Fluctuation theory of ambient noise imaging

Travel time estimation and reflector imaging can be carried out using the cross correlations of signals generated by ambient noise sources and recorded at sensor arrays. We study here the mean and variance of the estimated quantities both with respect to the distribution of the noise sources and with respect to the distribution of the randomly scattering medium. In particular, we discuss the trade-off between resolution enhancement due to illumination diversification by scattering and the associated signal-to-noise ratio reduction, also due to scattering.     

Seismic interferometry and ambient noise tomography in the British Isles

Traditional methods of imaging the Earth's subsurface using seismic waves require an identifiable, impulsive source of seismic energy, for example an earthquake or explosive source. Naturally occurring, ambient seismic waves form an ever-present source of energy that is conventionally regarded as unusable since it is not impulsive. As such it is generally removed from seismic data and subsequent analysis. A new method known as seismic interferometry can be used to extract useful information about the Earth's subsurface from the ambient noise wavefield. Consequently, seismic interferometry is an important new tool for exploring areas which are otherwise seismically quiescent, such as the British Isles in which there are relatively few strong earthquakes. One of the possible applications of seismic interferometry is ambient noise tomography (ANT). ANT is a way of using interferometry to image subsurface seismic velocity variations using seismic (surface) waves extracted from the background ambient vibrations of the Earth. To date, ANT has been used successfully to image the Earth's crust and upper-mantle on regional and continental scales in many locations and has the power to resolve major geological features such as sedimentary basins and igneous and metamorphic cores. Here we provide a review of seismic interferometry and ANT, and show that the seismic interferometry method works well within the British Isles. We illustrate the usefulness of the method in seismically quiescent areas by presenting the first surface wave group velocity maps of the Scottish Highlands using only ambient seismic noise. These maps show low velocity anomalies in sedimentary basins such as the Moray Firth, and high velocity anomalies in igneous and metamorphic centres such as the Lewisian complex. They also suggest that the Moho shallows from south to north across Scotland which agrees with previous geophysical studies in the region.     

Structure of the Mt Isa region from seismic ambient noise tomography

We use seismic tomography, exploiting group velocities derived from ambient noise, to delineate the crustal structure beneath Mt Isa and the surrounding blocks and basins. The depth extent of the blocks can be traced into the mid-crust and the spatial extent of the associated velocity anomalies mapped over an area of approximately 500 km by 500 km. The Proterozoic Mt Isa block is imaged as a region of elevated seismic velocities comparable to the Yilgarn craton in Western Australia, while the surrounding basins have relatively low velocities. Seismic velocity anomalies display correlations with the regional Bouguer gravity data and with high crustal temperatures in the region. There are a number of isolated low-velocity anomalies under the Millungera basin that suggest either previously unknown thermal anomalies or zones with high permeability, which can also produce lowered velocities.     

On the temporal stability of the coda of ambient noise correlations

We analyze the sensitivity of cross correlations to the anisotropy of the incident field in the context of seismic ambient noise monitoring of small velocity changes. Numerical simulations of elastic waves are performed in a 2D scattering plate with a focus on the comparative character of the direct and coda waves in the cross-correlation. We show that coda waves reconstructed from cross-correlations are far more robust than direct waves in the presence of azimuthal anisotropy of the incident field. We observe similar behavior with real data recorded on Erebus volcano, where a database of impulsive icequakes is used to simulate an anisotropic source field. We propose a simplified approach to evaluate the sensitivity of scattered waves to the anisotropy of the incoming noise field. We rely on previous results obtained for direct waves and on intrinsic properties of scattered waves to predict the errors produced by strong source anisotropy with numerical experiments. These results also yield realistic values for monitoring the accuracy to be expected with real data at crustal scales. Our analysis shows that high-precision noise-based monitoring could be performed with coda waves in the correlation functions, even in the presence of variations in the azimuthal distribution of the ambient noise field.     

On the amplitudes of correlations and the inference of attenuations,specific intensities and site factors from ambient noise

While techniques for retrieval of seismic velocities from wavelet arrival times in ambient noise correlations are now well established, interpretation of wavelet amplitudes remains unsatisfactory. It is clear that such amplitudes contain information on seismic attenuation, but they are also affected by ambient noise intensity, site amplification, and any nonlinear preprocessing that may have been applied to the noise signals. Disentangling these many factors in order to reliably recover seismic attenuation is challenging. It is argued here that noise intensity, while rarely isotropic or homogeneous, may nevertheless be modeled by a radiative transfer equation. It is then shown that this recognition sufficiently constrains the noise intensity that we may hope to fit measured correlation amplitudes to models for spatially varying attenuation and site amplification factors. One-bit preprocessing, it is shown, is not compatible with such fits except in the special case of spatially constant noise intensity. An alternative procedure for accelerating convergence is suggested. Numerical simulations for a case of homogeneous attenuation and homogeneous seismic velocity are presented in support of the assertions. Attenuation, site factors, and noise intensity are successfully retrieved from correlations of numerically simulated imperfectly diffuse waves measured on a linear array of sensors.     

利用背景噪声层析成像研究济南浅层横波速度结构

城市地球物理探测面临众多人文挑战,像城市交通、密布电网、参差楼群等,对应用不同方法进行数据处理分析提出了技术挑战,需要用创新的方式和技术进行城市探测。为探索和发展适用于城市地下空间资源开发利用的地球物理探测新技术,中国地质科学院地球深部探测中心第一次启动了城市地下空间勘查评价试点工程,并选择济南市作为试点城市,试验短周期密集台阵噪声层析技术,并取得了较好成效。获得的主要认识如下：(1)在非弥散场或非均匀噪声场源的人文干扰较为严重的城市区域,通过长时间的噪声信号的采集,可获得高信噪比的面波信号,因此密集台阵噪声成像技术适应于城市地下空间的背景岩层结构探测工作。(2)本次研究提取出了周期范围为0.2～1.5 s的高信噪比面波信号,并取得与实际地质特征相一致的横波速度结构信息。(3)从横波速度结构特征来看,研究区300 m以浅,主要岩性为灰岩且主要分布于研究区西侧,而侵入岩体主要分布于东侧,中间存在一个明显的分界面,指示存在一个近南北向的隐伏断裂。随着深度的增加,大面积的侵入岩体展布于深层,灰岩只在北侧局部有显现。总体来说,本项研究证明了密集台阵噪声层析方法能够适用于人文干扰严重的城市地下空间背景岩层结构探测,这一成果对认识研究区地下结构、地震防灾、工程应用具有重要指导意义。     

青藏高原东部基于噪声的面波群速度分布特征

通过收集青海、甘肃、四川三省的76个地震台记录的2008年1—12月三分量的连续噪声数据,利用噪声面波层析成像的方法获得了青藏高原东部的面波群速度分布特征。首先采用多重滤波方法提取了1 000多条台站对5～50 s的三分量面波群速度频散曲线,然后将研究区域划分为0.2°×0.2°的网格,利用O ccam方法反演了瑞利波(R-R)和勒夫波(T-T)的群速度分布。反演得到的群速度分布特征与地表地质和构造特征表现出较好的相关性,清晰地揭示了地壳内部的横向速度变化。层析成像的结果显示在短周期(8～20 s)内,拥有较厚的沉积层的四川盆地表现为明显的低速特征,而青藏高原东部则表现为较高的群速度分布特征;随着周期的增加(>20 s),群速度的分布特征呈现出与短周期相反的特性,青藏高原东部下方的速度远远低于四川盆地,这可能与青藏高原东部中、下地壳低速层相关联,同时也意味着研究区域的地壳结构具有明显的横向不均匀性。在群速度分布图上,龙门山不仅是四川盆地与青藏高原的地形和构造分界带,同时也对应着高群速度与低群速度的过渡带。     

Ambient noise tomography with a large seismic array

The emergence of large-scale arrays of seismometers across several continents presents the opportunity to image the Earth's structure at unprecedented resolution, but methods must be developed to exploit the capabilities of these deployments. The capabilities and limitations of a method called “eikonal tomography” applied to ambient noise data are discussed here. In this method, surface wave wavefronts are tracked across an array and the gradient of the travel time field produces estimates of phase slowness and propagation direction. Application data from more than 1000 stations from EarthScope USArray in the central and western US and new Rayleigh wave isotropic and anisotropic phase velocity maps are presented together with an isotropic and azimuthally anisotropic 3D Vs model of the crust and uppermost mantle. As a ray theoretic method, eikonal tomography models bent rays but not other wavefield complexities. We present evidence, based on the systematics of an observed 1ψ component of anisotropy that we interpret as anisotropic bias caused by backscattering near an observing station, that finite frequency phenomena can be ignored in ambient noise tomography at periods shorter than ～ 40 to 50 s. At longer periods a higher order term based on wavefront amplitudes or finite frequency sensitivity kernels must be introduced if the amplitude of isotropic anomalies and the amplitude and fast-axis direction of azimuthal anisotropy are to be determined accurately.     

Passive image interferometry for monitoring crustal changes with ambient seismic noise

The technique to retrieve Green’s functions by cross-correlation of seismic noise that is now often referred to as seismic interferometry opened the way to a completely new type of seismological observation – the continuous monitoring of changes in the subsurface medium. In this paper we review Passive image interferometry (PII) as the technique that makes use of the possibility to repeatedly retrieve Green’s functions in order to precisely infer medium changes by comparing Green’s functions that are retrieved at different times. PII is capable of identifying velocity changes below 0.1% and was applied successfully in different tectonic situations. We review three investigations of PII that demonstrate the wide range of possible applications. The first application that introduced the concept of PII in 2006 revealed hydrology related changes of subsurface velocity at Merapi volcano. The second application we present was the first noise based observation of co-seismic changes. And we finally review a recent investigation that documented velocity variations in the shallow subsurface of the moon.     

Monitoring volcanoes using seismic noise correlations

In this article, we summarize some recent results of measurements of temporal changes of active volcanoes using seismic noise cross-correlations. We first present a novel approach to estimate volcano interior temporal seismic velocity changes. The proposed method allows to measure very small velocity changes (≈ 0.1%) with a time resolution as small as one day. The application of that method to Piton de la Fournaise Volcano (La Réunion Island) shows velocity decreases preceding eruptions. Moreover, velocity changes from noise cross-correlations over 10 years allow to detect transient velocity changes that could be due to long-lasting intrusions of magma without eruptive activity or to pressure buildup associated to the replenishing of the magma reservoir. We also present preliminary results of noise cross-correlation waveform perturbation associated with the occurrence of dike injection and volcanic eruption. We show that such an analysis leads us to locate the areas of dike injection and eruptive fissures at Piton de la Fournaise Volcano. These recent results suggest that monitoring volcanoes using seismic noise correlations should improve our ability to forecast eruptions, their intensity and thus potential environmental impact.     

Attenuation of random noise in GPR data by image processing

Random noise in ground penetrating radar (GPR) data affects the signal-to-noise ratio, blurs the details, and complicates reconnaissance of the useful information. Many methods with different advantages and disadvantages have been proposed to eliminate or weaken the random noise. We have reviewed basic principles of various signal processing techniques including the curvelet transform (CT), non-local mean (NLM), median, and mean filters to remove the random noise and compared their performances using synthetic and actual GPR data. The performances of the four filters were analyzed on synthetic GPR data both in time and frequency domains. On noisy synthetic data, results indicate that the CT filter performs better than NLM, mean, and median filters at attenuating random noise and improving S/N of the GPR data. On the real data, the performance of only the NLM and CT filters was investigated. Comparing the results clearly shows the CT filter robustness for the random noise attenuation and simultaneously its signal preservation.     

Assessment of the stability of H/V spectral ratios from ambient noise and comparison with earthquake data in the Cologne area (Germany)

Situated in an active tectonic region the highly industrialised Cologne area (Germany) suffers from moderate-sized earthquakes. Our contribution to the mitigation of earthquake risk includes a microzonation study using ambient seismic noise and earthquake recordings from two field campaigns. An analysis of these data using the horizontal-to-vertical (H/V) as well as the classical spectral ratio (CSR) technique led to the following observations and conclusions: (1) The spatial variation in the thickness of the sedimentary cover is reliably retrieved using the fundamental resonance frequency estimated from the peak in the (H/V) ratio of ambient noise. (2) This fundamental resonance frequency is stable in time, but the amplitude of the peak (the amplification factor) is not. (3) The relative amplification variation of the H/V ratio in the area should therefore be checked systematically with repeated measurements before drawing conclusions about its significance. (4) The analysis of the H/V ratio of ambient noise provides the lower frequency bound, above which amplification may occur. (5) The shapes of the spectral ratios obtained by the different methods are generally in good agreement. However, the analysis of earthquake data shows that significant amplification of ground motion may also occur at frequencies higher than the fundamental one even when thick sediments are present.     

Geological variation in S-wave velocity structures in Northern Taiwan and implications for seismic hazards based on ambient noise analysis

Ambient noise analysis in Northern Taiwan revealed obvious lateral variations related to major geological units. The empirical Green’s functions extracted from interstation ambient noise were regarded as Rayleigh waves, from which we analyzed the group velocities for period from 3 to 6 s. According to geological features, we divided Northern Taiwan into seven subregions, for which regionalized group velocities were derived by using the pure-path method. On average, the group velocities in mountain areas were higher than those in the plain areas. We subsequently inverted the S-wave velocity structure for each subregion down to 6 km in depth. Following the analysis, we proposed the first models of geology-dependent shallow S-wave structures in Northern Taiwan. Overall, the velocity increased substantially from west to east; specifically, the mountain areas, composed of metamorphic rocks, exhibited higher velocities than did the coastal plain and basin, which consist of soft sediment. At a shallow depth, the Western Coastal Plain, Taipei Basin, and Ilan Plain displayed a larger velocity gradient than did other regions. At the top 3 km of the model, the average velocity gradient was 0.39 km/s per km for the Western Coastal Plain and 0.15 km/s per km for the Central Range. These S-wave velocity models with large velocity gradients caused the seismic waves to become trapped easily in strata and, thus, the ground motion was amplified. The regionalized S-wave velocity models derived from ambient noises can provide useful information regarding seismic wave propagation and for assessing seismic hazards in Northern Taiwan.     

Crustal structure beneath the central Tien Shan from ambient noise tomography

Through analysis of seismic ambient noise recorded by the GHENGIS array, we constructed a high‐resolution 3‐D crustal shear‐wave velocity model for the central Tien Shan. The obtained shear‐wave velocity model provides insight into the detailed crustal structure beneath the Tien Shan. The results obtained at shallow depths are well correlated with known subsurface geological features. Low velocities are found mainly beneath sedimentary basins, whereas high velocities are mainly associated with mountain ranges. At greater depths of ~43–45 km, high velocities were observed beneath the Tarim Basin and Kazakh Shield; these high velocities extend forward in opposite directions and tilt down towards the central Tien Shan to a depth of in excess of 50 km, most likely reflecting lateral variations in crustal thickness beneath the Tien Shan and surrounding platforms.     

Simulation of seismic-prospecting random noise in the desert by a Brownian-motion-based parametric modeling algorithm

Random noise has a negative impact on seismic-prospecting record processing. An important step to improve the methods aimed at the attenuation of random noise is to scientifically characterize the properties of the noise. Numerical modeling is useful to understand the nature of the random noise. In this study, we present a Brownian-motion-based parametric modeling algorithm for the simulation of seismic-prospecting random noise in the desert. The optimal Hurst exponent required to implement the method can be determined by comparing the spectral properties related to the noise data and the simulated results. The data used to analyze the properties of the noise were acquired in the Tarim Basin (Northwest of China). We verify the performance of the modeling algorithm by comparing the results obtained after the simulation with the real noise data in both the time domain and the spatio-temporal domain. The experimental results thus obtained prove the accuracy and efficiency of the proposed modeling algorithm. This study can be used as a basis to investigate the seismic-prospecting random noise characteristics and thus contribute to its mitigation.     

Site response evolution and sediment mapping using horizontal to vertical spectral ratios (HVSR) of ground ambient noise in Jammu city,NW India

The technique of ground ambient noise (micro tremor) measurement and analysis has been successful for site characterization in many places around the world. This technique has the advantage of being a fast and easy way to estimate the effect of ground motion characteristics due to an earthquake. Single station ground ambient noise (micro tremor) measurements were carried out at 136 sites in the municipal limit of Jammu city, NW Himalaya. This extensive survey allows the estimation of fundamental resonance frequencies (0.432 to 7 Hz) of the region and identifies the areas prone to site amplification. The thickness of the soft sediments has been derived using empirical relationship that comes out to be 14 to 295 mts above the bedrock. The results are in good agreement with the 1-D profile derived using MASW measurements from representative sites. The resonance frequency and sediment thickness is in good agreement with the geological distribution of sedimentary units, indicating a progressive decrease of the fundamental resonance frequencies from the northeastern part (where the bedrock outcrops is exposed) to the southwestern and southern side where a thick sedimentary cover is estimated.     

基于SVD的叠后地震资料随机噪声分离方法

笔者提出基于SVD的叠后地震资料随机噪声分离方法,在地震剖面的同相轴水平或接近水平时可以有效地分离出地震剖面中的随机噪声,提高地震剖面的分辨率。为了说明SVD随机噪声分离方法的有效性和高效性,建立模型试验,在合成地震记录中加入随机噪声,之后进行实际地震资料处理,分别用SVD方法和基于小波变换的分层阈值方法对加入随机噪声的合成记录和加入随机噪声的实际资料进行随机噪声分离处理。对比发现,SVD随机噪声分离方法相比于基于小波变换的分层阈值方法更加有效且高效。     

A study of the seismic response of the city of Benevento (Southern Italy) through a combined analysis of seismological and geological data

A previous analysis [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] of small magnitude earthquakes recorded at 12 sites within the city of Benevento has stressed the significant role played by near-surface geology in causing variability of the ground motion. In this paper, we extend the study of the seismic response from 12 sites to the entire urban area. Based on inferences from the comparison at the 12 sites between earthquake and ambient vibration results, we have collected ambient noise at about 100 sites within the city, intensifying measurements across the main shallow geological variations. We use borehole data to interpret ambient noise H/V spectral ratios in terms of near-surface geology comparing H/V curves to theoretical transfer functions of 1D models along five well-constrained profiles.

On the basis of geological, geotechnical, and seismic data, we identify three main typologies of seismic response in the city. Each type of response is associated to zones sharing common soil conditions and similar soil classes according to building codes for seismic design. Moreover, we find that the spatial variation of the seismic response in the ancient town area is consistent with the damage pattern produced by a very destructive, well-documented historical earthquake that struck the city in 1688, causing MCS intensity of IX–X in Benevento.

Finally, we use ground motions recorded during the experiment by Improta et al. [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] to generate synthetic seismograms of moderate to strong (Mw 5.7, Molise 2002 and Ms 6.9, 1980 Irpinia) earthquakes. We calibrate the random summation technique by Ordaz et al. [Ordaz, M., J. Arboleda, and S.K. Singh (1995). A scheme of random summation of an Empirical Green's Function to estimate ground motions for future large earthquakes, Bull. Seism. Soc. Am. 85, 1635–1647.] using recordings of these earthquakes available in Benevento. After a satisfactory fit between observed and synthetic seismograms, we compute response spectra at different sites and speculate on effects of the geology class at large level of shaking, including soil nonlinearity. We find that large discrepancies from design spectra prescribed by seismic codes can occur for a wide sector of Benevento, especially for periods < 0.5 s.     

S-wave velocity images of the Dead Sea Basin provided by ambient seismic noise

Based on passive seismic interferometry applied to ambient seismic noise recordings between station pairs belonging to a small-scale array, we have obtained shear wave velocity images of the uppermost materials that make up the Dead Sea Basin. We extracted empirical Green’s functions from cross-correlations of long-term recordings of continuous data, and measured inter-station Rayleigh wave group velocities from the daily correlation functions for positive and negative correlation time lags in the 0.1–0.5 Hz bandwidth. A tomographic inversion of the travel times estimated for each frequency is performed, allowing the laterally varying 3-D surface wave velocity structure below the array to be retrieved. Subsequently, the velocity-frequency curves are inverted to obtain S-wave velocity images of the study area as horizontal depth sections and longitude- and latitude-depth sections. The results, which are consistent with other previous ones, provide clear images of the local seismic velocity structure of the basin. Low shear velocities are dominant at shallow depths above 3.5 km, but even so a spit of land with a depth that does not exceed 4 km is identified as a salt diapir separating the low velocities associated with sedimentary infill on both sides of the Lisan Peninsula. The lack of low speeds at the sampling depth of 11.5 km implies that there are no sediments and therefore that the basement is near 10–11 km depth, but gradually decreasing from south to north. The results also highlight the bowl-shaped basin with poorly consolidated sedimentary materials accumulated in the central part of the basin. The structure of the western margin of the basin evidences a certain asymmetry both whether it is compared to the eastern margin and it is observed in north–south direction. Infill materials down to ∼8 km depth are observed in the hollow of the basin, unlike what happens in the north and south where they are spread beyond the western Dead Sea shore.     

基于地震资料有效信息约束的深度网络无监督噪声压制方法

地震资料处理是地震勘探中的关键环节,由于地下构造和地表条件的复杂性,地震资料的处理需要经过一系列复杂流程,从而形成多种不同类型的地震数据。不同种类的地震数据具有不同的数据特征,充分利用和发掘其中的数据特征,不仅可以充分发挥处理方法的技术潜力,消除各类非地质因素对地震资料处理质量的影响,同时可以增强地震资料处理的可靠性,改善地震资料的资料信噪比及分辨率,在复杂油气藏勘探开发中具有非常重要的基础作用。叠前地震成像道集（CRP）中的有效信号同相轴近似水平,叠后地震成像数据因为地层沉积的规律性,有效信号相比于随机噪声、成像画弧噪声等干扰具有规律、简单等特点。具体表现为CRP道集及叠后地震资料有效信号具有多尺度自相似性的特征,其高维Fourier （FK或FKK）域主要能量集中在低频、低波数区域。针对上述地震数据的特点,提出一种基于先验信息约束的深度网络地震资料无监督噪声压制方法。受到深度图像先验（DIP）的启发,神经网络的结构可以视为一种特殊的隐式先验信息,合理设计网络结构可以使得网络具有多尺度自相似性特征的提取能力。由于叠前地震成像道集数据和叠后地震成像数据有效信号的多尺度自相似性,而噪声不具备这一特性,因此,特定结构的网络可以从原始数据提取出有效信号,从而达到噪声压制的目的。叠前成像道集和叠后成像的实际数据随机噪声压制试验结果表明,本文方法具有良好的保真性与鲁棒性。此外,由于本文方法具有强大的特征提取能力,因此,对常规方法不易压制的弧状成像噪声也有良好的效果。