The influence of sea water velocity variation on seismic traveltimes,ray paths,and amplitude

The main factors affecting seismic exploration is the propagation velocity of seismic waves in the medium. In the past, during marine seismic data processing, the propagation velocity of sea water was generally taken as a constant 1500 m/s. However, for deep water exploration, the sound velocity varies with the season, time, location, water depth, ocean currents, and etc.. It also results in a layered velocity distribution, so there is a difference of seismic traveltime, ray paths, and amplitude, which affect the migration imaging results if sea water propagation velocity is still taken as constant for the propagation wavefield. In this paper, we will start from an empirical equation of seismic wave velocity in seawater with changes of temperature, salinity, and depth, consider the variation of their values, build a seawater velocity model, and quantitatively analyze the impact of seawater velocity variation on seismic traveltime, ray paths, and amplitude in the seawater velocity model.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

Irregular surface flattening,which is based on a boundary conforming grid and the transformation between curvilinear and Cartesian coordinate systems,is a mathematical method that can elegantly handle irregular surfaces,but has been limited to obtaining first arrivals only.By combining a multistage scheme with the fast-sweeping method(FSM,the method to obtain first-arrival traveltime in curvilinear coordinates),the reflected waves from a crustal interface can be traced in a topographic model,in which the reflected wavefront is obtained by reinitializing traveltimes in the interface for upwind branches.A local triangulation is applied to make a connection between velocity and interface nodes.Then a joint inversion of first-arrival and reflection traveltimes for imaging seismic velocity structures in complex terrains is presented.Numerical examples all perform well with different seismic velocity models.The increasing topographic complexity and even use of a high curvature reflector in these models demonstrate the reliability,accuracy and robustness of the new working scheme;checkerboard testing illustrates the method's high resolution.Noise tolerance testing indicates the method's ability to yield practical traveltime tomography.Further development of the multistage scheme will allow other later arrivals to be traced and used in the traveltime inversion.

A new scheme for fast calculation of seismic traveltimes and ray paths in heterogeneous media

A new method based on Huygens' principle and Fermat's principle is presented to calculate seismic traveltime and ray-paths in this paper. The algorithm can be easily understood and programmed, and can be applied to heteroge neous media in order to eliminate its disadvantage of slowness, we have improved the basic algorithm to speed its calculation to practical stage without the loss of its accuracy.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

A regression approach for seismic first-break picking

The picking efficiency of seismic first breaks(FBs)has been greatly accelerated by deep learning(DL)technology.However,the picking accuracy and efficiency of DL methods still face huge challenges in low signal-to-noise ratio(SNR)situations.To address this issue,we propose a regression approach to pick FBs based on bidirectional long short-term memory(Bi LSTM)neural network by learning the implicit Eikonal equation of 3D inhomogeneous media with rugged topography in the target region.We employ a regressive model that represents the relationships among the elevation of shots,offset and the elevation of receivers with their seismic traveltime to predict the unknown FBs,from common-shot gathers with sparsely distributed traces.Different from image segmentation methods which automatically extract image features and classify FBs from seismic data,the proposed method can learn the inner relationship between field geometry and FBs.In addition,the predicted results by the regressive model are continuous values of FBs rather than the discrete ones of the binary distribution.The picking results of synthetic data shows that the proposed method has low dependence on label data,and can obtain reliable and similar predicted results using two types of label data with large differences.The picking results of9380 shots for 3D seismic data generated by vibroseis indicate that the proposed method can still accurately predict FBs in low SNR data.The subsequent stacked profiles further illustrate the reliability and effectiveness of the proposed method.The results of model data and field seismic data demonstrate that the proposed regression method is a robust first-break picker with high potential for field application.

基于多声源波速结构成像的岩体异常区域超前辨识方法

异常区域超前辨识对于预防地下岩土工程灾害具有重要作用。为了满足地下工程高精度探测的需求,本文提出一种层析成像方法以辨识复杂岩体结构中的异常区域,结合了走时层析、阻尼最小二乘和高斯滤波等技术。该方法克服了空洞区域辨识中速度差限制,减轻了迭代中孤立速度突变所带来的影响。我们开展了数值和室内实验量化评估最短路径法(Shortest-Path Method,SPM)、动态最短路径法(Dynamic Shortest-Path Method,DSPM)和快速扫描法(Fast Sweeping Method,FSM)等正演模拟的识别精度和计算效率。结果表明,在数值和室内实验中DSPM和FSM均能清晰地辨识出异常区域。陕西震奥矿山现场应用结果证明了该方法可利用矿山开采中爆破、微震等多类声源对矿山内部未知结构进行波速场成像。本研究不仅实现了走时层析成像方法在异常区域识别中的应用,而且为地下岩土工程中潜在风险源的探测提供了新的思路。

A review of the influencing factors on teleseismic traveltime tomography

Teleseismic traveltime tomography is an important tool for investigating the crust and mantle structure of the Earth.The imaging quality of teleseismic traveltime tomography is affected by many factors,such as mantle heterogeneities,source uncertainties and random noise.Many previous studies have investigated these factors separately.An integral study of these factors is absent.To provide some guidelines for teleseismic traveltime tomography,we discussed four main influencing factors:the method for measuring relative traveltime differences,the presence of mantle heterogeneities outside the imaging domain,station spacing and uncertainties in teleseismic event hypocenters.Four conclusions can be drawn based on our analysis.(1)Comparing two methods,i.e.,measuring the traveltime difference between two adjacent stations(M1)and subtracting the average traveltime of all stations from the traveltime of one station(M2),reveals that both M1 and M2 can well image the main structures;while M1 is able to achieve a slightly higher resolution than M2;M2 has the advantage of imaging long wavelength structures.In practical teleseismic traveltime tomography,better tomography results can be achieved by a two-step inversion method.(2)Global mantle heterogeneities can cause large traveltime residuals(up to about 0.55 s),which leads to evident imaging artifacts.(3)The tomographic accuracy and resolution of M1 decrease with increasing station spacing when measuring the relative traveltime difference between two adjacent stations.(4)The traveltime anomalies caused by the source uncertainties are generally less than 0.2 s,and the impact of source uncertainties is negligible.

Joint 3D traveltime calculation based on fast marching method and wavefront construction

3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method （WFC）, which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.

An intersection method for locating earthquakes in complex velocity models

The intersection method is one of the basic approaches for locating earthquakes and is not only robust but also efficient. However, its location accuracy is not high, especially for focal depth because the velocity model used for the conventional intersection method is based on homogeneous or laterally homogeneous media, which is too simple. In order to improve the accuracy, we have modified the existing intersection method. In the modified approach, the earthquake loci are not assumed to be circular or hyperbolic and calculation accuracy is improved using a minimum traveltime tree algorithm for tracing rays. The numerical model shows that the modified method can locate earthquakes in complex velocity models.

Multi-wave amplitude-preserved AVO modeling considering wave propagation effects

Traditional AVO forward modeling only considers the impact of reflection coefficients at the interface on seismic wave field amplitude and ignores various propagation effects. Introducing wave propagation effects including geometric spreading, transmission loss, attenuation into seismic wave propagation, multi-wave amplitude-preserved AVO forward modeling for horizontally layered media based on ray theory is proposed in this paper. We derived the multi-wave geometric spreading correction formulas for horizontally layered media in order to describe the geometric spreading effect of multi-wave propagation. Introducing the complex traveltime directly, we built the relationship between complex traveltime and quality factor without the help of complex velocity to describe the attenuation of viscoelastic media. Multi-wave transmission coefficients, obtained by solving the Zoeppritz equations directly, is used to describe the transmission loss. Numerical results show that the effects of geometric spreading, attenuation, and transmission loss on multi-wave amplitude varies with offset and multi-wave amplitude-preserved AVO forward modeling should consider the reconstructive effect of wave propagation on reflection amplitude.

Optimized nonhyperbolic moveout correction equation of long-offset seismic data for TI media with an arbitrary spatial orientation

The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis（ATI）.In this paper,we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient（A_4） and NMO velocity for ATI media that were derived in our previous work.Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media,this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media.It can replace the time-consuming, multi-offset,and multi-azimuth ray tracing method for forward modeling of long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.

Reflection-based traveltime and waveform inversion with second-order optimization

Reflection-based inversion that aims to reconstruct the low-to-intermediate wavenumbers of the subsurface model, can be a complementary to refraction-data-driven full-waveform inversion(FWI), especially for the deep target area where diving waves cannot be acquired at the surface. Nevertheless, as a typical nonlinear inverse problem, reflection waveform inversion may easily suffer from the cycleskipping issue and have a slow convergence rate, if gradient-based first-order optimization methods are used. To improve the accuracy and convergence rate, we introduce the Hessian operator into reflection traveltime inversion(RTI) and reflection waveform inversion(RWI) in the framework of second-order optimization. A practical two-stage workflow is proposed to build the velocity model, in which Gauss-Newton RTI is first applied to mitigate the cycle-skipping problem and then Gauss-Newton RWI is employed to enhance the model resolution. To make the Gauss-Newton iterations more efficiently and robustly for large-scale applications, we introduce proper preconditioning for the Hessian matrix and design appropriate strategies to reduce the computational costs. The example of a real dataset from East China Sea demonstrates that the cascaded Hessian-based RTI and RWI have good potential to improve velocity model building and seismic imaging, especially for the deep targets.

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks,which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block,and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization,which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models.The damped least squares method is employed in seismic traveltime inversion,which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.

Fast and accurate calculation of seismic wave travel time in 3D TTI media

The Tilted tilted transversely isotropic(TTI)media,a kind of anisotropic medium,widely exists within the earth.For faster calculation of travel times in the TTI anisotropic media,we modifi ed a minimum traveltime tree algorithm with high effi ciency by dynamical modifi cation of the secondary wave propagation region during the spread of seismic waves.To manage the wavefront points in the modified version,we used a novel minimum heap sorting technique to reduce the time spent on selecting secondary waves points.In this study,seismic group velocities were obtained from analytical solutions in terms of phase angle,and the corresponding phase angles were determined by binary search rather than approximate equations for weakly anisotropic media.For the most time-consuming part of the secondary wave traveltime calculation,the parallel computation was initially performed using multiple cores and threads.Numerical examples showed that the improved method can calculate seismic travel times and ray paths faster and accurately in a 3D TTI medium.For four cores and eight threads,the computing speed increased by six times when compared to the conventional method.

2-D crustal structure of Changbaishan-Tianchi volcanic region determined by seismic traveltime inversion

2-D velocity structure and tectonics of the crust and upper mantle is revealed by inversion of seismic refraction and wide-angle reflection traveltimes acquired along the profile L1 in the Changbaishan-Tianchi volcanic region. It is used in this study that seismic traveltime inversion for simultaneous determination of 2-D velocity and interface structure of the crust and upper mantle. The result shows that, under Changbaishan-Tianchi crater, there exists a low-velocity body in the shape of an inverted triangle, and the crustal reflecting boundaries and Moho all become lower by a varying margin of 2-6 km, forming a crustal root which is assumed to be the Changbaishan-Tianchi volcanic system. Finally, we make a comparison between our 2-D velocity model and the result from the studies by using trial-and-error forward modeling with SEIS83.

Upper crustal structure under Jingtai–Hezuo profile in Northeastern Tibet from topography-dependent eikonal traveltime tomography

The Northeastern Tibetan plateau records Caledonian Qilian orogeny and Cenozoic reactivation by continental collision between the Indian and Asian plates. In order to provide the constraint on the Qilian orogenic mechanism and the expansion of the plateau,wide-angle seismic data was acquired along a 430 km-long profile between Jingtai and Hezuo. There is strong height variation along the profile,which is dealt by topography flattening scheme in our crustal velocity structure reconstruction. We herein present the upper crustal P-wave velocity structure model resulting from the interpretation of first arrival dataset from topography-dependent eikonal traveltime tomography. With topography flattening scheme to process real topography along the profile,the evenness of ray coverage times of the image area（upper crust）is improved,which provides upper crustal velocity model comparable to the classic traveltime tomography（with model expansion scheme to process irregular surface）. The upper crustal velocity model shows zoning character which matcheswith the tectonic division of the Qaidam-Kunlun-West Qinling belt,the Central and Northern Qilian,and the Alax blocks along the profile. The resultant upper crustal P-wave velocity model is expected to provide important base for linkage between the mapped surface geology and deep structure or geodynamics in Northeastern Tibet.

Marchenko imaging based on self-adaptive traveltime updating

Marchenko imaging obtains the subsurface reflectors using one-way Green’s functions,which are retrieved by solving the Marchenko equation.This method generates an image that is free of spurious artifacts due to internal multiples.The Marchenko imaging method is a target-oriented technique;thus,it can image a user specified area.In the traditional Marchenko method,an accurate velocity model is critical for estimating direct waves from imaging points to the surface.An error in the velocity model results in the inaccurate estimation of direct waves.In turn,this leads to errors in computation of one-way Green’s functions,which then affects the final Marchenko images.To solve this problem,in this paper,we propose a self-adaptive traveltime updating technique based on the principle of equal traveltime to improve the Marchenko imaging method.The proposed method calculates the time shift of direct waves caused by the error in the velocity model,and corrects the wrong direct wave according to the time shift and reconstructs the correct Green’s functions.The proposed method improves the results of imaging using an inaccurate velocity model.By comparing the results from traditional Marchenko and the new method using synthetic data experiments,we demonstrated that the adaptive traveltime updating Marchenko imaging method could restore the image of geological structures to their true positions.

Teleseismic P-Wave Tomography of the New Guinea-Solomon Arc System

A P-wave tomographic traveltime inversion was applied to obtain a new model of seismic velocity anomalies beneath the New Guinea-Solomon arc system(PN-SL).The P-wave traveltime data,obtained from the revised International Seismological Center catalog,were recorded by 82 seismic stations in the PN-SL.Under the constraints of the epicenter distance,magnitude,and the number of stations recorded,15009 effective P-wave traveltime data were selected from 2011 teleseismic events.The obtained model showed that the Solomon Sea Plate subducted beneath the New Britain Island along the New Britain Trench at an angle of>70°and that the slab can be traced down to a depth of approximately 800 km.Conversely,we cannot observe a high-velocity anomaly exhibited by the subducted Solomon Sea Plate in the deep mantle at the Trobriand Trench,and the slab stopped at a depth of<200 km.The double subduction of the Solomon Sea Plate strongly modified the subduction patterns of the early subducted Pacific and Australian plates in the mantle along the West Melanesian Trench and the Pocklington Trough,respectively.In addition,the subducted Solomon Sea Plate induced the melting of the upper mantle to form a low-velocity anomaly,which provided the deep dynamic source for the expansion of the Bismarck Sea.Based on the joint consideration of the tomography results and a petrological analysis,the low-velocity anomalies beneath the Solomon Sea and Woodlark Basin are closely related to the early subduction of the Pacific and Australian Plates,respectively.

Application of teleseismic tomography to the study of shallow structure beneath Shizigou in the western Qaidam basin

Teleseismic body wave traveltime tomography is used to inverse the three-dimensional seismic velocity structure beneath Shizigou in the western Qaidam basin. The travel time are picked from the continuous observation data on a small seismic array of stations deployed during 2004-2007. The tomographic results obtained indicate that a NW-trending low velocity anomaly just beneath the target region insert northeastwards with a high dip angle. In the north, northeast and east of the low velocity anomaly, some high-velocity anomalies distribute with the same strike and coverage as those of Shizigou anticline.