Th-P03-05
Separation of PS-wave Reflections from
Ultra-shallow Water OBC Data Using Elastic Wavefield
Decomposition
N. El Allouche* (Schlumberger Gould Research), J. van der Neut (Delft University of Technology) & G.G. Drijkoningen (Delft University of Technology)
SUMMARY
Elastic wave decomposition, aiming at separating the converted modes from the P-waves, is applied to high-resolution OBC data acquired in the River Danube, Hungary. The decomposition relies on accurate knowledge of the water-bottom elastic parameters and on a perfect sensor calibration and coupling. The available decomposition schemes require an adaptation to account for the shallow water depth in the survey area. In the presented method, the medium parameters are obtained from the inversion of the Scholte waves dispersion curves and the coupling filter was determined from the data. The coupling filter accounts for the imperfections in the geophone coupling and was corrected for by minimizing the contribution of the pressure and vertical component to the upgoing S-wave potential at near offsets. This criterion implies that these two components contain no converted energy at these offsets. The estimated coupling filter is applied to the geophone data used as an input to the decomposition scheme. The decomposed S-wave potential showed an improvement in the visibility of some converted modes, mainly at later arrivals.
Introduction
Multicomponent measurements using ocean-bottom cables (OBC) and seismometers (OBS) allow recording of the total wavefield and provide, consequently, better constraints to characterize the subsurface. Pure P-waves as well as converted PS-modes are recorded in this configuration. The converted modes are particularly interesting for shallow marine environments because they carry information about the S-wave velocity in the sediments. In contrast to P-waves, S-waves are only sensitive to the lithology and show a strong correlation to geotechnical parameters.
Processing of PS-waves is challenging because it requires the separation of these modes from the pure P-waves and the estimation of both P- and S-wave velocity models. The wavefield can be separated in the Radon domain, based on differences in moveouts between the two types of waves, or using the theoretically underlined elastic wavefield decomposition (e.g. Dankbaar 1985; Wapenaar et al. 1990). The decomposition filters derived from the two-way wave equation are applied to the horizontal and vertical components of the particle velocity and the pressure component, and combined to obtain upgoing and downgoing P- and S-wave potentials. Further processing of the data is facilitated and errors in the velocity model of the subsurface are reduced after applying the decomposition step. Several successful examples of wavefield decomposition have been published over the past decades (e.g. Amundsen and Reitan 1995; Schalkwijk et al. 2003; Muijs et al., 2004). These papers describe adaptive procedures aiming at estimating the medium parameters at the decomposition level (as required from the theory) and finding coupling filters to account for differences in sensor responses. The same adaptive procedures cannot be applied to data acquired in ultra-shallow water (<20 m) because the defined criterion to estimate the calibration filter, for example, are not fulfilled in this specific environment. A different adaptive scheme is required. In this work, we discuss an alternative approach adopted to separate PS-waves from an OBC data set acquired in a river (~4 m). The focus is put on estimating the calibration filter that accounts for the response differences between the hydrophone and the geophones for the high-frequency part of the data.
P/S wavefield decomposition filters
The elastic wavefield decomposition filters relate the vertical component of the stress field ࢀ
ሬሬԦࢠሺࢠሻjust below the water bottom (equivalent to the pressure recorded by the hydrophone) and the components of the particle velocity ࢜ሬሬԦሺࢠሻto the upgoing P- and S-wave potentials containing
reflections from the subsurface. This relation can be written in the frequency-slowness domain (ω, p) as (Schalkwijk et al. 2003)
ࡰሬሬԦିሺ࣓ǡ ǡ ࢠሻ ൌ ሺࣘିǡ ࣒ିሻࢀൌ െࡺ
ିሺ࣓ǡ ǡ ࢠ
ሻࢀሬሬԦࢠሺࢠሻ ࡺିሺ࣓ǡ ǡ ࢠሻ࢜ሬሬԦሺࢠሻ, (1)
where ࣘିand ࣒ି denote the upgoing P- and S-wave potential, respectively.
ࡺିሺ࣓ǡ ǡ ࢠሻ ൌ ቌ െ െ ࢙ ቍ and ࡺିሺ࣓ǡ ǡ ࢠሻ ൌ ࣋ࢉ࢙ ൮ െࢉ࢙షି ࢉ࢙షି ࢙ ൲ǡ (2) where ൌ ൫ࢉିെ ൯ Ȁ and ࢙ ൌ ൫ࢉ࢙ିെ ൯ Ȁ
are the vertical slownesses of the P- and S-waves at depth level z1, just below the water bottom. cp and cs denote the P- and S-wave velocities, respectively, at depth z1. The decomposition filters ࡺିand ࡺି are applied to separate the upgoing
S-wave potential࣒ି including PS-reflections from shallow-water OBC data. Field acquisition and preprocessing
Multicomponent OBC data were acquired in the Danube River downstream Budapest, Hungary. The acquisition and preprocessing of these data (discussed in detail by Allouche et al. (2010)) resulted in four densely sampled receiver gathers, corresponding to the three components of the particle velocity
and the pressure. During the survey, the receiver cable was released into the water. Hence, the orientation of the geophones is not exactly known. To correct for this, the horizontal components are rotated by minimising the energy in the crossline direction (perpendicular to the cable orientation). Because the subsurface can be laterally varying, only the direct arrival or the Scholte waves can be used for the minimisation procedure. In this case, we use the direct arrival to rotate the common-receiver gathers. The obtained rotated horizontal component is shown in Figure 1, together with the vertical and pressure components. Only these three gathers are processed.
(a) (b) (c)
Figure 1 The common-receiver gathers used for the decomposition: a) the pressure component, b) the
vertical component and c) the rotated radial component.
Separation of PS-waves from OBC data Medium parameters at the water bottom
Wavefield decomposition requires the knowledge of the seismic parameters at the water bottom (equation (2)). These parameters can be estimated from the data by applying the decomposition in an adaptive scheme as discussed by Schalkwijk et al. (2003) and Muijs et al. (2004). In this procedure, a filter is estimated by imposing a specific criterion that is valid in a selected time window. The filter is subsequently inverted to obtain the density and the P- and S-wave velocities.
The medium parameters of the water bottom can also be estimated from the Scholte wave. The dispersion curves of these interface waves, strongly present in these data, can be inverted to obtain the required elastic parameters. Kruiver et al. (2010) used this technique to infer density and P- and S-wave velocity profiles from the presented common-receiver gathers. For the upper layer of the sediments, they found the following values: cp = 1650 m/s, cs = 400 m/s, and ρ = 1500 kg/m3. These
results are used here to compute the decomposition operators. Sensor calibration
Variations in instrument response between the hydrophone and the geophone can affect the results of the decomposition. Each sensor has its specific transfer function that modifies the measured wavefield while converting it to voltage. The transfer function is dependent on the sensitivity factor K, the damping factor H and the angular resonance frequency ω0. The sensor specifications of the OBC are
known and are used to account for the response differences in the data. The corresponding transfer function R varies with angular frequency ω and can be computed using (Pieuchot, 1984)
ܴሺ߱ሻ ൌ ఠమ
ఠమିଶுఠఠబିఠ బమ
(3)
For the cable deployed in the survey, K=20.9 V/m/s for the geophone and K=4.58 V/bar for the hydrophone. Furthermore, the resonance frequency is 10 Hz and the damping H is 0.7 for both the geophone and the hydrophone.
Estimating the coupling filter
The objective of applying the decomposition step is to separate the S-waves from the P-waves and, consequently, assess the presence of converted energy in the shallow marine subsurface. Therefore, our emphasis is placed on obtaining the upgoing S-wave potential ߰ି. This potential is a weighted summation of the pressure and the vertical and horizontal components of the particle velocity as given
by equation (1). The weighting factors are only applied to the high-frequency part of the data. The Scholte waves and the low-frequency S-wave associated with the near field are filtered. However, a straightforward summation of these weighted components did not give satisfactory results. This is due to the coupling effect of the geophone compared to that of the hydrophone. To improve the results of the decomposition, a filter accounting for this effect can be estimated from the data.
In the procedure adopted by Schalkwijk et al. (2003), a criterion based on minimising the downgoing waves in the upgoing wave component was formulated to determine the calibration filters. However, such an approach is not applicable for this data set, acquired in very shallow water, because an upgoing wave can hardly be distinguished from a downgoing wave. Alternatively, we can define a different criterion to estimate the coupling filter. For the high-frequency data discussed here, we assume that the PS-converted energy, in the pressure and the vertical recordings, can be neglected at near offsets. This can be explained by the small conversion coefficients of plane waves for small angles of incidence, mainly in shallow unconsolidated sediments. Based on this assumption, we state that no upgoing S-wave energy is present in the sum of the hydrophone and the vertical component at small offsets after applying the decomposition filters. This is then used as a criterion to determine the coupling filter. Assuming that the hydrophone has a perfect coupling, we write for the upgoing S-wave potential from equations (1) and (2)
߰ିൌ െ ଶೞܲ ܨሺ߱ሻߩܿ௦ ଶቂݒ ௭െ ቀ ೞషమିଶమ ଶೞ ቁ ݒ௫ቃǡ (4)
where Fc denotes the filter describing the geophone coupling. A least-squares optimization procedure
is formulated based on this criterion to obtain Fc. The least-squares error is defined as
אൌ σ σ ଵଶቚܨሺ߱ሻߩܿ௦ଶݒ௭െ ଶೞቚ
ଶ
Ǥ (5)
This coupling filter Fc is estimated from data windows selected in the (τ, p) domain as shown in
Figure 2. The upper two windows correspond to the pressure and the vertical component of particle velocity and are used as an input for the minimisation step. The data resulting from applying the filter and the residual energy after subtraction are displayed in the lower windows.
In the following step, the vertical and horizontal components recorded by the geophone are convolved with the estimated filter, multiplied by the decomposition filters in the (ω, p) domain and summed with the pressure data to obtain the upgoing S-wave potential.
Figure 3 shows a comparison between the obtained S-wave potential and the radial component. Some minor differences can be noticed between the two records. The decomposed result shows slight improvements in the appearance of converted waves. However, there is also a leakage of P-wave energy to the upgoing S-wave potential (see the arrows in Figure 3), suggesting that the medium parameters used for the decomposition are inaccurate. This can be explained by the fact that the Scholte waves, inverted to estimate these values, have a frequency content that is much lower than the reflections considered here.
Conclusions
Elastic wave decomposition, aiming at separating the converted modes from the P-waves, was applied to OBC data acquired in the River Danube, Hungary. The shallow depth of the water, encountered in the survey area, required an adaptation of the available decomposition schemes. The decomposition relies on accurate knowledge of the water-bottom elastic parameters and on a perfect calibration and coupling of the sensors. In the presented method, the medium parameters are obtained from the inversion of the Scholte waves dispersion curves and the coupling filter was determined from the data. The coupling filter accounts for the imperfections in the geophone coupling and was corrected for by minimizing the contribution of the pressure and vertical component to the upgoing S-wave potential at near offsets. This implies that these two components contain no converted energy at these offsets. The decomposed result shows an improvement in the visibility of some converted modes, mainly at later arrivals.
Figure 2 Estimation of the coupling filter Fc. Data windows extracted from (a) the pressure component and (b) the vertical component. c) The vertical component after applying the coupling filter and (d) the residual energy after subtracting the filtered vertical component from the pressure.
Figure 3 Comparison between the horizontal component, before applying the decomposition and
coupling filters (left) and the resulting upgoing S-wave potential (right). References
Allouche, N., Drijkoningen, G.G., and van der Neut, J. [2010] Methodology for dense spatial sampling of multicomponent recording of converted waves in shallow marine environments. Geophysics, 76(1), T1-T11.
Amundsen, L., and Reitan, A. [1995] Decomposition of multi-component sea-floor data into upgoing and downgoing P- and S-waves. Geophysics 60(2), 563-572.
Dankbaar, J.W.M. [1985] Separation of P- and S-waves. Geophysical Prospecting 33, 970-986. Kruiver, P., Deak, A., and Allouche, N. [2010] Extraction of geotechnical properties from Scholte waves in underwater environments. 72nd EAGE Conference & Exhibition Extended Abstracts. Muijs, R., Robertsson, J.O.A., and Holliger, K. [2004] Data-driven adaptive decomposition of multicomponent seabed recordings. Geophysics 69, 1329-1337.
Pieuchot, M., [1984] Seismic instrumentation (Handbook of geophysical exploration) Geophysical Press Amsterdam.
Schalkwijk, K.M., Wapenaar, C.P.A., and Verschuur, D.J. [2003] Adaptive decomposition of
multicomponent ocean-bottom seismic data into downgoing and upgoing P- and S-waves. Geophysics
68, 1091-1102.
Wapenaar, C.P.A, Hermann, P., Verschuur, D.J., and Berkhout, A.J. [1990] Decomposition of multicomponent seismic data into primary P- and S-wave responses. Geophysical Prospecting 38, 633-661.
