Estimation of Deep Soil Profiles in Lima Peru
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July 2011, Volume 5, No. 7 (Serial No. 44), pp. 618-627 Journal of Civil Engineering and Architecture, ISSN 1934-7359, USA Estimation of Deep Soil Profiles in Lima Peru Diana Calderon1, Fernando Lazares2, Zenon Aguilar2, Toru Sekiguchi1 and Shoichi Nakai1 1. Department of Urban Environment System, Faculty of Engineering, Chiba University, Chiba, Japan 2. CISMID, Faculty of Civil Engineering, National University of Engineering, Lima, Peru Abstract: Deep shear-wave velocity profiles at eight places in Lima Peru were estimated based on the inversion of dispersion curves. The dispersion curves were calculated from small and large microtremor arrays using two methods: the F-k proposed by Capon (1969) and the CCA proposed by Cho et al. (2004). For the purpose of large array measurement we introduced a new type of sensor. Important results are the relative shallow depths to the basement rock in the area classified as alluvial gravel that covers most of the area of Lima city; and the relative large depth to the bedrock in places identified as VSV and CMA. It is recommended that this study be complemented with PS loggings in order to verify the estimated profiles. Key words: Microtremor array, dispersion curve, inversion, soil profile, H/V spectrum. conditions that characterize areas of low or high 1. Introduction probability to be affected by earthquakes is of great This study is a part of the project “Enhancement of importance, especially in places like Lima that have Earthquake and Tsunami Disaster Mitigation scarce information as to deep soil structures. Technology in Peru”, in which Japanese Government, In this context, the study aims to obtain a primary represented by Chiba University, and the Peruvian idea of the Lima’s soil structure down to depths government, represented by the National University of extending to the bedrock, which will make possible Engineering (UNI), are working together with the future analysis of the dynamic characteristics of the objective to estimate seismic risks, hazards and surface soils of Lima vulnerabilities in Lima, the capital of Peru, and two To accomplish this objective, small and large other cities of the country. In particular, the results of microtremor array measurement campaigns were this study will focus on Lima city only. carried out at eight places in the city that are the most Lima is situated in the central coast of Peru, representative of the soil dynamic behavior and bordered by the Pacific Ocean, in a zone of high demographic aspects; for the large array seismic activity known as the Ring of Fire. measurements new long-period sensors of Lima has a long history of being hit by strong microtremor were introduced. earthquakes, the latest big event occurred in 1974. At 2. Area of Study that time, severe damage in a few small scattered areas was reported [1], which suggests a soil effect may We have carried out microtremor array have occurred in these areas. measurements at eight places distributed in the Lima Due to the high seismicity of this area and to the Metropolitan area. Fig. 1 shows a map of the Lima’s rapidly growing urbanization, a study of the soil surface soil distribution estimated in 2005 [9], and the places where the microtremor arrays were measured. Corresponding author: Diana Calderon, PhD Candidate, research fields: microtremor array measurements, seismometer Table 1 shows a list of the measured places with array measurements, estimation of dispersion curves, inversion details of their exact location. of dispersion curve alone and joint-inversion of receiver function and dispersion curve. E-mail: [email protected]. Estimation of Deep Soil Profiles in Lima Peru 619 arrays, each set made of circular arrays of 100, 200, 500 and 1000 m radius. In almost all the arrays six sensors were used except in CMA and in VSV where four sensors were used. The objective of these arrays measurements was to estimate the soil profile characteristics, such as the shear-wave velocities and the thicknesses of each layer constituting the soil profile. 3.1 Implementation of Microtremor Sensors Two types of sensor of microtremors were introduced to Peru through this project. One was the well-known GEODAS sensor (with natural period of 1 second), which we used to measure small size arrays, with radius less than 50 m; in these arrays the sensors were connected with cables to the data acquisition hardware. The other was a sensor produced by Tokyo Fig. 1 Location of microtremor arrays over the soil Sokushin Company with a natural period of 5 seconds. distribution map [9]. These sensors were used for large array measurements Table 1 Symbols and location of the measured points in because no cable is needed to make the measurements; this study. the sensors are synchronized by a GPS device. ID District Institution Latitude Longitude UNI- CMD Rimac -12.013995° -77.050580° 4. Method of Analysis CISMID Lima Central Park PQR -12.071319° -77.033171° 4.1 Phase-Velocity Dispersion Curve Cercado of Lima Direction of DHN Callao -12.064413° -77.155016° Hydrograph We used two methods to construct the dispersion School CMA Callao -12.060734° -77.123570° curve; the high resolution F-k method [2], and the “Maristas” Villa El School Centerless Circular Array (CCA) method [3]. VSV -12.213421° -76.938803° Salvador “6066” 4.1.1 The high Resolution F-k Method Puente Private PPI -11.852260° -77.074035° The calculation of the dispersion curve through the Piedra House La University La F-k method is based on the calculation of EMO -12.082051° -76.938943° Molina Molina wave-numbers of predominant waves for different La MOL Municipality -12.077994° -76.917278° Molina frequencies; these wave-numbers are obtained from the signal power spectrum that is the representation of 3. Microtremor Array Measurements the signal power in a wave-number space. From Ref. [2] the formulation of the power spectrum is given by: Two measurement campaigns were carried out, the −1 ⎡ K ⎤ first consists of eight sets of small arrays (Fig. 1); each ′ P (kx ,k y , f ) = ⎢ ∑qmn ( f )⋅exp{}− i2π []kx (xn − xm ) + k y (yn − ym ) ⎥ n,m=1 set is made of linear arrays of 0.5 and 2 m sensor ⎣ ⎦ (1) distance, and circular arrays of 10, 20 and 45 m radius. where Pَ is the F-k power spectrum, K is the number The second campaign consists of four sets of large of channels, kx is the wave-number in the x-direction, 620 Estimation of Deep Soil Profiles in Lima Peru and ky is the wave-number in the y-direction, and f is developed is formulated in such a way that the the frequency. (xn, yn) are the coordinates of the microtremor records, obtained with sensors placed sensor n, and (xm, ym ) are the coordinates of sensor m. around the circumference of a circle, are first qmn(f) is the inverse of a Hermitian matrix whose integrated into intermediary quantities called “spectral elements are formed by the cross spectrum between ratios” before information on the phase velocities is channels m and n. This cross-spectrum or cross-power extracted from them. spectrum is calculated using the direct segment This can be explain by considering a circular method. According to this method, the value of data seismic array of radius r in a field of microtremors, point L in each channel is divided into M whose vertical component is z(t,r,θ), expressing their mono-overlapping blocks of N data points. That is, time histories in Fourier series with respect to θ π L=M·N. If the Fourier transform of the data in the lth Z 0 (t,r) = z(t,r,θ )dθ (5) segment, mth channel and frequency f is Sml(f), ∫ −π N S ()f = ()N −1/ 2 a N eirf π ml ∑ r m,r−(l−1)N Z (t,r) = z(t,r,θ )exp(iθ )dθ (6) r=1 (2) 1 ∫ m = 1,…..,K −π Their power spectral densities are denoted by l = 1,……,M Gz0z0(r,r; ω ) and Gz1z1(r,r; ω ) respectively (where where ar are weights which are used to control the ω is the angular frequency), and are represented as: shape if the frequency window used in estimating the M cross-power spectral density, and for simplicity it is 2 2 Gz0z0 (r,r;ω) = 4π ∑ f i (ω)J 0 (rki (ω)) (7) i=1 assumed that ar =1, r =1,….,N. M Then the estimate of the cross-power spectrum is 2 2 Gz1z1 (r,r;ω) = 4π ∑ f i (ω)J1 (rki (ω)) (8) 1 M i=1 p ( f ) = S ( f )S* ( f ) mn M ∑ ml nl where M is the number of Rayleigh wave modes l =1 (3) present, fi(ω) is the intensity of the ith mode, J0() and m, n =1,…,K J1() are the zeroth-and first-order Bessel functions of *: conjugate the first kind respectively, and ki(ω) stands for the Another important parameter is the coherence of the wave number of the ith mode. The spectral ratio is noise between seismometers m and n, cohmn(f), given given by by M α (ω)J 2 (rk (ω)) E[ p ] G (r,r;ω) ∑ i 0 i mn Z 0Z 0 i=1 (9) cohmn ( f ) = = M 2 2 GZ1Z1 (r,r,ω) 2 E[Sm ] E[Sn ] α (ω)J (rk (ω)) (4) ∑ i 1 i i=1 where E is the ensemble average and 0 <|cohmn(f)| ≤ 1. where The physical significance of cohmn(f) = 0 is that the M α (ω) = f (ω) / f (ω), f (ω) = f (ω) spectral components of the noise, at frequency f, i i ∑ i i=1 observed on the mth and nth are uncorrelated.