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Shear-wave statics using receiver functions Dirk-Jan van Manen1 , Johan Robertsson2 , Andrew Curtis3 , Ralf Ferber3 and Hanneke Paulssen1 Dept. of Geophysics, Utrecht University, The Netherlands 2 WesternGeco Oslo Technology Centre, Asker, Norway 3 Schlumberger Cambridge Research, Cambridge, United Kingdom 1 Summary We extend the seismological receiver function method to the exploration seismic domain to solve the problem of shear-wave statics for multicomponent data. The method relies on crosscorrelation or deconvolution of vertical with radial component traces in the common-receiver domain followed by a stacking step. This procedure is repeated for each receiver, resulting in a profile of high-resolution stacked receiver functions; events corresponding to shallow mode-converted waves constrain the shear-wave static. The method is applied to a line of commercial multicomponent seabed seismic data and gives results in good agreement with a conventional statics method, although results on some other lines require additional interpretation. In contrast to seismological receiver function analysis, the main converted wave energy in the receiver functions originates from reflection at shallow interfaces rather than conversion of upgoing wavefields. Introduction The use of multicomponent receivers for commercial seismic data acquisition in marine (i.e., seafloor) environments has gradually been accepted and multicomponent technology is receiving new interest on land as well. The advantages of multicomponent recordings are well known and reside in the ability to record mode-converted waves with the horizontal components. Although there is consensus that multicomponent technology will play an important role in the future of seismic data acquisition, several issues must be resolved before its potential is fully realized. One problem that the industry experiences applying multicomponent technology is the distortive effect the near surface has on the deeper reflected wavefield, better known as the statics problem. The near surface, both in seabed and in land acquisition, is generally associated with low, laterally varying shear-wave velocities. On land, the P-wave velocity can also be low. These properties often lead to large P- and S-wave traveltime perturbations in the deeper reflected wavefield, which vary from receiver-to-receiver. These perturbations, when they remain uncorrected, can lead to a significant loss of high frequencies in subsequent processing. In this paper, we extend the seismological receiver function method to the exploration and production seismic domain to solve the shear-wave statics problem for multicomponent data. We start by reviewing the receiver SEG International Exposition and 72nd Annual Meeting function method. We then propose a new data processing flow to estimate the S-statics and apply this to a line of commercial multicomponent (4C) seabed seismic data. Finally, we discuss the observations and give some potential applications beyond shear-wave statics estimation, to end with some conclusions. Although we focus our discussion on the seabed seismic case, the proposed method should also work for land multicomponent data. Receiver functions in seismology The receiver function method is a well-known seismological method to investigate the structure of the earth’s crust and upper mantle. It relies on the observation of shear-waves in the coda of a teleseismic P-wave resulting from mode conversion of the P-wave at major crustal or upper-mantle discontinuities. The receiver function method exploits the recording of these phases on separate components; P-waves on the vertical and S-waves on the radial (Figure 1). By deconvolving the vertical from the radial component the receiver function is formed, containing events related to crust and upper-mantle structure only (Langston, 1979). In a typical receiver function study, receiver functions are inverted for a horizontally layered model using the Thomson-Haskell propagator matrix formalism (Paulssen et al., 1993). In the simplest implementation, however, the receiver function provides a measure of the difference in traveltime between the main phase and the mode-converted branches through the upper mantle or crust. The tangential receiver function, when it contains significant energy, provides information on dip of the main convertors or anisotropy within the crust and upper mantle (Levin and Park, 1997). Statics using receiver functions When strong contrasts in material properties exist in the shallow subsurface (e.g., 250 m) at a seismic survey location, significant mode-conversion of up- and downgoing wavefields will take place at these interfaces. Moreover, the natural separation of P-waves on the vertical and S-waves on the horizontal components is also well known for industrial multicomponent seismic data. This suggests that, by applying the receiver function method to exploration seismic data, information about the compressional- and shear-wave properties of the near surface can be obtained. We focus on seabed seismic data because source and P- Main Menu Shear-wave statics using receiver functions air water seabed the natural domain because all energy arriving at the same receiver probes the same near-surface structure. Preprocessing also typically includes muting or gaining part of the input data. crust PS PSconverted P P-transmitted P Moho upper-mantle shallow interface deeper regions P-upgoing P-transmitted P-projection dt=ts-tp MODEL DATA radial vertical component component PS-projection PS-converted Fig. 1: Schematic illustration of the receiver function method. Up- and downgoing waves partially mode convert upon transmission or reflection at shallow interfaces. By calculating receiver functions, information about near surface structure is obtained. II. Receiver function calculation The second step is the calculation of receiver functions for the full or a restricted range of source-receiver offsets in a common receiver gather. The receiver functions are calculated using a stabilized deconvolution technique known as the water level method. This method has been described in detail in connection with the receiver function method by Langston (1979). It works in the frequency domain by filling the troughs of the denominator in the spectral division up to a fraction, c, of its maximum to prevent the division from exploding. Typically, we use a value c = 0.05 when calculating the receiver functions for real data. III. Stacking wave statics are considered insignificant for this environment. This allows us to deal with the S-statics directly. More importantly, since the shear-wave velocities in the seabed are extremely low, the events in the receiver function are dominated by the shear-wave traveltime and, hence, a direct measure of the S-static. When the P-wave traveltime through the near surface cannot be neglected, the P-statics must be found separately and added to the traveltime differences given by the receiver functions. In this step, the receiver functions obtained for a common receiver gather are stacked. The stacked trace amplitude is normalized by the number of input receiver functions. Note that no moveout correction is applied before stacking the receiver functions; we explicitly rely on the signal to be static as a function of offset. Furthermore, we assume that the difference in P- and S-wave traveltime through the near surface at a given receiver location is constant and independent of reflection depth or offset (i.e., slowness). In contrast to the receiver function method in seismology, this gives the opportunity to use long time windows for receiver function calculation, containing not a single event, but a range of reflections. Moreover, we can take advantage of the large amount of data present in a typical seismic survey by stacking receiver functions obtained for different offsets, resulting in a single, high signal-to-noise (S/N) ratio receiver function per receiver. The process of calculating and stacking receiver functions is repeated for all receivers. Because the stacked receiver functions only contain events related to near surface structure, shallow mode-converted waves measuring the shear-wave static will be visible in a profile of these stacked receiver functions and can subsequently be picked. Data processing We now propose a seismic processing flow to find the shear-wave statics based on the receiver function methodology. The approach is divided in four main steps, each described briefly below. I. Preprocessing Before the receiver functions are calculated, the data must be rotated into radial-transverse coordinates to maximize the projection of the shear-waves on the radial component. Furthermore, the data must be sorted to the common receiver gather domain. Although the receiver function calculation can be done in any domain, this is SEG International Exposition and 72nd Annual Meeting IV. Plotting and picking Results To test the approach, several shot lines of commercial multi-component seabed seismic data were available. We show the results on one of them. The data were recorded on the North Sea continental shelf. The sampling rate was 2 ms and the source and receiver intervals were 50 m and 25 m, respectively. The line consisted of 180 shot positions, inline with and directly over a cable of 174 receivers. In Figure 2 top and middle panels, the pressure and radial components are shown for a typical common receiver gather. We calculate the receiver functions using the pressure instead of the vertical component. The main results that will be shown, however, have also been obtained using the vertical component, although at a slightly higher noise level. The result of calculating the receiver functions is shown in the bottom panel. We have restricted the range of lag times in the receiver functions to [-0.4,0.4] s. Main Menu Shear-wave statics using receiver functions 0 This range should be chosen in accordance with shearwave static delays expected. Note the complicated behavior in the central part of the receiver function gather. At large offsets, however, some approximately flat events can be seen. Next, the traces are stacked to form a single receiver function for this receiver gather. We have also tested crosscorrelation of the vertical and pressure with the radial component, because our main interest is in phase information only. The results were similar to those obtained using stabilized deconvolution, however inferior in resolution and are not shown here. Discussion In contrast with the receiver function method in seismology, mode conversion of the upgoing wavefields does not seem to play a significant role in the formation of the events observed in the receiver function profile. We attribute the lack of such energy to the small incidence angles, and hence, small conversion coefficients involved with the central cone of reflection data. In other survey areas, however, such energy may result in a significant signal. We explain the signal observed in the receiver function profile by PS-waves, mode-converted upon reflection at shallow interfaces and the corresponding P-reflections. We also consider the possibility of headwaves propagating along shallow interfaces, emitting both P- and S-waves upward into the near surface. Such waves would also explain the static traveltime differences SEG International Exposition and 72nd Annual Meeting 0.6 Time [s] 0.8 1 1.2 1.4 1.6 1.8 2 −3000 −2000 −1000 0 1000 2000 3000 1000 2000 3000 Offset [m] 0 0.2 0.4 0.6 0.8 Time [s] To test which part of the input data contributes most to the statics event observed in the receiver functions, a simple muting experiment was done. The central cone of reflection data is muted from the input data. The black solid lines in Figure 2 indicate the top mute boundary. Subsequently, the whole processing was repeated. The profile of stacked receiver functions is shown in Figure 3, middle panel. Note that the results have an even higher S/N ratio, although the general features remain unchanged. We have concluded that the central cone of reflection data does not contribute significantly to the shear-wave statics event in the stacked receiver function profile. This was also confirmed by the inverse muting experiment for which the results are shown in the bottom panel. Note that the shear-wave statics signature is faintly visible, however the S/N ratio is significantly lower and the receiver functions are much more low frequency. 0.4 1 1.2 1.4 1.6 1.8 2 −3000 −2000 −1000 0 Offset [m] −0.4 −0.3 −0.2 −0.1 Time lag [s] In Figure 3 (top) the results are shown when the process of calculating and stacking receiver functions is repeated for all common receiver gathers. The profile contains only a few events and has a very high S/N ratio. Note how the events at 0.1 s and 0.3 s, already visible in Figure 2 (bottom), are amplified through the stacking. A shear-wave statics solution available for this line, obtained independently using a residual statics method, is plotted on top of the profile in blue. This profile serves as a reference solution. In green, the maximum of the event in the receiver functions is picked automatically. Note the good agreement between the events in the receiver function profile and the reference solution. 0.2 0 0.1 0.2 0.3 0.4 −3000 −2000 −1000 0 1000 2000 3000 Offset [m] Fig. 2: Typical common receiver gather input data with a t2 gain applied. (Top) Pressure recording. (Middle) Radial component of particle velocity. (Bottom) Receiver function gather calculated by deconvolution of the pressure from the respective radial component traces. The gather is scaled uniformly. observed at far offsets, contributing most to the signal. We have repeated the processing on several other lines of data for which residual statics profiles were available, with mixed results. For some lines, the long wavelength match Main Menu Shear-wave statics using receiver functions 0 Residual statics Receiver function statics 0.05 0.1 Time lag [s] 0.15 0.2 0.25 0.3 0.35 0.4 0 500 1000 1500 2000 2500 3000 3500 4000 Offset [m] neglected. Further research is needed to resolve this. Finally, it is interesting to consider additional applications of the receiver function method to exploration seismic data, given the results that we have obtained. Calculation of tangential receiver functions, or stacking radial receiver functions for a narrow azimuthal range, could provide information about shallow anisotropy. Another aspect that we have not considered here is amplitude information. Because the receiver function combines information on both P- and S-waves having propagated through the near surface, the amplitude is a measure of the differential attenuation in the near surface, and hence, seems to offer a possibility of inverse-Q filtering horizontal component data. The shortest wavelength amplitude variations could be diagnostic of receiver coupling effects. 0 Residual statics Receiver function statics 0.05 0.1 Time lag [s] 0.15 0.2 0.25 0.3 0.35 0.4 0 500 1000 1500 2000 2500 3000 3500 4000 Offset [m] Conclusion We have demonstrated the potential of the receiver function method in an exploration and production seismic setting to investigate the near surface and the distortive effect it has on the deeper reflected wavefield. In the simplest approach, the receiver function method can give information about the shear-wave statics. These traveltime perturbations generally limit multi component seismic data quality. A data processing approach was proposed and tested on a line of commercial multicomponent seabed seismic data. The processing gave results consistent with a conventional statics solution, although results on some other lines require further investigation. 0 Residual statics Acknowledgments 0.05 We thank Everhard Muyzert and Valerie le Mezo for valuable input. The first author thanks WesternGeco and Schlumberger for hospitality during stays in which most of this work was done. We acknowledge the permission to publish these results. 0.1 Time lag [s] 0.15 0.2 0.25 References 0.3 0.35 0.4 0 500 1000 1500 2000 2500 3000 3500 4000 Offset [m] Fig. 3: Profiles of stacked receiver functions. In blue an Sstatics solution is shown, obtained independently using a conventional statics method. (Top) Unmuted input data (Middle) reflection data mute (Bottom) Direct wave and shallow reflections mute. Langston, C., 1979, Structure under Mount Rainier, Washington, inferred from teleseismic body waves: J. Geophys. Res., 84, 4749–4762. Levin, V., and Park, J., 1997, P-SH conversions in a flatlayered medium with anisotropy of arbitrary orientation: Geophys. J. Int., 131, 253–266. Paulssen, H., Visser, J., and Nolet, G., 1993, The crustal structure from teleseismic P-wave coda–I. Method: Geophys. J. Int., 112, 15–25. between the events in the receiver functions and the conventional shear-wave statics solution was poor. One explanation for more complicated results is the fact that the shallow P-waves involved reflect at different locations than the PS-converted waves, leading to lateral averaging or significant P-wave traveltimes that can no longer be SEG International Exposition and 72nd Annual Meeting Main Menu