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SOFT SEDIMENT CHARACTERIZATION FROM PASSIVE
MOTION MEASUREMENTS OF THE SEAFLOOR
By: Carlos Huerta-Lópeza, Jay Pulliamb, Yosio Nakamurab, and Kenneth H. Stokoe IIc. ABSTRACT
We present an In-situ evaluation of the response of seafloor sediments to passive dynamic loads. Horizontal-to-vertical (H/V) spectral ratios are used to characterize the local sediment response in terms of the distribution of ground motions with their respective resonant frequencies (Nakamura, 1989). Ambient noise as well as distant earthquakes are used as generators of the passive dynamic loads. Also, 1-D wave propagation modeling using a modified Thomson (1950) and Haskell (1951) method, known as the stiffness matrix method developed by Kausel and Roesset (1981), is used to estimate sediment properties (mainly shear stiffness, density and material damping) and theoretical amplification factors of the shallow sediment layers. The objectives in this study were threefold: 1., to characterize the local site effect produced by shallow marine sediments at an experimental site in the Gulf of México (GOM); 2., to characterize the site in terms of its physical properties (layering and sediment properties); and 3., to estimate the transfer function of the top 50-m thick soil system; as well as the transfer function of each individual layer in the discrete soil model.
We observed that in the range of 0.35-2.5 Hz; the horizontal amplitudes increased by an order of magnitude at 0.35 Hz, and by at least two orders of magnitude at 2.0 Hz relative to the vertical amplitude, which is an indication of the local site effect. The site effect appears to be less significant at frequencies lower than 0.35 Hz. The theoretical H/V spectral ratios modeled with a 1-D, 50-m thick (discretized as a 3 layer system resting over a half-space with a water layer on the top) sediment system is largely consistent with the experimental H/V spectral ratios that exhibit a clear peak at 1.9 Hz, interpreted here as the fundamental mode of the sediment system. Once the “best” model was selected, we estimated the shear wave (SH) transfer function and the respective physical properties of the theoretical model. The modeling results were consistent between earthquake (i.e. strong input signal) and noise (background, micro-seismic noise) records recorded with the prototype BroadBand Ocean Bottom Seismograph (BBOBS) developed by the University of Texas Institute for Geophysics (UTIG).
Modeling H/V spectral ratios of data recorded by the three-component UTIG BBOBS offers a fast and inexpensive means of obtaining information of the preferential vibration modes of soft sediment systems for use in designing marine structures such as oil drilling and production platforms. This method makes use of background noise rather than coherent input signals so that it is not necessary to supply an active source to conduct the study, nor wait for an earthquake. The method is well suited for modeling shallow sediments, which cover the great majority of the seafloor. The BBOBS is small, lightweight and inexpensive and operates autonomously so that it is simple and quite inexpensive to use. a: Department of Civil Engineering/Institute for Geophysics University of Texas at Austin and Seismology Dep. CICESE, México. [email protected] b: Institute for Geophysics University of Texas at Austin. [email protected], [email protected] c: Department of Civil Engineering (Geotechnical Engineering) University of Texas at Austin. [email protected]
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I. INTRODUCTION
Local soil conditions have significant effects on the characteristics of ground motions created by dynamic excitation, such as that generated by earthquakes. This relationship implies that the site effect problem can be defined in terms of certain ground motion parameters, the input wave field, and various characteristics of the site. We may expect that the same site would respond differently depending on the dynamic input in terms of the type of incident waves, the coherency of the incident wave field, and the direction of their approach. On the other hand, if the wave field is always incoherent and composed of waves coming from various directions, the site response would not vary and its effect would more likely be stable. A detailed knowledge of the site conditions in terms of geometry, topography, sediment thickness, sediment velocity (stiffness), density and sediment damping are essential to capture the essence of the physical process involved in the site effect. When considering a broad classification of a site as either soil or rock, it is said that the site effects do not exist for frequencies higher than a few Hz and that there is no need to consider site effects in terms of the peak ground acceleration or the response spectra for high frequencies. However, what happens is that under the broad classification of a site as soil or rock, the site conditions affecting high frequencies are not captured. The truth is that indeed site effects exist at higher frequencies.
In designing critical and/or strategic facilities, accounting for “site effects” associated with ground motions is an important step that requires significant input from several disciplines that range from seismology (engineering and/or engineering seismology) to geotechnical engineering. Our discussion herein is centered on the effects of shallow soil layers on the ground motion, which is basically a wave propagation phenomenon.
We studied the local site effect by means of the horizontal-to-vertical (H/V) spectral ratios (Nakamura, 1989) in order to characterize the site response in terms of the distribution created in the H/V spectral ratio. Also a one-dimensional (1-D) wave propagation model using the modified Thomson (1950)-Haskell (1953) propagation matrix method, known also as the stiffness matrix method developed by Kausel and Roesset (1981), was performed to estimate soil properties and theoretical amplification factors of shallow soil layers. II. BACKGROUND
Overview of site characterization techniques
Local site effects resulting from dynamic input have been documented and studied since the 1950’s by Kanai, et al. (1956), Gutenberg (1957) and more recently by Roesset and Whitman (1969), Aki (1957,1988, 1993), Seale and Archuleta (1989), Anderson, et al. (1996), Bard (1995), Field and Jacob (1993, 1995), and Theodulidis et al. (1996) among others.
The study of the response of a soil deposit to dynamic loads, caused either by seismic excitation or prescribed forces, falls into the area of wave propagation theory. The formalism to study the propagation of waves in layered media was first presented by Thomson (1950) and Haskell (1953) based on the use of transfer matrices in the frequency-wavenumber domain. The solution technique resolves the loads in terms of their spatial and temporal Fourier transforms, and formally corresponds to the use of the method of separation of variables to find solutions to the wave equation. In the transfer matrix method, the state vector (Z), which relates displacement (D) and stress (τ) at a given interface, is related to the one at the adjacent interface by the expression , where Hjjj ZHZ =+1 j is the transfer matrix of the jth layer, and is a function of the
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frequency of excitation ω, the wave numbers k (in-plane) and l (out-of-plane), the soil properties, and the thickness of the layer. For the particular case of plane waves (plane strain), l is zero, and Hj then has a structure such that motions in vertical planes (SV and P waves) are uncoupled from motions in horizontal planes (SH waves).
In engineering seismology, studies of site characterization and local site effects are carried out by means of instrumental as well as numerical approaches. In other words, site effects can be measured in-situ through direct observation of dynamic motions or estimated by numerical modeling based on available geotechnical information. Bard (1995) presents a detailed general review of the current methodologies in use for analysis of local site effects.
II.1. INSTRUMENTAL APPROACH
The main challenge of instrumental measurements, which represent direct in-situ measurements, is to remove the source and path effects from observations to define the site characteristics. The above problem can be solved using two methods. The first one is known as the reference site technique that was first introduced by Borcherdt (1970). This method consists of comparing simultaneous records at nearby sites (source and path effects are assumed to be identical at both sites) through spectral ratios. The problem with this technique is that it is only applicable to data acquired using dense local arrays. The second method is known as the non-reference site technique, which is divided in the two following different approaches: a) the parameterized source and path inversion (Field and Jacob 1994) and b) the spectral ratios approach using the horizontal and vertical components of the shear wave part, which is a combination of the “receiver-function” technique Langston (1979) and the technique proposed by Nakamura (1989) using ambient noise recordings. Because of the promising results reported in the literature and the simplicity, (and hence the inexpensiveness) of Nakamura’s technique, this technique was used in this study and is described in detail below.
II.1.1. SPECTRAL METHODS
Microtremor spectra
Peak site frequencies can be determined from average absolute spectra of microtremors. This spectral feature exhibits a gross correlation with the site geological conditions, which is used as qualitative index of the soil characteristics. The peak frequencies are also interpreted as the resonant frequencies of the site. This spectral method is the simplest and crudest spectral method and was introduced long ago in Japan for site response estimates.
Spectral ratios
These ratios are obtained from ambient noise recordings. Such spectral ratios are reliable only in the long period range (> 5 s) where the noise origin is the same for the studied sites, which includes the reference site (Borcherdt (1970)).
Nakamura’s Technique
The main drawback of Nakamura’s technique is its lack of analytical and theoretical support (Lachet and Bard, 1994) and the difficulty to explain how it discriminates source effects from pure site effects. However, its simplicity, inexpensiveness and the successful results reported in the literature justify its use in both qualitative and quantitative ways. Nakamura
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(1989) introduced the horizontal-to-vertical (H/V) spectral ratio of noise records (microtremors) and proposed, based on empirical observations, that the H/V spectral ratio is a reliable estimation of the site response to shear (S) waves. His argument is that dividing the horizontal spectra by the vertical spectral “reference” component removes the source as well as the effects of Rayleigh waves. The basic assumption is that the local site conditions do not significantly influence the vertical component of the ground motion. This technique has been applied to weak and strong ground motions by several researchers. According to Chang and Alvarez (1999), Theodulidis and Bard (1995), Theodulidis et al., (1996), and Raptakis et al. (1997) among others, the results obtained with this method are more stable than those obtained with raw noise spectra. In addition to the above, in soft soil sites the H/V spectral ratio clearly defines the resonance peaks, which are well correlated with the preferential vibration mode of the site, and reveals the overall frequency dependence of the site response. However, it fails to provide higher harmonics, and the peak amplitude is different from the amplification measured on spectral ratios.
Small aperture arrays
Aki (1957) proposed that noise recordings on small aperture arrays could be used through spatial correlation analysis to measure phase velocities of surface waves and invert the surface velocity structure to compute the site response. This technique may be used to complement other geotechnical engineering techniques to obtain velocity profiles.
II.2. NUMERICAL APPROACH
The challenge of the numerical approach is the theoretical representation of complex “real world” sites in terms of the geometry of the structure and the complexity of the incident wave field. Researchers have been working in four different directions to address this complexity: (i) analytical methods, mainly used for simple geometries; (ii) ray trace methods, which are basically high frequency techniques and do not work well for wavelengths comparable to the size of the heterogenities of the media; (iii) boundary-based techniques, such us boundary integral techniques (Mosessian and Dravinsky, 1990, and 1992; Clouteau, 1990; Clouteau et al., 1993; Hisada et al., 1993), which are feasible to apply when the site model consists of a limited number of homogeneous geological units; and (iv) domain based techniques, such as finite element or finite difference methods (Graves and Clayton, 1992; Frankel and Vidale, 1992; Frankel, 1993; Graves, 1993; Yomoguida and Etgen, 1993), which allow one to work with complex structures and rehological models but require large computational resources. However, simple 1-D wave propagation techniques generally provide satisfactory results and are now used routinely in engineering practice, despite the impressive computational capacity currently available to pursued more sophisticated numerical modeling approaches. In the forward modeling process of a layered system used herein, the 1-D wave propagation stiffness matrix method developed by Kausel and Roesset (1981) is used. III. INSTRUMENTATION AND DATA ACQUISITION
In this study, a three-component broadband sensor (PMD-2123) manufactured by Precision Measurement Devices, Inc. was used in the ocean bottom seismograph (OBS) package of the University of Texas, Institute for Geophysics (UTIG). Rather than the traditional force-balance pendulum design, The PMD sensor is based on a molecular-electronic transducer
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(MET), which offers several attractive attributes for our application, including portability, very low power consumption, tolerance to tilt (up to 5 degrees), and wide-band frequency response. The instrument’s low cost and autonomous operation (for a periods of a year or more) make it useful not only for regional and teleseismic broadband seismology but also for the characterization of local site effects of marine layered systems.
III.1. CHARACTERISTICS OF PMD SENSOR AND UTIG OBS RECORDING PACKAGE
The most innovative characteristics of the broadband PMD sensor are, in addition to the ones mentioned above: (i) it uses an MET as the "mechanism" to detect the ground motions (hence, there are “no mechanical parts in the system"); (ii) the system is completely sealed, isolating it from variations of atmospheric pressure; and (iii) its dimensions and weight are 17.8 cm in diameter by 11.8 cm in height, and 4.5 kg, respectively. The nominal sensitivity (gain constant) of the sensor is 1500 V/(m/s). The UTIG OBS recording package has fourth-order Butterworth anti-alias filters and a low-pass cut-off frequency that can be set by plug-in resistor blocks for the requirements of the experiment. The amplifier gain is dynamically adjusted by software instructions to utilize the full range of the analog-to-digital converter (ADC), yet clipping of large-amplitude signals is avoided. The ADC has 14-bits of resolution with a maximum range of 10 Vpp. Figure 1 shows the UTIG BBOBS. A complete description of the UTIG OBS characteristics can be found in Nakamura and Garmany, 1991.
III.2. GULF OF MEXICO (GOM) EXPERIMENTAL SITE
The GOM data were acquired in the summer of 1999. We conducted two cruises on board the R/V Longhorn in the northwestern Gulf of México. The first cruise, cruise No. 736 on July 14-16, 1999, was for deployment of the BBOBS. The second cruise, cruise No. 741 on August 11-13, 1999, was for its recovery. The test site, located in the middle of a basin in the mid-slope of the northwestern Gulf of México, was selected for deployment based on the following considerations: (i) it was within easy reach, approximately 150 nautical miles ESE from Port Aransas, Texas, the home port of R/V Longhorn; (ii) it is flat over a sufficiently broad area to accommodate the instrument (the sensor is not mounted on gimbals, and thus cannot tolerate a slope greater than about five degrees); (iii) the area has sedimentary evidence of recent structural activity, likely to have been caused by tectonically active salt domes (Satterfield and Behrens, 1990; Bill Behrens, personal communication 1999); (iv) it is near one of the teleseismically determined earthquake epicenters in the central and northern Gulf of México (Frohlich, 1982); and (v) it is on the mid-continental slope, deep enough not to worry about the instrument being caught in a fishing net.
We first surveyed the pre-selected area using a 3.5-kHz echo sounder to find a location sufficiently flat to accommodate the instrument. Once the BBOBS was deployed (July 15, 1999) and the instrument had settled on the seafloor at 1478 m below sea level, we shot two short crossing seismic lines over the instrument using a small (60 in3) air gun for the purpose of locating and orienting the instrument on the seafloor. The recording began at 12h: 00m: 00.5s CDT, and continued for four weeks on three channels (components: vertical (V), horizontal-1 (H-1), and horizontal-2 (H-2)) at a sampling rate of 40 samples per second. On the day of recovery of the BBOBS (August 12, 1999), we first repeated shooting two short crossing seismic lines over the instrument with the small air gun to locate and orient the instrument on the seafloor and then sent an acoustic signal to release the instrument from its anchor on the seafloor. The end of the recording was 12h: 08m: 49.1s CDT. Details about the cruise activities can be
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found in the Nakamura (1999a and b). The recovered instrument contained all of the seismic data since its deployment during the first cruise. Figure 2 shows the location of the GOM experimental site and the locations of the buoy weather stations.
Figure 1. UTIG Ocean Bottom Seismograph (OBS) package.
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Figure 2. Location map of experimental GOM site and weather buoy stations.
IV. DATA PROCESSING
IV.1. DATA PREPARATION AND SELECTION
Simulated drum records of ocean bottom ground motion versus time were plotted for visual inspection. On these records, we selected the record and sample numbers of independent segments to plot or process. The visual inspection was mainly concerned with the selection of the desired types of signals to use in the frequency domain analysis, which consisted of power spectral density (PSD) estimations of the time series. For the background noise analysis, we avoided the time periods with seismic events and other transient signals. While visually inspecting the records, the existence of several local, regional, and teleseimic events were clearly evident. Significant differences in background noise levels between horizontal and vertical components were also evident. Transient signals of short duration, whose shape looked like a hump, a type of instrumental noise we encountered in this prototype instrument, were more often present in the horizontal components. Figure 3 shows a 12-hour record of vertical (channel 1) and N-S horizontal (channel 2) motions of typical signals collected with the UTIG BBOBS at the GOM experimental site.
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(a)
(b)
Figure 3. 12-hour simulated drum record measured with the UTIG BBOBS (note the different scale factor between (a) and (b)).
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For unit conversion from digital units (DU) to physical units of ground motion in velocity (m/s), we used the nominal conversion factors (of the whole system: sensor and recording package) of 2.6x10-9 (m/s)/DU. The D.C. offset was removed from the selected time series. Plots of the prepared time series segments were useful to double-check the amplitude levels of the recorded ground motions for comparison with published data from similar studies. In computing PSD from background noise, more stable and reliable PSD estimates were obtained with larger ensembles of time series in the averaging process. In general, for the background noise analysis, we used time series segments of 36 minutes and 16 seconds (36m 16s) each, which contained 87,040 sample points per channel. For cases in which we wanted to do the analysis for a whole day, we divided the day into four intervals of approximately 6 hours, starting at midnight. Each interval was formed by ten segments of 36m 16s, each with a total of 870,400 sample points per channel. For the whole day, the total number of sample points was 3,481,600 per channel. We either manually or by an implemented automatic algorithm excluded seismic events and/or transient signals from the procedure of obtaining the PSD spectra. The automatic removal of transient signals and seismic events was the adopted option when working with the whole data set. The total volume of the data set, continuously collected at a sample rate of 40 samples per second per channel, was 28 days.
IV.2. PSD SPECTRUM ESTIMATES
In general, this processing follows general rules of Fourier analysis, as described, for example, in books by Kanasewish (1981), Oppenheim and Shafer (1975), and Bendat and Piersol (1971). PSD spectral estimates were obtained using time series segments of 36m 16s (87,040 samples), and averaging 82 sub-segments of 4096 points each in length with an overlap of 75%. The mean value of each sub-segment was removed and a Hanning window of 4096 points was applied to each sub-segment. The averaged PSD estimates were then normalized by multiplying by the frequency increment ∆f, and the amplitude scaling factor (which equals two due to the symmetry property of the DFT) and dividing by the number of data points, N. Finally, after the instrument correction was applied, the spectral amplitudes were transformed to units of acceleration.
IV.3. INSTRUMENT TRANSFER FUNCTION; (SENSOR AND UTIG OBS RECORDING PACKAGE)
It is important to correct the PSD amplitudes outside the low and high cut-off frequencies, where the transfer function is not flat. We computed the frequency domain transfer function for each PMD sensor using the instrument parameters provided by the manufacturer. For the PMD sensors, the zeros and poles, as well as the normalization factors, were the only required parameters to evaluate their respective transfer functions.
The analytical expression to compute the transfer function, provided by the manufacturer is:
)()(*1000)(
4
ifPififW
N
= , in which (1) )(* 1 nNnNN SifaP −Π= =
where W(if) denotes the transfer function (in terms of the Laplace variable if), if denotes complex frequency, Sn denotes the complex poles of the transfer function, aN denotes the normalization factor, and PN represents the polynomial product of the poles of the transfer function. The overall normalization factor was 1000/aN.
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IV.3.1. INSTRUMENT CORRECTION
The nominal sensitivity (gain constant) of the PMD sensors was 1500 V/(m/s). When no instrument correction was applied, just the nominal conversion factor of the whole system (2.6x10-9 (m/s)/DU) was applied to the time series for the unit conversion from DU to velocity for the spectral analysis processing. Finally, by applying the ω2 factor to the velocity PSD estimates, PSD estimates corresponding to the acceleration spectral amplitudes of the absolute ground motion were obtained.
The instrument correction was applied in three steps. In the first step, the unit of the time series was converted from DU to V/(m/s) (as it was at the sensor output) by multiplying the DU by the factor 10 V/(214×312.5) and the PSD estimates were obtained according to the above description of PSD estimates. In the second step, the PSD estimates thus obtained were divided by the sensor transfer function. Significant changes in the PSD estimates were evident only in the low band of frequencies. Finally, the third step of the instrument correction consisted of correcting the PSD spectral amplitudes above the high cut-off frequencies of the anti-alias filter. Simply dividing the sensor corrected PSD estimates by the transfer function of a 10-Hz Butterworth low pass filter, with –24 dB/octave, did this. This last step was optional and only necessary if we were interested in recovering signals above the anti-alias cut-off frequency. V. EXPERIMENTAL AND NUMERICAL RESULTS
The objectives of analyzing the local site effects were: (i) to identify at which frequency or frequency band the spectral amplitudes were enhanced by the effect of the shallow 30 to 50 m soft sediments of the Gulf of México seafloor; (ii) to characterize the site in terms of its physical properties; and (iii) to characterize the site in terms of its fundamental resonant frequency. From the seismological perspective, the upper 30 to 50 m is an extremely thin skin of the whole structure through which the seismic waves travel. On the other hand, in engineering and/or engineering seismology, the top 30 to 50 m is a reasonable depth for borings and detailed site characterization. As an example, for an earthquake at a depth of 5 to 10 km, 30 m would represent at most 0.6% of the path. For a signal of 10 Hz, this thickness barely equals a wavelength of a shear wave, unless the velocity is less than 300 m/s. From this perspective, it is not obvious that this sediment layer should play a critical role. However, it has been observed that the effect of shallow soil layers plays a very significant role on dynamic ground motions.
V.1. THE STIFFNESS MATRIX APPROACH
Consider a layered soil system, and let us isolate a single layer and preserve the equilibrium by applying external loads at the upper and the lower interfaces. Then, from
we have: jjj ZHZ =+1
=
1
1
2221
1211
2
2
ττ v
v
v
vD
H HH HD
(2)
where 1τr and 2τ
v are the external load vectors at the upper and lower interfaces, respectively, Hij are submatrices of the transfer matrix Hj, and 1D
v and 2D
vare the displacement vectors at the
respective upper and lower interfaces.
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In the following, the stiffness matrix approach for a single layer is described in which an SH wave (also known as the anti-plane (out of plane) problem) propagates from bottom to top. The reader should consult Kausel and Roesset (1981) for a complete description of the stiffness matrix derivation for the whole wave field, for a single layer, or for multi-layered soil systems.
The anti-plane problem considers a traveling wave restricted to the x-z plane, as is schematically illustrated in Figure 4. In this figure, α denotes the angle of incidence of the incoming wave; l, m, and n are the direction cosines for the displacements U, V, and W in a 3-D plane; and represent the amplitudes of SH-waves traveling in the positive and negative directions of the z-axis; and C
SHA 'SHA
s, ρ, ξ, and σ are the shear wave velocity, density, material damping ratio, and the Poisson’s ratio of the soil layer, respectively.
)
Figure 4. SH
The stiffness matrix meth
(i) it has the freedom to use the wwaves that may be of interest, (incidence angle of the input wavwe can easily follow the evolutilayered soil system. VI. SIGNAL ANALYSIS
We first studied the corrsources of noise at the site. For noise power with the weather absolute value of 68-s windows from the time series in the powestations (Buoys 42002, 42019, aBBOBS GOM site. The stationsto the GOM site. The i(www.ndbc.noaa.gov/stuff/westgulf). height, wind gusts, wind directioshows the power estimation ofcompared with the power estimaand H-2) recorded by the BBOBS
From the analysis of bothvariables that best correlated wit
α
-wod hol
ii) ie mon
elatithe conwith
r-estnd
420nforThen, d
bution. seth th
ASH
ave traveling in an is
developed by Kausele field of waves (P, St is well suited to motion at the base in wof the wave field as
on of the PSD of thGOM data set, we stditions. The BBOB no overlap. Seism
imation processing. 42020 in Figure 2) 19 (at 116 km) and 4mation was obtai data from these buoominant wave perio
oy station 42019 fo of the background n
s of data (the buoy e observed seismic b
A’SH
olated single la
and Roesset (V, and SH) or
odel thin layerhich the layer
it passes thro
e ambient noisudied the correS power wasic events and We used data located in the2002 (at 176 kned from thy stations werd, and averager these time soise (for the th
and BBOBS dackground no
z(n)
yer.
1981) w the ins, (iii) ed sys
ugh the
e withlation comptransiefrom th surroum) wee NOe meas waveeries, ree co
ata), it ise wer
y(m)
adepit tem i
pof utentsrendre Aur pewhmp
wae t
x(l
hCs; ρξ; σ
s used because: endent seismic
can handle any rests, and (iv)
nterfaces of the
ossible external the background d as the RMS were excluded e weather buoy ing area of the the closest ones A’s web site ements of wave riod. Figure 5 ich were later onents: V, H-1
s clear that the he wave height
43
and the wind speed. This correlation is shown in more detail in Figure 6 for stations 42019 and 42002. In Figure 6, it can also be seen that there is a time shift between the power of wind speed and the power of the BBOBS data. We associate this time shift as a time delay between the wind speed measured at a distances of 116 and 176 km with respect to the GOM site. The major conclusion reached from this figure is the obvious dependency of the background noise power level with the power level of the wave height and wind speed at the surface of the sea.
VI.1. EXPERIMENTAL H/V SPECTRAL RATIOS
We used not only background noise but also earthquakes to cover weak and moderate ground motions in this analysis. We first tested with background noise time series of 36m 16s with different power levels, which implicitly means different levels of PSD spectral amplitudes. The H/V spectral ratio of the time series with high power level (day 201, record 220) is shown in Figure 7a. The H/V spectral ratio of the time series with low power level (day 205, record 339) is shown in Figure 7b. It is important to see that the H/V spectral ratio obtained with the low power level (day 205) time series does not define the 1.9-Hz peak as well as the one obtained with the time series of high power level (day 201). According to Godin and Chapman (1999), the existence of the shear modes in the seafloor sediments is the result of an infrasonic noise field generated in the water column that interacts with the elastic seabed and readily excites the soft sediments. The strongest generation of shear waves would occur at the large impedance contrast at the sediment/rock boundary. Multiple transits in the sediment layer by the shear wave gives rise to resonances at frequencies that favor constructive interference. The above statement supports our interpretation that measurements with low power level “energy”, as the time series of day 205, do not have enough energy to excite the system to produce a signal-to-noise ratio large enough to define the system response (shallow soil system).
By taking a large number of background noise segments, the signal-to-noise problem cited above was solved because averaging them increased the signal-to-noise ratio. This processing also helped to obtain smooth curves due to the averaging process. In the statistical sense, the averaging process removes the non-deterministic part of the signal. These new results of the experimental H/V spectral ratios using more than a single 36m 16s segment for both high- and low-power levels are shown in Figures 7c, and 7d, respectively. The improvement and definition of the resonance peaks at 1.9, 3.9, and 6.3 Hz, which we associate with local site effect, is evident. We also plotted in Figures 7a, 7b, 7c and 7d the theoretical H/V spectral ratio whose similarities, respect to the experimental H/V spectral ratio, will be discussed in section VI.2.
We also used four earthquakes in this analysis, which were grouped as follows. Two of them had the same magnitude (Ms = 5.1). One was located in the California-Nevada border region (Figure 8a) and the other was in the Gulf of California (Figure 8b). Of the other two earthquakes, one was located in Central America (Nicaragua, Ms = 4.9, Figure 8c), and the other was located in South America (Ecuador, Ms = 5.9, Figure 8d). The general characteristics of the H/V spectral ratios obtained with earthquake signals are consistent with the characteristics we observed with background noise. However, note that the H/V spectral ratio obtained with data from the earthquakes located in the California-Nevada region and in Central America, do not show the 3.9 and 6.5 Hz peaks. These peaks are well defined in the H/V spectral ratio obtained with background noise measurements and with data from the earthquakes located in the Gulf of California (Magnitude = 5.1) and in South America (Magnitude = 5.9).
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Figure 5. Power of: wind speed, wind direction, wind gusts, wave height, dominant period, and
average wave period at station 42019.
High power level
F
Low power level
igure 6. Correlation between power of: wind speed (a), and wave height (b) with power of: vertical, horizontal-1, and horizontal-2 channels of BBOBS data.
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Figure 7. Modeled and experimental H/V spectral ratio obtained from background noise using a
single 36m 16s, segment (a, and b); and from multiple 36m 16s, segments (c, and d).
Figure 8. Modeled and experimental H/V spectral ratio obtained from earthquakes.
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VI.2. MODELING THE LOCAL SITE RESPONSE OF GOM SITE To characterize the local site response of the experimental GOM site, the upper 50-m
deep sedimentary layer of the Gulf of México seafloor was modeled as a discrete system composed of three layers resting over a half-space. In this model, the water “layer” of 1475 m was added to the top of the seafloor to better match the site conditions. As a result, the final model was a four-layer system in which the upper layer was water. The geometry and initial model parameters are shown in Figure 9.
We took as the reference for the local site response the H/V spectral ratios computed with the background noise measurements. The forward modeling process was started by propagating vertically incident P-, SV-, and SH-wave fields of unit amplitude through the vertical column. The theoretical H/V spectral ratios at the desired interfaces were calculated. The theoretical and observed H/V spectral ratios were compared and the inversion process was iterated until a theoretical H/V spectral ratio that best fit (under the least squares criteria) with the experimental H/V spectral ratio from the noise and/or earthquake measurements was found.
The forward modeling process was quite successful. This success can be seen by observing in Figures 7 and 8 that there is a fairly good agreement between the computed and observed H/V spectral ratios for both the background noise and the earthquakes, particularly at the peak located at 1.9 Hz.
Once the theoretical H/V spectral ratio that best matched the observed H/V spectral ratio was determined, the following were computed: (i) the transfer function of the 50-m soil system that was representative of the experimental GOM site (Figure 10f); (ii) the transfer function of each individual layer of the discrete sediment model (Figures 10a (5-m thick); b (10-m thick), and c (35-m thick)); (iii) the cumulative contribution of the first and second layers (Figure 10d (15-m)) as well as the second and third layers (Figure 10e (45-m)); and (iv) the final model parameters.
The following characteristics in Figure 10 are important when viewing these results: (i) the upper five meters of the marine sediments have a single amplification peak at 4.5 Hz (Figure 10a); (ii) for the 10-m thick layer, the amplification peaks are at 2.9 and 6.2 Hz, while a de-amplification trough is at 4.5 Hz (Figure 10b); (iii) three significant amplification peaks for the 35-m thick third layer are located at 1.9, 3.8, and 9 Hz, and one significant de-amplification trough is at 6.2 Hz (Figure 10c); (iv) the cumulative effect of the upper 15 m (the first and second layers) shows two single-amplification peaks at 2.9 and 6.2 Hz, which reduces significantly the amplification of the upper 5-m thick layer (Figure 10d); (v) the cumulative effect of the second and third layers (45 m in total thickness) shows amplification peaks at 1.9, 3.9, 6.2, and 9 Hz, and a single de-amplification trough at 4.5 Hz (Figure 10e); and (vi) the transfer function of the upper 50-m, the whole three-layer sediment system, shows four amplification peaks at 1.9, 3.9, 6.2, and 9 Hz. The final parameters of the model we obtained from the inversion process are given in Table 1.
Table 1. Final estimated model parameters for GOM experimental site. Thickness
m Vs
(m/s) Density (ρ)
kg/m3 Shear modulus (G)
kg/ms2 Damping (ξ) Fraction of %
Poisson’s ratio (σ)
1475 ~0 1000 0.0000E+00 0.001 0.49995 90 1300 0.1053E+08 0.01 0.4500
10 190 1400 0.5054E+08 0.005 0.4000 35 400 1700 0.2720E+09 0.005 0.3500 ∞ 3000 2100 0.1890E+11 0.000 0.2500
47
Vs m/s
Density (ρ) kg/m3
Damping (ξ) (Fraction of %)
Poisson’s ratio (σ)
0.00 1000 0.001 0.49
180 1500 0.002 0.45 200 1600 0.001 0.40 400 1900 0.001 0.35
1500 2500 0.000 0.25
Z=0 m
1
2
3
e
Figure 9. Initial model of the upper 50 m of the seafloor of the
(e)(d)
(b)(a)
Figure 10. Transfer functions of the individual layers of 5, 10, and 3the cumulative first and second layers (15 m, d), the second and thi
whole 50-m, three-layer soil system under a water
Half-spac
Layer #4
Layer #
Layer #
Z=1475 m
Z=1480 m
Z=1490 m
Z=1525 m
Z=∞ m
Gulf of M5 m thicknrd layers ( layer (f).
OBS
Layer #
éxico site.
(f)
(c)
ess (a, b, and c), 45 m, e), and the
48
V II. DISCUSSION AND CONCLUSIONS
In this study, we experimentally measured the velocity ground motion at the seafloor in a Gulf of México (GOM) site. These measurements were used to calculate the H/V spectral ratios in the frequency band of 0.1 to 10 Hz. The H/V spectral ratios were used to evaluate the local site effect caused by the soft marine sediments. The local site effect was compared with numerical simulations obtained with the stiffness matrix method developed by Kausel and Roesset (1981) assuming 1-D wave propagation. No similar attempt was found in a literature review of related topics. We found that by: (i) using Power Spectra Density (PSD), instead of the classical Fourier spectra, (ii) using a large number of time series, and using (iii) large duration time series of six hours or more, the averaging process defined the peaks of the experimental H/V spectral ratio even at low energy levels of background noise. This simply means that an increase in the signal-to-noise ratio of the system occurred due to this signal processing. In the statistical sense, the averaging process removed the non-deterministic part of the signal and helped to obtain smooth curves. The characteristics of the experimental curves of the H/V spectral ratios, obtained either with background noise or earthquakes were associated with the preferential vibration modes of the layered sediment system. These results were consistent with the numerically simulated H/V spectral ratios, particularly at resonant peaks located at 2, 3.9, and 6.5 Hz. We also ended with a proposed geometry and physical parameters of a layered sediment system from the iterative, forward-modeling process in which the theoretical H/V spectral ratio that best matched the experimental H/V spectral ratio was found. Shear wave velocities as low as 90 m/s for the top 5-m thick layer of the marine sediments and 190 m/s for the following 10-m thick layer of sediments agrees with soft sediment velocities reported in the literature for marine sediments and some other non-marine sediments sites such as the soft clays of the México City valley. However, it should be noted that our forward modeling scheme does not identify a unique solution.
Is important to point out that the H/V spectral ratio obtained with data from the earthquakes located in the California-Nevada border region and in Central America, do not show the 3.9 and 6.5 Hz peaks. These peaks are well defined in the H/V spectral ratio obtained with background noise measurements and with data from the earthquakes located in the Gulf of California (Magnitude = 5.1) and in South America (Magnitude = 5.9). Our current interpretation of this difference suggests that this effect could be produced by directivity of the energy arrival, or by differences in the energy levels at frequencies larger than 2.3 Hz, due to the change in magnitude for the Nicaragua earthquake (Magnitude = 4.9), and in the epicentral distance for the California-Nevada border region earthquake (Magnitude = 5.1). Further work should address this observation in the future.
Modeling H/V spectral ratios of the data recorded by three-component UTIG BBOBS, offers a fast and an inexpensive means of obtaining information of the preferential vibration modes of soft sediment systems for use in design of marine structures, such as oil drilling and production platforms. This method makes use of background noise rather than coherent input signals so that it is not necessary to supply an active source to conduct the study, neither wait for an earthquake. The method is well suited for modeling shallow sediments, which cover the great majority of the seafloor. Also, the BBOBS is small, lightweight and inexpensive and operates autonomously so that it is simple and quite inexpensive to use.
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V III. ACKNOWLEDGMENTS This work was supported by grant number 003658-225-1997 of the Texas Higher
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