SOURCE ARRAY SCALING FOR WAVELET DECONVOLUTION*

A seismic source array is normally composed of elements spaced at distances less than a wavelength while the overall dimensions of the array are normally of the order of a wavelength. Consequently, unpredictable interaction effects occur between element and the shape of the far field wavelet, which is azimuth-dependent, can only be determined by measurements in the far field. Since such measurements are very often impossible to make, the shape of the wavelet—particularly its phase spectrum—is unknown. A theoretical design method for overcoming this problem is presented using two scaled arrays. The far field source wavelets from the source arrays have the same azimuth dependence at scaled frequencies, and the far field wavelets along any azimuth are related by a simple scaling law. Two independent seismograms are generated by the two scaled arrays for each pair of source-receiver locations, the source wavelets being related by the scaling law. The technique thus permits the far field waveform of an array to be determined in situations where it is impossible to measure it. Furthermore it permits the array design criteria to be changed: instead of sacrificing useful signal energy for the sake of the phase spectrum, the array may be designed to produce a wavelet with desired amplitude characteristics, without much regard for phase.     

WHY WATERGUNS?*

A single watergun generates a ‘stand-alone’ narrow pulse of acceptable energy content and broad-band spectrum. When multiple units of equal volume are fired simultaneously and are accurately synchronized, carefully depth-controlled and spaced beyond their near-field interactive distance, the energy measured in the far-field increases proportional to the square of the number of individual units employed. When these multiple units are configured in areal array designs based on distance weighting or varying density distribution of the equal elements, further gains in downward directivity and attenuation of horizontally traveling interference accrue. Such pattern designs take account of the spectral content of the particular watergun used, while the wavenumber response is concentrated to attenuate the dominant interference at water velocity. Finally, the high-frequency content, and high repeatability and synchronizing accuracy of the new generation of waterguns improves the high resolution potential to help combat natural earth absorption losses. We should, therefore, keep the ‘in-line’ dimensions at both source and receiver as short as possible. Unacceptable interference that persists during subsequent processing can be controlled by the long-array simulation technique.     

SIGNATURE AND AMPLITUDE OF LINEAR AIRGUN ARRAYS *

During the last few years many airgun arrays have been designed with the objective of generating a short signature of high amplitude. For linear arrays of non-interacting airguns two rules have been derived that may help in the design or evaluation of airgun arrays. To achieve a short pressure pulse, the total available air volume has to be distributed over the individual guns in such a way that the tail of the signal, owing to the added bubble signals, becomes as flat as possible. When we think of ordering airguns according to volume, this flat signal tail can be achieved by designing the volumes such that the difference in bubble times of two adjacent guns is proportional to their volume to the power 2/3. The amplitude expected from a linear array of non-interacting airguns is limited by the physical length of the array. A graph of measured values tends to confirm this relation. No relation has been found between the total volume of an array and its amplitude. The graph also detects inefficient use of available array length of existing arrays.     

A Scheme for Initial Beam Deployment for the International Monitoring System Arrays

v--vThe International Monitoring System (IMS) includes a diverse set of seismic arrays with different configurations. These configurations have apertures ranging from less than 1 to more than 25 km and minimum interelement spacings varying from 0.1 to 3.6 km. This paper presents a scheme for initial beam deployment for this variety of seismic arrays. Beamforming is equivalent to a spatiotemporal bandpass filter of which passband is defined by the minimum and maximum wavenumbers, which are functions of the geometry configuration of the array. Deployment of steered-beams for signal detection is based on the wavenumber resolution of the array, slowness and frequency distributions of seismic phases, and coherence properties of seismic signals and noises among sensors. Within the wavenumber passband, all possible slowness values are determined by the resolution for each frequency band, and those that are outside the range of seismological interest are excluded. The appropriate azimuthal distribution for each selected slowness is determined from the azimuthal resolution. Using this approach, detection beams for each array are rationally deployed in the slowness-azimuth and frequency domain.     

微震记录的空间自相关法误差特性分析

本文定量研究了当面波能量分布不遵循各向均匀的假设时,运用空间自相关法（SPAC法）出现的误差.通过分析合成微震记录,研究了方位局限的入射、站台的数量对空间自相关系数的影响,明确了一些圆形排列的SPAC系数偏差空间构造.它可分为两个部分：低频域的零偏差部分和高频域的偏差部分.在高频偏差域,存在排列特色的周期特性.其角度周期是排列圆周上相邻站点之间夹角的一半.研究中要强调的是对于每种圆形排列存在一些特殊的入射方向的现象（如,对三角形排列,那些方向角度为 15°, 45°, 75°,…）.当瑞利波沿着这些角度之一传播时,在SPAC谱中,有效的无偏差频率范围扩展到先前研究结果的两倍.这个现象为提高野外SPAC法勘探精度提供了一个新的可能.     

地震台阵监测能力综述

根据各大网站地震目录和前人研究成果,分析全球地震台网与地震台阵、我国区域台网与地震台阵的监测能力,阐述了地震台阵与密集台网/台阵的区别。研究表明,对同一地区所检测的地震数,地震台阵是地震台网的3-10倍,而震级下限可降低1.2-2级。一般情况下,以微弱信号检测为目的的地震台阵监测能力均优于以结构研究为目的的密集台网/台阵,2种台阵是目的、性质、孔径、形状、台间距、技术手段、研究方法均不同的监测系统。     

Scattering of elastic waves by a fracture zone containing randomly distributed cracks

We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ ^–1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ ^–1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ ^–1 is proportional tok ^–1 independently of model parameters and the wave modes. If the seismological observation thatQ ^–1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.     

Wavenumber response of Shanghai Seismic array

Seismic array can be traced back to 1950s when it mainly aimed at detecting and distinguishing the signals of nuclear explosion and seismic signals. The research on seismic array includes seismic array techniques and applications of array in geophysics. Array techniques involve array design and data processing methods (Anne, 1990). Nowadays, the continuous development of seismic array￠s theory could relate to many scientific issues in geophysical field (Tormod, 1989; Mykkeltveit, Bungum, 1984). Seismic array is mainly applied to detect weak events. The response characteristic of array is an important indication of array￠s detection ability. Therefore, when we study an array or construct an array, one of the neces-sary works is to calculate the response characteristics of the array (Harjes, 1990). The aperture and layout of array are two dominating geometrical features. The typical aperture of interna-tional array is generally from several to tens kilometers. For instance, arrays with aperture of dozens kilometers aperture are KSA, WRA, YKA, etc, while arrays with several kilometer aperture are ARC, FIN, GEE, etc. Moreo-ver, in the view of array￠s layout, NOR, GER, etc have circle layout, while WRA, YKA, etc have decussating layout. This paper mainly discusses the relation between deployment of array and wavenumber response. With the example of constructing Shanghai Seismic Array, this paper provides one practical solution to search the proper array deployment. In this paper, the simple delay beam technique is adopted to calculate the response characteris-tics of array. Certainly, the different processing methods have different result, but the result from the simple delay beam processing could be enough to reflect the feature of an array.     

Characterization of regional and local scattering effects from small-aperture seismic array recordings

In 1998, four small-aperture arrays separated by 20 km have been deployed in the southern French Alps in order to record the natural seismicity during two consecutive months. One of the main objectives of this experiment was to characterize the heterogeneities that influence the wavefield propagation, by analysis of the coda characteristics recorded by each of the seismic arrays.The time-azimuth-velocity characteristics of the coda phases have been obtained using a high-resolution wavenumber decomposition method.A statistical analysis, using the coda characteristics of the whole data set (20 regional earthquakes) recorded by the four arrays has been performed and lead to the calculation of the density of scattered energy within the medium. Three regional heterogeneous areas (> 10 km) have been characterized, and are located in the N–NE, W and S directions from the four arrays. Scattered energy is also located at local distances (< 10 km) from the four arrays.The comparison of the waveforms recorded (i) with one of the array, for different groups of earthquakes, and (ii) with the four arrays, for one group of earthquakes, show that the geometrical configuration of the source–scattering area–recording site system can strongly influence the energetic distributions related to the secondary phases of the seismograms.In particular cases, we experimentally show that the interactions of the direct wavefield with the heterogeneous structures of the medium can be sufficiently energetic to induce secondary scattered phases that dominate the seismic motions recorded at a given site. In such case, these effects should be taken into account for the quantification of the expected ground motion recorded during an earthquake.     

Slowness Corrections — One Way to Improve IDC Products

—?The first step to identify and locate a seismic event is the association of observed onsets with common seismic sources. This is especially important in the context of monitoring the Comprehensive Nuclear-Test-Ban Treaty (CTBT) at the International Data Center (IDC) being developed in Vienna, Austria. Well-defined slowness measurements are very useful for associating seismic phases to presumed seismic events.¶Shortly after installation of the first seismic arrays, systematic discrepancies between measured and theoretically predicted slowness values were observed, and therefore slowness measurements of seismic stations should be calibrated. The observed slownesses measured with small aperture arrays, some of which will be included in the International Monitoring System (IMS) now being implemented for verifying compliance with the CTBT, show large scatter and deviations from theoretically expected values. However, in this study a method is presented, by which mean slowness corrections can be derived, which show relatively stable patterns specific to each array.¶The correction of measured slowness values of these arrays clearly improved the single array location capabilities. Applying slowness corrections with seismic phases observed by ARCES, FINES, GERES, and NORES, and associated to seismic events in the bulletins of the prototype International Data Center (pIDC) in Arlington, VA, also clearly demonstrates the advantages of these corrections. For arrays with large slowness deviations that are due to the influence of a dipping layer, the corrections were modeled with a sine function depending on the measured azimuth. In addition, the measured values can be weighted with the corresponding uncertainties known from the process of deriving the mean corrections.     

Microseismic feasibility studies – assessing the probability of success of monitoring projects

In this paper we present a workflow for microseismic feasibility studies that allows a thorough assessment of the probability of success of the monitoring project to be made. The workflow includes the following elements: assessment of the value of information to establish the business case; identification of hardware options to investigate deployment options; survey of analogue cases to confirm the do‐ability of the project; modelling of event location errors and detectability to establish the most favourable array geometry; generation of full waveform synthetics to anticipate undesired seismic features. A study comprising all these elements provides the reference frame for discussions with service companies, limiting misunderstandings and avoiding missed opportunities.     

Orientation error estimation of buried seismographs in array observation

Array observation is an efficient tool to investigate various characteristics of earthquake ground motion. However, seismographs used in arrays may involve unexpected errors in their orientations. Methods of orientation error estimation were developed in three-dimensional space by comparing recorded ground motions at a reference point with those at a checking point. A maximum cross-correlation method and a maximum coherence method were proposed and their accuracy was demonstrated. The earthquake ground motions recorded in the Chiba array and in two other arrays were used in numerical examples. Non-trivial orientation errors were detected for all these arrays. The cross-correlation coefficients and the coherence values between two points increased significantly by correcting the estimated orientation errors.     

IMAGING CAPABILITY OF CROSS-HOLE SEISMIC REFLECTION SURVEYS1

In seismic migration, it is important to sample a range of dips around the local structural dip at each image point. Meaningful images are obtained only where this condition holds. For cross-hole seismic reflection surveys, the distribution of dips sampled at each image point is controlled principally by the survey geometry, including source and receiver array lengths and their element spacings. Using a real data set as an example, we show how survey geometry can limit imaging capability close to the boreholes and even in the middle of the section between the boreholes. At the processing stage, effective removal of direct waves and accurate estimation of the velocity field are essential for optimizing image quality. For migration, we propose a generalized Berryhill (GB) scheme which is based on the Kirchhoff integral and takes into account both the near-field and far-field terms. This should improve the ability to image close to source and receiver arrays, provided that the element spacing in the nearby array is small enough.     

Robust dual‐sensor data sea‐surface ghost attenuation for quality control purposes

Three‐dimensional receiver ghost attenuation (deghosting) of dual‐sensor towed‐streamer data is straightforward, in principle. In its simplest form, it requires applying a three‐dimensional frequency–wavenumber filter to the vertical component of the particle motion data to correct for the amplitude reduction on the vertical component of non‐normal incidence plane waves before combining with the pressure data. More elaborate techniques use three‐dimensional filters to both components before summation, for example, for ghost wavelet dephasing and mitigation of noise of different strengths on the individual components in optimum deghosting. The problem with all these techniques is, of course, that it is usually impossible to transform the data into the crossline wavenumber domain because of aliasing. Hence, usually, a two‐dimensional version of deghosting is applied to the data in the frequency–inline wavenumber domain. We investigate going down the “dimensionality ladder” one more step to a one‐dimensional weighted summation of the records of the collocated sensors to create an approximate deghosting procedure. We specifically consider amplitude‐balancing weights computed via a standard automatic gain control before summation, reminiscent of a diversity stack of the dual‐sensor recordings. This technique is independent of the actual streamer depth and insensitive to variations in the sea‐surface reflection coefficient. The automatic gain control weights serve two purposes: (i) to approximately correct for the geometric amplitude loss of the Z data and (ii) to mitigate noise strength variations on the two components. Here, Z denotes the vertical component of the velocity of particle motion scaled by the seismic impedance of the near‐sensor water volume. The weights are time‐varying and can also be made frequency‐band dependent, adapting better to frequency variations of the noise. The investigated process is a very robust, almost fully hands‐off, approximate three‐dimensional deghosting step for dual‐sensor data, requiring no spatial filtering and no explicit estimates of noise power. We argue that this technique performs well in terms of ghost attenuation (albeit, not exact ghost removal) and balancing the signal‐to‐noise ratio in the output data. For instances where full three‐dimensional receiver deghosting is the final product, the proposed technique is appropriate for efficient quality control of the data acquired and in aiding the parameterisation of the subsequent deghosting processing.     

Comment on “Slowness-azimuth corrections of teleseismic events for IMS primary arrays in China” by Hao and Zheng

Knowledge about backazimuth and slowness deviations at seismic arrays can be used as a tool to study subsurface lateral heterogeneity and improve the ability to locate events. Recently, Hao and Zheng (J Seismol 13:437–448, 2009) estimated the backazimuth and slowness deviations for teleseismic P waves recorded by the HILR array and the LZDM array using f–k analysis. They attributed the significant deviations at the LZDM array to dipping structures beneath the array. However, another possible factor, namely the altitude variations of array elements, was not taken into consideration during the slowness estimation process. For the LZDM array, the maximum altitude difference is ~15% of the array aperture and not negligible. In this study, we made some numerical experiments to investigate the difference between the estimated and theoretical slowness vectors when ignoring the altitude difference. The results reveal that remarkable artificial slowness shift is produced. Assuming a P-wave velocity of 5.4 km/s immediately beneath the array, the magnitude of slowness shift increases from 1.4 to 2.2 s/° when the theoretical slowness decreases from 16 to 4 s/°. For a 10° emergence angle, the backazimuth deviation reaches nearly 40°, and the relative slowness deviation can be greater than 60%. It is also shown that ignoring the altitude difference gives rise to a northeastward slowness shift, opposite to the southwestward shift proposed by Hao and Zheng, suggesting that they have heavily underestimated the slowness residuals at the LZDM array. Note that the elevation of one of the array stations is much lower than others. Avoiding the use of this station, the elevation variation range of array stations decreases by nearly one half, and the artificial backazimuth and slowness deviations decrease by more than one half.     

上海地震台阵的标定方法

地震台阵标定可以校正视慢度和后方位角，从而进一步校正震源位置，有助于提高地震定位精度及地震类型鉴别研究等。此外，台阵标定也可校正由于台阵接收系统而导致视慢度和后方位角的偏差。     

Coda pattern and multipath propagation of Rayleigh waves at NORSAR

The coda of Rayleigh waves from fifteen earthquakes recorded at the Norwegian Seismic Array (NORSAR) have been analyzed in wavenumber space at periods of 40 and 20 sec. The power at 40 sec drops off faster vs. time, which reduces the probability of interference between events. On the other side, the capability of the array to resolve signals under various conditions is better at 20 sec. Since also the frequency distribution of signal power varies, one cannot determine any specific frequency as generally having the best signal/interference ratio. The detection problem is also complicated by considerable multipath propagation, which is most severe at 20 sec. Multipath arrivals with as much as 40–60° azimuthal deviation are frequently identified. Travel path solutions for different events are proposed, and usually the rays have been found to be refracted or reflected at continental boundaries. An atmospheric nuclear explosion from Lop Nor has been used to illustrate these various aspects of the problem of detecting one Rayleigh wave in the presence of another.     

THEORETICAL AND EXPERIMENTAL INVESTIGATIONS FOR CAVITY RESEARCH WITH GEOELECTRICAL RESISTIVITY METHODS*

The exact localization of subterranean cavities and the determination of their dimensions is very important for the planning of geotechnical and mining activities. It is a complicated geophysical task often at the limit of detection. Nevertheless geophysical investigation is the only alternative to a dense and expensive grid of boreholes. This report tests the usefulness of geoelectrical resistivity methods for cavity detection under some new aspects. The basis for evaluation was a theoretical analysis of different conventional and focussing measuring arrays and of special arrays for a geoelectrical research between two boreholes. The limit of detectability of a cylindrical cavity of defined cross-section and depth was calculated for the different measuring arrays on the basis of computation of the apparent resistivity ρa. Furthermore, the influence of possible errors (current supply of the electrodes and the distance between the electrodes) is discussed for focussed systems. The second part of the article is directed at the behaviour of the apparent resistivity ρa, the disturbing potential δV_d caused by the cavity and the normal potential δV₀ of the measuring array all in relation to a homogeneous earth. Some new results are presented. In the last part of the article theoretical results are compared with some field measurements.     

天然源面波勘探台阵对比试验

为了对比天然源面波勘探不同台阵布局的探测效果, 筛选出探测成果可靠、 效率高和便于野外施工的天然源面波勘探台阵阵形, 在天水市黄土覆盖区的同一场地分别用4种常见的阵形进行数据采集试验, 并对各种阵形数据使用空间自相关法或扩展空间自相关法提取相应的频散曲线, 通过反演得到了试验点地下的浅层速度结构模型. 分析对比试验结果表明: 4种台阵提取的频散曲线数值很相近; 频散谱能量集中度较高的是嵌套式等边三角形和圆形台阵, L形和直线形台阵相对分散; L形台阵低频段(4—8 Hz)比直线形台阵差, 其高频段(8—40 Hz)比直线形台阵好. 针对直线形台阵在高频段信噪比较低的情况, 在确保探测成果可靠性的前提下, 为了提高探测效率, 提出了在同一直线形台阵开展天然源与人工源面波联合勘探的数据采集方法. 实验结果证实, 这种联合勘探方法不仅可弥补直线形台阵高频段的不足, 确保探测精度和结果的可靠性, 而且还能实现“高低”频兼顾, 即“深浅”兼顾.      

Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system

Helmholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques such as series expansions and Picard iterations. These techniques can accommodate in principle any variation of the wavenumber with position and are applicable to scalar wave propagation in one, two and three dimensions, with the latter two cases requiring radial symmetry. As shown in the examples, good solution accuracy can be achieved in the near field region, irrespective of frequency, for the particular case examined, namely a wavenumber which increases (or decreases) as the square root of the radial distance from source to receiver. Finally, the resulting Green's functions can be used as kernels within the context of boundary element type solutions to study scalar wave scattering in inhomogeneous media.