Extended Spatial Autocorrelation Research Articles

Seismo-Stratigraphic Model for the Urban Area of Milan (Italy) by Ambient-Vibration Monitoring and Implications for Seismic Site Effects Assessment

In this paper, we present the work carried out to characterize the spatial variability of seismic site response related to local soil conditions in the city of Milan and its surroundings, an area with ∼3 million inhabitants and a high density of industrial facilities. The area is located at the northwestern end of the Po Plain, a large and deep sedimentary basin in northern Italy. An urban-scale seismo-stratigraphic model is developed based on new passive and active seismic data, supported by the available geological data and stratigraphic information from shallow and deep vertical wells. In particular, 33 single-station and 4 ambient-vibration array measurements are acquired, together with 4 active multichannel analyses of surface waves (MAWS). To estimate the resonant frequencies of the sediments, the horizontal to vertical spectral ratio technique (HVSR) is applied to the ambient-vibration recordings, whereas to determine the Rayleigh-wave dispersion curves from the passive array, the data are analysed using the conventional frequency-wavenumber, the modified spatial autocorrelation and the extended spatial autocorrelation (ESAC) techniques. The array data are used to determine the local shear wave velocity profiles, VS, via joint inversion of the Rayleigh-wave dispersion and ellipticity curves deduced from the HVSR. The results from HVSR show three main bands of amplified frequencies, the first in the range 0.17–0.23 Hz, the second from 0.45 to 0.65 Hz and the third from 3 to 8 Hz. A decreasing trend of the main peaks is observed from the northern to the southern part of the city, allowing us to hypothesize a progressive deepening of the relative regional chrono-stratigraphic unconformities. The passive ambient noise array and MASW highlight the dispersion of the fundamental mode of the Rayleigh-wave in the range 0.4–30 Hz, enabling to obtain detailed Vs. profiles with depth down to about 1.8 km. The seismo-stratigraphic model is used as input for 1D numerical modelling assuming linear soil conditions. The theoretical 1D transfer functions are compared to the HVSR curves evaluated from both ambient noise signals and earthquake waveforms recorded by the IV. MILN station in the last 10 years.

ESPAC-based 2D mini-array microtremor method and its application in urban rail transit construction planning

Conventional geophysical methods face many challenges in urban areas from limited site accessibility to severe industrial interferences. With the fast-paced development in urban area and urban light rail transit system, it is highly desirable to have a high-resolution geophysical method, which is suitable for the complex urban condition with strong background noises and, at the same time, is environment-friendly.In this paper, we introduce a 2D mini-array microtremor survey method, based on the extended spatial auto-correlation (ESPAC) method. It first uses the ESPAC to extract the dispersion curve of the Rayleigh wave from the microtremor data recorded using the mini array, then reconstructs the apparent S-wave velocity (Vx) structure of the stratigraphic rock formations by the Vr–Vx transformation, and finally, the 2D Vx profile is obtained by using Vx velocity imaging. This method not only makes full use of the multi-mode Rayleigh waves of dispersion curve, but also reduces the uncertainty during inversion caused by the potential pattern misjudgment when inverting the dispersion curve directly. Since the Vx is generally sensitive to the change of rock mass density, its profile is a natural and reliable reflection of the changes in rock properties. This technique provides an accurate and cost-effective tool for mapping complex near-surface geological anomalies such as karst cavities, fractured zone, and the soil/bedrock interface, which are frequently encountered in many urban engineering projects, such as urban rail transit development. The successful application of the microtremor survey in Guangzhou Metro Line 10 project demonstrates that this method can be very effective in identifying the soil/bedrock interface, mapping the severely weathered rock formations, and detecting the abandoned underground structures.

Shear-wave velocity measurements and their uncertainties at six industrial sites

This study assesses the variability of shear-wave ( VS) profile determinations for a suite of methods at six industrial sites. The methods include active, consisting of multi-channel analysis of surface waves (MASW), as well as passive, consisting of refraction microtremor (ReMi), and extended spatial autocorrelation (ESAC). The purpose is to ascertain the effect of the higher level of ambient noise on the results from the different methods, as only a few of these many methods are commonly used for site characterization. The measured dispersion curves are in fair agreement with one another. The average coefficient of variation (CoV; the percentage ratio of the standard deviation to the mean) for the dispersion curves varied from 2.5% to 12.6%. In contrast, over the VS-depth domain, the average shear-wave velocity profiles to a depth z ( VS,Z) vary from 11.6% to 16.5% between the various methods at the different sites. This indicates that the variance among the individual methods can lead to significant misinterpretation of the shallow subsurface, while the average VS,Z is much more robust. This reaffirms its use (mainly as VS,30) in building codes and within ground motion prediction equations (GMPEs). At all six sites, because of inversion processes, the variability within each method ranges from 4% up to 14%. There is no correlation between the test type and the CoV. Our study focused on surface-wave measurements in noisy industrial environments, where the signals processed are typically complex. Despite this complexity, our results suggest that such tests are also applicable to industrial zones, where the noisy environment constitutes an energy source.

Two dimensional determination of peak acceleration distributions during earthquakes

In this study, the two dimensional peak acceleration values between the bedrock and the ground surface is examined by using the soil bedrock model formed for a profile in the Bomova Plain in the east of Izmir Bay. For this purpose, two dimensional soil bedrock model was created for profile using microgravity and Extended Spatial Autocorrelation (ESPAC) method results. The S-wave velocities obtained from the ESPAC method were used to determine the density for microgravity modelling. After the density determination process, microgravity data on the profile were obtained by forward Talwani modelling. The obtained model is divided with gridding the data at regular intervals. In the study area, a recorded earthquake data used for deconvolution by soil-bedrock model known strong ground motion station BYN, and then transfer to the interface of bedrock in addition to obtain required bedrock data. Then, the calculated site- specific bedrock earthquake data was transferred from the bedrock surface of the grid model to the soil surface and layer boundaries. By combining these peak acceleration values for the profile, the two dimensional peak acceleration distribution for the profile was calculated.

Modal analysis of Rayleigh waves using classical MASW-MAM approach: Site investigation in a reclaimed land

Surface wave tests such as the multi-channel analysis of surface waves (MASW) and microtremor array measurements (MAM) offer a fast and convenient way of measuring the shear wave velocity (Vs) of the ground for geotechnical site investigation due to their non-intrusive nature. However, it has been widely reported that the accuracy and resolution of the Vs profile depend on the construction of the dispersion image and its interpretation. While many advanced computational techniques have been proposed to process surface waves into a final Vs profile, we opted for the classical ‘picking and inverting’ approach in the current study. This is in view of the lower required computation power as well as the relatively uniform geology of the site. Surface wave tests (MASW, MAM and horizontal-to-vertical spectral ratio) were carried out at a remote reclaimed land in Singapore. A systematic methodology for the modal analysis of Rayleigh waves based on combined MASW and MAM tests is presented. The MAM dispersion image was constructed using the phase shift method, the extended spatial autocorrelation (ESAC), and the refraction microtremor (ReMi) method but a meaningful dispersion curve could only be obtained using the phase shift. Due to the modes of energy in the low frequency regime being unclear in the dispersion image, an idealized synthetic model of the site was set up to guide the mode identification process. The combined dispersion curve and HVSR profile were jointly inverted to construct the final Vs profile, which agreed quite well with the seismic cross-hole tomography experiments and bore-log information. It is also demonstrated that the inversion of the fundamental mode alone led to slight errors and low resolution in the final velocity profile, even for such a simple soil stratigraphy.

Precision of VS30 values derived from noninvasive surface wave methods at 31 sites in California

We study the inter- and intra-method variability of VS30 results by inverting/forward-modeling individual dispersion data for 31 seismographic stations located in California where combinations of surface-wave methods were applied and the minimum recorded wavelength from each method satisfies the 30-m depth criteria. These methods consist of noninvasive geophysical (active and passive surface-wave techniques) multi-station approaches, including the Multi-channel Analysis of Surface Waves (MASW; Rayleigh and Love waves), Spectral Analysis of Surface Waves (SASW), Microtremor Array [using Extended Spatial Autocorrelation (ESAC) processing methods], and Refraction Microtremor (ReMi) methods. Depending on the apparent geologic or seismic complexity of the site, field crews applied one or a combination of these methods whenever economically feasible to estimate the one-dimensional shear-wave velocity (VS) profile and calculate VS30, the time-averaged VS to a depth of 30 m. For each of the 31 sites, we find both types of variability in VS30 estimates generally remain insignificant (arithmetic mean of 5% difference). We also find similar results (3%) when we evaluate individual-method based VS30 estimates against composite-method based estimates. We note that VS30 values vary insignificantly when using a combination of complementary methods, e.g., active MASW data combined with passive MAM data, and that the most reliable results are also based on close fitting of the theoretical dispersion data to the representative (experimental) dispersion data.

The Passive Surface Wave Methods for Shallow Engineering Exploration Based on the ESPAC Technology

ESPAC method is a rapidly emerging field of seismological research, which can reflect the physical properties of the Earth’s medium. In the process of using the ESPAC method, sometimes the noise of the original data is relatively large, and the raw data of each seismometer needs to be preprocessed, including operations such as de-averaging, de-trending, re-sampling, normalization, and filtering. The selection of the normalized method and the selection of the bandwidth of the filter are particularly important, and it will produce the wrong result if not handled properly. This article attempts to use the extended spatial autocorrelation (ESPAC) method to extract Rayleigh-wave phase velocity dispersion curves from the vertical component of the seismic stations’ microtremors, and proposes feasible and effective solutions to the selection of the normalized method and bandwidth of bandpass filtering.

Comparative analyses of seismic site conditions and microzonation of the major cities in Gangwon Province, Korea

To determine the seismic site conditions and microzonation of Chuncheon, Wonju and Gangneung cities in the Gangwon Province, Korea, the dispersion curves of Rayleigh waves were derived at 313 sites by the extended spatial autocorrelation (ESPAC) method. Using the shear-wave velocities (Vs) determined from dispersion curves, average depth to the bedrock (Db) and Vs at the top of the bedrock (Vsb), the overburden layer (Vso) and the top 30 m depth layer (Vs30) were determined. The resonance frequencies (fr) were then computed using both Db and Vso. The estimated averages of the three cities were 13 ± 7 m for Db, 472 ± 109 m/s for Vsb, 248 ± 44 m/s for Vso, 411 ± 157 m/s for Vs30 and 5.8 ± 2.8 Hz for fr. Microzonation maps based on the proxy-based Vs30 indicated that the three cities were mainly categorised into National Earthquake Hazards Reduction Program (NEHRP) classes B, C and D, with a minor proportion of A. Although no area was estimated to be in class E using the proxy-based Vs30, the Vs30 values derived from the recorded Rayleigh waves at 13 sites in Gangneung were less than 180 m/s. This indicates a greater vulnerability to seismic amplification during large earthquakes in this city, which had the smallest Vso, Vs30 and fr, and the greatest Db of the three cities. Microzonation maps, together with information for fr, can be effectively used for seismic risk assessments, urban planning, and disaster management.

Sensitivity of ground motion parameters to local shear-wave velocity models: The case of buried low-velocity layers

Seismic site response analysis is an important procedure used to obtain parameters such as peak ground motion values. These are needed by the engineering community for reliable seismic design, analysis and retrofitting of structures. One of the inputs for such analysis is the shear-wave velocity profile (VS) of the site. Surface wave methods are increasingly being used to obtain these profiles. However, these are characterised by uncertainties related to the measurements and the model used for interpretation (e.g. the inadequacy of 1D assumption). Moreover, the inversion procedure is also highly non-unique because numerous profiles are able to fit the experimental dispersion curve/s. Even though the uncertainties are not commonly included in site response analysis, their propagation from the dispersion curves to the inversion procedure can lead to significant differences in the site response analysis results.In a previous study, VS profiles were obtained at 20 sites on the Maltese islands (Central Mediterranean) using the Horizontal-to-Vertical Spectral Ratio (H/V), the Extended Spatial Auto-Correlation (ESAC) technique and the Genetic Algorithm. The geology of all the sites is characterised by a layer of clay, which can be up to 75m thick, buried under the Upper Coralline Limestone, a fossiliferous coarse grained limestone. The effect of a thick buried low VS layer, which gives rise to a velocity inversion, in ground response is not well understood and/or documented.The above concerns raised the need for carrying out tests with the aim of better clarifying and understanding which parameters have the most influence on site response analysis and to assess the consequences of inversion non-uniqueness on ground motion amplification and response. From the first part of the study, it was observed that the thickness of the clay layer has the greatest effect on the ground response results. By obtaining ground motion parameters from equivalent profiles, the consequences of the uncertainty in the inversion process, which can be serious at times, are revealed.

Suitability of 10 Hz vertical geophones for seismic noise array measurements based on frequency‐wavenumber and extended spatial autocorrelation analyses

ABSTRACTMicrozonation studies using ambient noise measurements constitute a promising way for seismic hazard evaluation in urban areas. Among the existing techniques, seismic noise array measurements have become a valuable tool for estimating Vs profiles and thus, the characteristics of a soil structure. Although methods based on analysis of seismic noise are simpler, cheaper and faster than borehole drilling and down‐hole or cross‐hole logs to derive shear‐wave velocity profiles, array deployment requires the use of several stations (broadband or short‐period sensors) that are not always available. In this paper, we have compared the results obtained by 10 Hz‐vertical‐geophone arrays with the results provided by 1 Hz‐sensor arrays. Two sites in the Bajo Segura Basin (SE Spain), with different soil characteristics, were chosen for array deployment. The comparison is carried out in terms of dispersion curves by using frequency‐wavenumber (f‐k) and extended spatial autocorrelation (ESAC) techniques. Both analyses show a good agreement using either 1 Hz sensors or 10 Hz geophones; moreover, they demonstrate that it is possible to extend the analysis in a frequency range much below the natural frequency of the geophones. The results of our study confirm the suitability of standard seismic refraction/reflection equipment also for ambient noise array measurements, which constitutes a cheaper and faster way for investigating soil characteristics.

Multimode inversion with amplitude response of surface waves in the spatial autocorrelation method

SUMMARY Microtremors are usually analysed without any consideration of the higher modes of surface waves. However, recent studies have demonstrated that higher modes contain useful information for improving the inverted S-wave velocity model. In this study, we propose two inversion methods that consider higher modes by using the amplitude response of each mode, which can avoid mode misidentification in the spatial autocorrelation (SPAC) method. One method is to compare the observed phase velocities by the extended spatial autocorrelation (ESPAC) method with the effective phase velocities calculated from theoretical dispersion curves and the amplitude responses of each mode. In the other method, SPAC coefficients are fit directly by comparing theoretical SPAC coefficients determined from dispersion curves and amplitude responses with the observed ones. The latter, direct-fitting approach is much simpler than the method using effective phase velocities. To investigate the effectiveness of these methods, a simulation study was conducted. Simulated microtremors that included higher modes were successfully inverted by the proposed multimode methods. The observed phase velocities and SPAC coefficients determined from field data were also consistent with theoretical ones constructed by the proposed methods except at low frequencies. The inversion using effective phase velocities required prior information about an infinite half-space to obtain a better S-wave velocity model whereas the direct-fitting inversion worked well without prior information, suggesting the direct-fitting method is more robust than the method using effective phase velocities. We conclude that our proposed inversion methods are effective for estimating the S-wave velocity structure even if higher modes of surface waves are predominant in observed microtremors.

Soil characterization in urban areas of the Bajo Segura Basin (Southeast Spain) using H/V, F–K and ESAC methods

Abstract Bajo Segura Basin, placed in the south of Alicante province (southeast Spain), is a region of moderate seismicity, which presents frequent seismic episodes. This region, as the rest of south-eastern part of Spain, is growing both economically and demographically. Hence, the presence of soft soils in a seismic region where many towns and villages are placed shows the importance of an adequate characterization of the site effects study in this area. The present work investigates the use of noise measurements for soil characterization by the application of H/V method and array techniques: extended spatial autocorrelation (ESAC) and frequency–wave number (F–K) in three urban areas of the Bajo Segura Basin. The application of these methods will help us to estimate the resonance frequencies, as well as shear-wave velocity profiles, having a better understanding of the sediment depth and site effects phenomena at the studied places. The estimated velocity profiles are used to model the fundamental mode Rayleigh wave ellipticity curves and the S-wave site transfer functions. Finally, the correlation between this curves and the experimental H/V analysis has allowed us a better assessment of the site response in the studied areas.

VS30 Estimates Using Constrained H/V Measurements

Abstract Most seismic codes adopt the average shear-wave velocity as a key parameter in the first 30 m of subsoil ( V S 30 ). Estimates of V S 30 are therefore required for both large- and small-scale seismic microzonation. We propose a technique to measure the V S 30 based on the horizontal to vertical spectral ratio (H/V) of microtremor recorded at a single station. The H/V is fitted with a synthetic curve using the independently known thickness of a superficial layer of the subsoil as a constraint. The proposed procedure consists of three steps: (1) identify the depth of a shallow stratigraphic horizon from independent geotechnical data, (2) identify its corresponding H/V marker, and (3) use it as a constraint to fit the experimental H/V curve with the theoretical one. The synthetic H/V curve is calculated by assuming a stratified one-dimensional (1D) soil model and a tremor wave field from distant random sources that are composed of Rayleigh and Love waves. This technique has been validated on different geological settings following a triple check procedure: (1) the theoretical Rayleigh-wave phase velocity dispersion curves calculated for the model derived from the H/V fit were compared to the experimental curves measured with the 2D extended spatial autocorrelation (ESAC) method and the 1D refraction microtremor (ReMi) array surveys; (2) the V S profiles and (3) the V S 30 estimates obtained by the proposed technique were compared to those obtained by using the latter array techniques. Finally, the inferred stratigraphy was compared to the geological model. The proposed technique is not meant to provide accurate V S profiles but has the potential to provide V S 30 estimates that are coherent with those measured through ESAC and ReMi and to satisfy law requirements. Furthermore, the H/V is found to be capable in detecting deviations from 1D subsoil geometry over the length of a few meters, the correctness of which was confirmed by direct drilling.

Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy

The town of Potenza (Southern Italy) is one of the test sites for preparing ground-motion scenarios within the framework of the Italian Dipartimento Protezione Civile-Instituto Nazionale di Geofisica e Vulcanologia (DPC-INGV) 2004-2006 pro- jects. An area in the neighboring village of Tito was selected to evaluate different techniques for estimating site effects involving a 40-m-deep instrumented borehole. This two-sensor vertical array records teleseismic, regional, and local seismicity. Close to the borehole, three seismological microarrays (utilizing short-period sen- sors and digitizers with a high dynamic range) were installed in May 2005 to record seismic noise. Differing acquisition geometries allowed the checking of any depen- dency in the derived dispersion curves based on the adopted analysis method (ex- tended spatial autocorrelation (ESAC) and frequency wave-number (F-K)). In gen- eral, the ESAC method appears to provide more reliable results in the low-frequency range. Furthermore, the soil-velocity profiles obtained from the microarray data were compared with the S-wave velocity profile derived from down-hole measurements. A good agreement was observed in the depth range well constrained by the data. Finally, empirical site responses were compared with those calculated numerically from the S-wave velocity profiles obtained from the microarray data. Although this comparison did not resolve a preference among the derived models, it showed the importance of downgoing waves in modifying the site response at the Tito site.

A Comparison of ESAC and FK Methods of Estimating Phase Velocity Using Arbitrarily Shaped Microtremor Arrays

Focusing on a comparison of the accuracy of the extended spatial autocorrelation (ESAC) method and the frequency–wavenumber spectrum (FK) method, we carried out short-period microtremor measurements of arbitrarily shaped array configurations at a site with a well-known velocity structure at shallow depths. Using both techniques, we measured phase velocities for frequencies between 2.5 Hz and 13.5 Hz and compared the results with the theoretical Rayleigh-wave-dispersion characteristics of both the fundamental and the first higher modes calculated from the PS logging data. Next, we tried to estimate the S -wave velocity structure to a depth of 43 m by fitting the theoretically calculated phase velocities to the experimental data, taking into consideration both the higher mode contributions as well as the fundamental mode. The theoretical dispersion characteristics were successfully fitted to the results analyzed by the ESAC method but not by the FK method. The estimated S -wave velocity structure from the ESAC method results was in good agreement with the PS logging profile. We also confirmed, using the model, that the S -wave transfer function due to vertical incidence coincided with that from the PS logging data. As a result of the study, we conclude that the ESAC method gives more accurate results than the FK method in determining the Rayleigh-wave phase velocity from records of short-period microtremors using arbitrarily shaped array configurations. The ESAC method can also provide a better estimate of the S -wave velocity structure and site amplification than the FK method.