Modelling and inversion of single-ended refraction data from the shot gathers of multifold deep seismic reflection profiling—an approach for deriving the shallow velocity structure

A multifold crustal-scale deep seismic near-vertical reflection profile generates a large number of single-ended shot gathers, which provide redundant data sets because of overlapping coverage of the shallow refractors. We present an approach for deriving the shallow velocity structure by modelling and inversion of single-ended seismic refraction first arrival traveltime data. We apply this method to a data set acquired with a 12-km long spread with 100 m spacing of shots and receivers, of the Neoproterozoic Marwar basin in the NW Indian shield. The approach is shown to be quite successful for delineating the shallow refractor depths, steep dips and velocities, even in the absence of regular reverse refraction profiles. The study reveals two-layered sedimentary formations, Malani volcanics and a complicated basement configuration of the Marwar basin, and provides a measure of resolution and uncertainty of the estimated model parameters. A seismic section of the near-trace gather is found to be qualitatively consistent with the derived structural features of the basin. The relative highs and lows, observed in the Bouguer gravity profile, further corroborate the derived velocity model. The present approach can be especially useful in offshore areas and elsewhere, where the single-ended multifold seismic profiles are the only available data sets.     

双平方根单程波动方程叠前τ偏移方法

本文将常规双平方根（DSR）单程波动方程从深度域变换到双程垂直走时（τ）域，由此推导出可从数学上实现“沉降观测”的单程波DSR传播算子. 其递归波场延拓算法包含波数域针对常速背景的相移处理和空间域针对横向速度扰动的相位校正，可以应对上覆地层速度横向变化对构造成像的影响. 结合零炮检距、零时间成像条件，提出了在τ域进行波场延拓与成像的DSR方程叠前偏移新方法. 为了克服其全三维偏移算法在实际应用中可能面临的困难，本文采用稳相近似，在crossline常炮检距偏移理论基础上推导了实用的共方位角叠前τ偏移方法. 数值试验表明，DSR方程叠前τ偏移在强横向非均匀介质中的成像精度与分辨率优于传统的时间域成像技术.     

井间地震走时波形层析成像方法

提出了井间地震走时波形顺序反演方法。该方法先利用井间地震走时反演得到速度模型的低频成分 ,然后用井间地震波形反演获得速度模型的高频成分。数值模型试验和实际应用结果表明 ,该方法反演稳健 ,提高了走时成像的分辨率 ,克服了波形成像易于陷入局部极小的缺陷 ,实现了快速高分辨率成像。     

Multifractal modeling and spatial point processes

The multifractal model can be applied to spatial point processes. It provides new, approximately power-law type, expressions for their second-order intensity and K (r) functions. The box-counting and cluster dimensions are different but mutually interrelated according to multifractal theory. This approach is used to describe the underlying spatial structure of gold mineral occurrences in the Iskut River area, northwestern British Columbia. The box-counting and cluster dimensions for the example are estimated to be 1.335±0.077 and 1.219±0.037, respectively. The relatively strong clustering of the gold deposits is reflected by the fact that both values are considerably less than the corresponding Euclidean dimension (=2).     

Three-dimensional geometrical ray theory and modelling of transmitted seismic energy of data from the Nevada Test Site

This paper presents a geometrically based algorithm for computing synthetic seismograms for energy transmitted through a 3-D velocity distribution. 3-D ray tracing is performed to compute the traveltimes and geometrical spreading (amplitude). The formulations of both kinematic and dynamic ray-tracing systems are presented. The two-point ray-tracing problem is solved by systematically updating the initial conditions and adjusting the ray direction until the ray intersects the specified endpoint. The amount of adjustment required depends on the derivatives of the position with respect to the given starting angles between consecutive rays. The algorithm uses derivatives to define the steepest-descent direction and to update the initial directions. The convergence rate depends on the complexity of the model.
Test seismograms compare favourably with those from a 2-D asymptotic ray theory algorithm and a 3-D Gaussian-beam algorithm. The algorithm is flexible in modelling arbitrary source and recorder geometries for various smoothly varying 3-D velocity distributions. The algorithm is further tested by simulating surface-to-tunnel vibroseis field data. Shear waves as well as compressional waves may be approximately included. Application of the algorithm to a data set from the Rainier Mesa of the Nevada Test Site produced a good fit to the transmitted (first arrival) traveltimes and amplitudes, with approximately 15 per cent variation in the local 3-D velocity.     

UPPER CRUSTAL VELOCITY STRUCTURE AND CONSTRAINING FAULT INTERPRETATION FROM SHUNYI-TANGGU REFRACTION EXPERIMENT DATA

The urban active fault survey is of great significance to improve the development and utilization of urban underground space, the urban resilience, the regional seismic reference modeling, and the natural hazard prevention. The Beijing-Tianjin metropolitan region with the densest population is one of the most developed and most important urban groups, located at the northeastern North China plain. There are several fault systems crossing and converging in this region, and most of the faults are buried. The tectonic setting of the faults is complex from shallow to deep. There are frequent historical earthquakes in this area, which results in higher earthquake risk and geological hazards. There are two seismicity active belts in this area. One is the NE directed earthquake belt located at the east part of the profile in northern Ninghai near the Tangshan earthquake region. The other is located in the Beijing plain in the northwest of the profile and near the southern end of Yanshan fold belt, where the 1679 M8.0 Sanhe-Pinggu earthquake occurred, the largest historical earthquake of this area. Besides, there are some small earthquake activities related to the Xiadian Fault and the Cangdong Fault at the central part of the profile.
The seismic refraction experiment is an efficient approach for urban active fault survey, especially in large- and medium-size cities. This method was widely applied to the urban hazard assessment of Los Angeles. We applied a regularized tomography method to modeling the upper crustal velocity structure from the high-resolution seismic refraction profile data which is across the Beijing-Tianjin metropolitan region. This seismic refraction profile, with 185km in length, 18 chemical explosive shots and 500m observation space, is the profile with densest seismic acquisition in the Beijing-Tianjin metropolitan region up to now. We used the trial-error method to optimize the starting velocity model for the first-arrival traveltime inversion. The multiple scale checker board tests were applied to the tomographic result assessment, which is a non-linear method to quantitatively estimate the inversion results. The resolution of the tomographic model is 2km to 4km through the ray-path coverage when the threshold value is 0.5 and is 4km to 7km through the ray-path coverage when the threshold value is 0.7. The tomographic model reveals a very thick sediment cover on the crystalline basement beneath the Beijing-Tianjin metropolitan region. The P wave velocity of near surface is 1.6km/s. The thickest sediment cover area locates in the Huanghua sag and the Wuqing sag with a thickness of 8km, and the thinnest area is located at the Beijing sag with a thickness of 2km. The thickness of the sediment cover is 4km and 5km in the Cangxian uplift and the Dacang sag, respectively. The depth of crystalline basement and the tectonic features of the geological subunits are related to the extension and rift movement since the Cenozoic, which is the dynamics of formation of the giant basins.
It is difficult to identify a buried fault system, for a tomographic regularization process includes velocity smoothing, and limited by the seismic reflection imaging method, it is more difficult to image the steep fault. Velocity and seismic phase variations usually provide important references that describe the geometry of the faults where there are velocity differences between the two sides of fault. In this paper, we analyzed the structural features of the faults with big velocity difference between the two sides of the fault system using the velocity difference revealed by tomography and the lateral seismic variations in seismograms, and constrained the geometry of the major faults in the study region from near surface to upper crust. Both the Baodi Fault and the Xiadian Fault are very steep with clear velocity difference between their two sides. The seismic refraction phases and the tomographic model indicate that they both cut the crystalline basement and extend to 12km deep. The Baodi Fault is the boundary between the Dachang sag and the Wuqing sag. The Xiadian Fault is a listric fault and a boundary between the Tongxian uplift and the Dachang sag. The tomographic model and the earthquake locations show that the near-vertical Shunyi-Liangxiang Fault, with a certain amount of velocity difference between its two sides, cuts the crystalline basement, and the seismicity on the fault is frequent since Cenozoic. The Shunyi-Liangxiang Fault can be identified deep to 20km according to the seismicity hypocenters.
The dense acquisition seismic refraction is a good approach to construct velocity model of the upper crust and helpful to identify the buried faults where there are velocity differences between their two sides. Our results show that the seismic refraction survey is a useful implement which provides comprehensive references for imaging the fault geometry in urban active fault survey.     

A method of obtaining a velocity-depth envelope from wide-angle seismic data

Summary. Due to the non-uniqueness of traveltime inversion of seismic data, it is more appropriate to determine a velocity-depth ( v-z ) envelope, rather than just a v-z function. Several methods of obtaining a v-z envelope by extremal inversion have been proposed, all of which invert the data primarily from either x-p , or T-p , or both domains. These extremal inversion methods may be divided into two groups: linear extremal and non-linear extremal. There is some debate whether the linearized perturbation techniques should be applied to the inherently non-linear problem of traveltime inversion. We have obtained a v-z envelope by extremal inversion in T-p with the constraint that the inversion paths also satisfy x-p observations. Thus we use data jointly in r-p and x-p , and yet avoid the linearity assumptions.
This joint, non-linear extremal inversion method has been applied to obtain a v-z envelope down to a depth of about 30 km in the Baltimore Canyon trough using x-t data from an Expanding Spread Profile acquired during the LASE project. We have found that the area enclosed by the v-z envelope is reduced by about 15 per cent using x-p control on the T-p inversion paths, compared to the inversion without x-p control.