attenuation structure of the Tibetan lithosphere under the Hi-CLIMB array. Numerical modeling is performed using the spectral-element method (SEM) for laterally varying upper-mantle velocity and attenuation, and the seismic attributes considered include the Pn travel-time, envelope amplitude, and pulse frequency. The results from the SEM modeling provide two alternative models for the upper-mantle beneath the Hi-CLIMB array in Tibet. The first model is derived from the 3D velocity model of Griffin et al. (Bull Seism Soc Am 101:1938–1947, 2011) with a constant upper-mantle velocity gradient, and laterally varying upper mantle attenuation. The second model has a laterally varying upper-mantle velocity gradient, and constant upper-mantle attenuation. In both cases, the Qiangtang terrane is distinguished from the Lhasa terrane by a change in Moho depth and upper-mantle velocities. The lower upper-mantle velocities, as well as higher Pn attenuation, suggest hotter temperatures beneath the Qiangtang terrane as compared to the Lhasa terrane. Although the fits to the Pn amplitude and pulse frequency data are comparable between the two models, the first model with the constant upper-mantle velocity gradient fits the travel times somewhat better in relation to the data errors.     

P‐wave velocity distribution in basalt flows of the Enni Formation in the Faroe Islands from refraction seismic analysis

The main objective of this work is to establish the applicability of shallow surface‐seismic traveltime tomography in basalt‐covered areas. A densely sampled ～1300‐m long surface seismic profile, acquired as part of the SeiFaBa project in 2003 ( Japsen et al. 2006 ) at Glyvursnes in the Faroe Islands, served as the basis to evaluate the performance of the tomographic method in basalt‐covered areas. The profile is centred at a ～700‐m deep well. V_P, V_S and density logs, a zero‐offset VSP, downhole‐geophone recordings and geological mapping in the area provided good means of control. The inversion was performed with facilities of the Wide Angle Reflection/Refraction Profiling program package ( Ditmar et al. 1999 ). We tested many inversion sequences while varying the inversion parameters. Modelled traveltimes were verified by full‐waveform modelling. Typically an inversion sequence consists in several iterations that proceed until a satisfactory solution is reached. However, in the present case with high velocity contrasts in the subsurface we obtained the best result with two iterations: first obtaining a smooth starting model with small traveltime residuals by inverting with a high smoothing constraint and then inverting with the lowest possible smoothing constraint to allow the inversion to have the full benefit of the traveltime residuals. The tomogram gives usable velocity information for the near‐surface geology in the area but fails to reproduce the expected velocity distribution of the layered basalt flows. Based on the analysis of the tomogram and geological mapping in the area, a model was defined that correctly models first arrivals from both surface seismic data and downhole‐geophone data.     

北京平原地区VS30估算模型适用性研究

本文使用基于钻孔测井数据的3类模型,即常速度外推模型、速度梯度模型、双深度参数外推模型,通过对北京地区460个深度超过30m的钻孔剪切波速资料进行分析,详细探究了V_S30估算模型在本研究区的适用性。研究结果表明双深度参数外推模型在估算V_S30上准确度很高,其不需要大量的数据进行回归分析,且不具有区域独立性,可以为全球包括北京地区场地类别划分提供依据,进而在震害快速评估中用于确定场地影响,是一种值得推广的估算模型。     

Fresnel zone inversion for lateral heterogeneities in the earth

We propose a different kind of seismic inversion from travel-time or waveform inversion for lateral heterogeneities in the earth: Fresnel zone inversion. Amplitude and phase delay of data in several frequency ranges are inverted for model space around ray paths with a width corresponding to the considered frequency so that primary effect of finiteness of wavelength be included. For vertically heterogeneous media, Fréchet derivatives for inversion are obtained very efficiently using the paraxial ray approximation, with nearly similar amounts of computation compared to travel-time inversion. As an example, Fréchet derivatives are computed for a teleseismic observation system for a three-dimensional structure in the lithosphere beneath an array of seismic stations. Even if the used frequency is around 2 Hz, the width of Fréchet derivatives cannot be neglected, particularly near the bottom of the lithosphere. Sensitivity of model parameters to observations is, moreover, different in our approach from conventional travel-time inversion: it is zero along ray paths but large slightly away from them. Some model calculations show that travel-time inversion, particularly with models divided into very fine meshes or blocks, might give misleading results. An example of inversion for a simple Camembert model, in the event that travel-time inversion gives no reliable results, shows how this technique works with much smaller data sets and computation than waveform inversions.     

Application of autoregressive extrapolation to the cross-borehole tomography

Autoregressive (AR) extrapolation of travel-time data is tested using several synthetic tomography examples using a cross-borehole geometry. Earlier studies have shown crossborehole tomography using travel-times can have reduced resolution because of the limitations on ray coverage. We apply AR extrapolation to partial travel-time data and then compare the tomographic inversions using the full data and the extrapolated data. Both the overall patterns of the extended data and the tomographic reconstructions with the extended data show that AR extrapolation can effectively extend the synthetic crossborehole tomographic data to a broader coverage and can improve the cross-hole reconstruction images.     

射线追踪的微变网格方法

本文给出一种适用于叠前数据速度分析和叠前深度偏移的快速射线追踪方法──微变网格法；该方法不仅精度高，而且计算速度极快，可适用于当前计算条件下的地球介质速度反演和叠前深度偏移成像的要求．     

微测井约束分步层析静校正技术在古峰庄地区的应用

针对地表剧烈起伏,速度纵、横向变化大的复杂区,层析静校正较以往的折射波静校正方法有明显的优势,但是受初至时间拾取精度、炮检距的选择、近地表模型约束等问题的影响,层析反演的精度还不能满足低幅度构造预测的需求,为此提出微测井约束分步层析的静校正方法,即将浅层速度模型与最终近地表模型分步进行层析反演,并应用微测井信息约束浅层速度模型层析反演,有效地提高了近地表速度模型反演的精度,通过在古峰庄地区的应用较好地解决了复杂地表条件下的静校正问题,低幅度构造预测精度得到提高.     

采用射线寻迹的井间层析成像

本文采用二维井间观测走时反演地震波速,用迭代射线寻迹走时成像方法进行层析成像.作者导出三次多项式插值基函数计算离散网格内的折射率分布,还给出了具有自己特点的二步扫描法,不但加快了正演计算时间,同时方便地建立走时残差与模型修正量的关系.考虑到实际应用时,震源与接收器常不位于同一平面,为此进行了校正,并给出了校正方法,提高了重建精度. 数值的与实际应用的结果表明,本文给出的层析成像算法是快速的、稳定的、适用的.     

Optimization of Cell Parameterizations for Tomographic Inverse Problems

—?We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cells are used as building blocks for construction of non-overlapping irregular cells. The construction algorithms are not computationally intensive and not particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model sampling or a priori estimates of model resolution. The link between a particular cell j in the regular basic grid and its host cell k in the irregular grid is provided by a pointer array which implicitly defines the irregular cell model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomographic equations is computed once on the regular basic cell model. After grid construction, the basic matrix equation is mapped using the pointer array on a new matrix equation in which the model vector relates directly to cells in the irregular model. Next, the mapped system can be solved on the irregular grid. This approach avoids forward computation on the complex geometry of irregular grids. Generally, grid optimization can aim at reducing the number of model parameters in volumes poorly sampled by the data while elsewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided and grid construction can aim at improving the conditioning of the inverse problem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocity inversion and global travel-time tomography.     

采用射线寻迹的井间层析成像

本文采用二维井间观测走时反演地震波速,用迭代射线寻迹走时成像方法进行层析成像.作者导出三次多项式插值基函数计算离散网格内的折射率分布,还给出了具有自己特点的二步扫描法,不但加快了正演计算时间,同时方便地建立走时残差与模型修正量的关系.考虑到实际应用时,震源与接收器常不位于同一平面,为此进行了校正,并给出了校正方法,提高了重建精度. 数值的与实际应用的结果表明,本文给出的层析成像算法是快速的、稳定的、适用的.     

Crust and Upper Mantle Structure in the Caribbean Region by Group Velocity Tomography and Regionalization

An overview of the crust and upper mantle structure of Central America and the Caribbean region is presented as a result of the processing of more than 200 seismograms recorded by digital broadband stations from SSSN and GSN seismic networks. Group velocity dispersion curves are obtained in the period range from 10s to 40s by FTAN analysis of the fundamental mode of the Rayleigh waves; the error of these measurements varies from 0.06 and 0.09 km/s. From the dispersion curve, seven tomographic maps at different periods and with average spatial resolution of 500 km are obtained. Using the logical combinatorial classification techniques, eight main groups of dispersion curves are determined from the tomographic maps and eleven main regions, each one characterized by one kind of dispersion curves, are identified. The average dispersion curves obtained for each region are extended to 150s by adding data from a larger-scale tomographic study (Vdovin et al., 1999) and inverted using a nonlinear procedure. A set of models of the S-wave velocity vs. depth in the crust and upper mantle is found as a result of the inversion process. In six regions we identify a typically oceanic crust and upper mantle structure, while in the other two the models are consistent with the presence of a continental structure. Two regions, located over the major geological zones of the accretionary crust of the Caribbean region, are characterized by a peculiar crust and upper mantle structure, indicating the presence of lithospheric roots reaching, at least, about 200 km of depth.     

Development and Applications of Double-difference Seismic Tomography

Double-difference (DD) tomography is a generalization of DD location; it simultaneously solves for the three-dimensional velocity structure and seismic event locations. DD tomography uses a combination of absolute and more accurate differential arrival times and hierarchically determines the velocity structure from larger scale to smaller scale. This method is able to produce more accurate event locations and velocity structure near the source region than standard tomography, which uses only absolute arrival times. We conduct a stability and uncertainty analysis of DD tomography based on a synthetic data set. Currently three versions of the DD tomography algorithms exist: tomoDD, tomoFDD and tomoADD. TomoDD assumes a flat earth model and uses a pseudo-bending ray-tracing algorithm to find rays between events and stations while tomoFDD uses a finite-difference travel-time algorithm and the curvature of the Earth is considered. Both codes are based on a regularly distributed inversion grid, with the former for a local scale and the latter for a regional scale. In contrast, tomoADD adapts the inversion mesh to match with the data distribution based on tetrahedral and Voronoi diagrams. We discuss examples of applying DD tomography to characterize fault zone structure, image high-resolution structure of subduction zones, and determine the velocity structure of volcanoes.     

联合利用走时与波形反演技术研究地壳三维速度结构(Ⅱ)——应用

使用阻尼最小二乘法进行震源参数和地壳三维速度结构的走时联合反演．所用资料为Ｓ波和Ｐ波到时差,并用人工地震资料的二维解释结果作为三维速度模型的特定约束条件．为建立初始模型,又利用天然地震构成了准二维剖面．在走时反演基础上,利用遗传算法进行了几个地震事件的波形反演尝试,并对走时反演获得的地壳速度结构模型的局部进行了修正．以３４°～４２°Ｎ,９４°～１１２°Ｅ作为研究区域,在该区域中收集了１９８６年以来大量地震的Ｓ波和Ｐ波到时差资料,７条人工地震二维速度剖面资料和２个数字化地震台的几个地震的三分向记录资料．对这些资料进行了处理,最后得出了０～２５ｋｍ深度不同截面的速度分布,并对所得结果进行了分析．     

Finite-frequency tomography in a crustal environment: Application to the western part of the Gulf of Corinth

In this paper we investigate finite-frequency effects in crustal tomography. We developed an inversion procedure based on an exact numerical computation of the sensitivity kernels. In this approach we compute the 3D travel-time sensitivity kernels by using (1) graph theory and an additional bending to estimate accurately both rays and travel-times between source/receiver and diffraction points and (2) paraxial ray theory to estimate the amplitude along theses rays. We invert both the velocity and the hypocentre parameters, using these so-called banana-doughnut kernels and the LSQR iterative solver. We compare the ray-theoretical and the finite-frequency tomography to image the intermediate structures beneath the Gulf of Corinth (Greece), which has long been recognized as the most active continental rifting zone in the Mediterranean region. Our dataset consists of 451 local events with 9233 P- first-arrival times recorded in the western part of the Gulf (Aigion area) in the framework of the 3F-Corinth European project. Previous tomographic images showed a complex velocity crustal model and a low-dip surface that may accommodate the deformation. Accurate velocity models will help to better constrain the rifting process, which is still a subject of debate. The main results of this study show that finite-frequency tomography improves crustal tomographic images by providing better resolved images of the 3D complicated velocity structure. Because the kernels spread the information over a volume, finite-frequency tomography results in a sharpening of layer boundaries as we observed for the shallower part of the crust (down to 5 km depth) beneath the Gulf of Corinth.