GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 19, 1981, doi:10.1029/2003GL018090, 2003
Improved inversion for seismic structure using transformed, S-wavevector receiver functions: Removing the effect of the free surface Anya Reading, Brian Kennett, and Malcolm Sambridge Research School of Earth Sciences, Australian National University, Canberra, Australia Received 2 July 2003; revised 20 August 2003; accepted 29 August 2003; published 4 October 2003.
[1] The determination of structure from the inversion of teleseismic receiver functions may be improved by removing the contribution of the free surface. The free surface interaction gives rise to the highest amplitude signal on standard receiver functions and yet this initial pulse tells us little about the receiver structure below the surface layer. We apply a transformation to P, S and Horizontal wavevector components, which removes the free surface response and hence the initial P-pulse. A ‘‘pure’’ receiver function is calculated by deconvolving the S-wavevector component with the P-wavevector. In general, converted phase amplitudes within the receiver function waveform are better matched by the inverse algorithm, resulting in an improved estimation of seismic structure. In particular, low amplitude receiver function waveforms, often associated with poorly constrained structure, now yield a successful INDEX TERMS: 7203 Seismology: Body wave inverse. propagation; 7218 Seismology: Lithosphere and upper mantle; 7260 Seismology: Theory and modeling; 7299 Seismology: General or miscellaneous; 7294 Seismology: Instruments and techniques. Citation: Reading, A., B. Kennett, and M. Sambridge, Improved inversion for seismic structure using transformed, S-wavevector receiver functions: Removing the effect of the free surface, Geophys. Res. Lett., 30(19), 1981, doi:10.1029/ 2003GL018090, 2003.
1. Introduction [2] Estimating seismic structure from teleseismic receiver functions is a popular method of using earthquake energy to explore the crust and upper mantle. Assuming an isotropic, horizontal-layered crust, most of the converted energy which provides information on receiver structure is found on the radial component. The receiver function is formed by deconvolving the radial component with the vertical component to remove the influence of the source and sourceside structure [Ammon, 1991]. Radial receiver functions calculated in this way have often been used in both forward and inverse modeling of seismic structure [e.g., Langston, 1979; Ammon and Zandt, 1993] although the influence of the free surface, notably the high-amplitude initial P-pulse, is dominant. Most receiver function inversions minimize the misfit between the observed and synthetic waveforms. The large free-surface effect is therefore modeled as well as the desired seismic structure. [3] A transformation to remove the free-surface effects from three-component seismograms, reconstructing the in-
coming P and S-wavevectors together with the (horizontal) H-wavevector, was described by Kennett [1991]. It may be termed the PSH-wavevector method. The S-wavevector contains all the converted (i.e., SV) motion while the H-wavevector describes the transverse, horizontal (i.e., SH) motion. We use the transformed wavevectors to determine S-wavevector receiver functions from the P-wave coda of teleseismic events. These are inverted for structure using the recently developed Neighbourhood Algorithm (NA), [Sambridge, 1999]. The relationship between seismic receiver structure and the associated waveform is highly non-linear and is well explored by such an adaptive, Monte Carlo-style approach. Although the NA has been successfully applied to radial receiver function inversion [e.g., Agostinetti et al., 2002; Bannister et al., 2003], we aim to improve the determination of structure by removing the need to fit the large P-pulse. [4] S-wavevector receiver functions are part of the wider PSH-wavevector approach. As a full vector transformation, it differs from the popular LQT approach [Vinnik, 1977; Kind et al., 1995: Dahl-Jensen et al., 2003] which is based upon a geometric rotation of components (Figure 1). The two methods both reduce the initial P-pulse which facilitates more effective modeling but the PSH method removes the P-pulse entirely. The PSH method also gives the most complete representation of the converted waveform since, in theory, all the P-to-S converted energy should be included in the S-wavevector.
2. Minimizing the Effect of the Free Surface [5] The observed seismogram, consisting of a vertical component, Z, and horizontal (radial and transverse) components, R and T, which are rotated according to the azimuth of the receiving station from the earthquake, is a product of the free surface displacement matrix and the actual wavevector components, P, S and H. [6] These wavevector components may be extracted by taking linear combinations of the spectral elements of the rotated seismograms. A full description is given by Kennett [1991]. The transformation may be summarized by 0
1
0
VPZ
B B C B B C B VPR BSC¼B B C B @ A B @ 0 H
Copyright 2003 by the American Geophysical Union. 0094-8276/03/2003GL018090$05.00
SDE
P
3
- 1
VSZ VSR 0
10 1 Z CB C CB C B C 0 C CB R C CB C CB C VHT A@ T A 0
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READING ET AL.: S-WAVEVECTOR RECEIVER FUNCTION
Figure 1. Seismic energy arriving at a receiver. a) station/ event reference frame, ZRT, b) ray coordinate reference frame, LQT, as used by Vinnik [1977] and c) the PSH wavevector reference frame as used in this study. Incidence angle = i. with VPZ ¼ 1 2b20 p2 =ð2a0 qa0 Þ; VSR ¼ 1 2b20 p2 = 2b0 qb0 ; VPR ¼ pb20 =a0 ;
VSZ ¼ pb0
and VHT ¼ 1=2:
[7] The vertical slownesses are 2 1=2 qa0 ¼ a2 0 p
2 1=2 and qb0 ¼ b2 : 0 p
[8] We illustrate the effect of the transformation on the observed receiver function and on the inversion for seismic structure using three contrasting stations. MBWA (Figure 2), is a ‘‘good average’’ station for any receiver function study, being located on the Archaean Pilbara Craton of Western Australia [Betts et al., 2002]. Seismic recordings in this
Figure 2. Broadband station locations and approximate source-receiver paths. MBWA = Marble Bar (GSN/IU network); WT08 and WS03 are temporary stations which were part of the WACRATON experiment run by RSES, ANU [Reading et al., 2003 and Reading and Kennett, 2003]. Background seismicity is shown for the year June 2002 to May 2003. Epicentral distances of events are (clockwise from bottom left, for each station, in decimal degrees): MBWA, 45.3, 42.2, 34.2, 46.0, 50.7, 33.5; WT08, 32.7 and (approx. for event cluster) 39.0; WS03, 44.0, 46.6.
Figure 3. Observed receiver functions, radial (upper) and S-wavevector component (lower), for the stations used in this study. Note the absence of the initial P-pulse on the S-wavevector (transformed) receiver waveform. MBWA is a 6-event stack, WT08 a 9-event stack and WS03 a 2-event stack. region routinely show Moho arrivals indicating a sharp Moho at a depth of 30 km [Reading and Kennett, 2003]. Records from WT08 show exceptional conversions from the Moho of the central Yilgarn Craton [Reading et al., 2003], another Archaean block within Western Australia. WS03 is a poor example of a receiver waveform, showing a low signal-to-noise ratio and a low-amplitude Moho conversion. The station is located in the Yerrida Basin at the northern extremity of the Yilgarn Craton, which was strongly influenced by the Capricorn Orogen [Betts et al., 2002]. [9] The location of Australia with respect to regions of high seismicity around the Pacific plate inevitably leads to an uneven distribution of back-azimuth directions (Figure 2) of the observed earthquakes which make up the receiver function stacks (Figure 3). For MBWA, WT08 and WS03 we do not observe any significant difference in receiver waveform at different azimuths and assume that a 1-D model provides an adequate representation, at least for the determination of the first-order features, of the crust and upper mantle seismic structure. This assumption is most problematic for WT08, where the recorded events were dominated by events occurring at one back-azimuth over the deployment period. Independent evidence from an active
READING ET AL.: S-WAVEVECTOR RECEIVER FUNCTION
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Figure 4. Observed (black) and synthetic (blue) receiver functions i) radial and ii) S-wavevector) and associated seismic velocity models iii) radial and iv) S-wavevector). The P:S velocity ratio and S-velocity structure corresponding to the bestfit seismic structure are shown by red lines. The best fit is determined by minimizing the least-squares difference between observe and modeled waveforms. The yellow-green model density plots indicate the proportion of better-fitting models in that region of parameter space. All models were calculated with the same number of iterations so the wider swath of green in the left-hand velocity plot for WS03 (velocity inverted from radial receiver function) shows the distribution of profiles is wide and not constrained well by the data. P:S ratios are shown since they are part of the velocity profile although their determination is not affected by the S-wavevector approach. source experiment [Goleby et al., 2000] close to WT08 shows crustal structure with very gently dipping layers, such that a 1-D approximation remains appropriate [Cassidy, 1992]. [10] The Z, R and T components for each station were transformed to P, S and H-wavevectors and used to calculate S-wavevector receiver functions (analogous to radial receiver functions) by deconvolving the S-wavevector with the P-wavevector using an adaptation of the method used by Shibutani et al. [1996]. The necessary effective velocities were determined empirically by finding the values which most completely remove the initial P-pulse. For stations MBWA and WT08, located on old cratonic crust, moderately fast P and S velocities (5.8 and 3.4 kms1) were appropriate, whereas slower velocities (5.5 and 3.1 kms1) were used for station WS03, in the Yerrida Basin. The empirically determined effective velocities are consistent with expected values, given the geological setting
of the stations. The receiver functions were stacked (to improve the signal-to-noise ratio) and are shown in comparison with the radial receiver function waveforms (Figure 3).
3. Improved Inversion for Structure [11] The best-fit structure beneath each station obtained from the radial receiver function and the S-wavevector receiver function are compared in Figure 4. For station MBWA, the fit between observed and synthetic receiver functions is improved, and although the overall structure (e.g., depth to Moho) does not change substantially, some low-velocity zones were removed and it is now possible to fit the converted waveform corresponding to a sharp Moho. WT08 shows such a high-amplitude Moho phase conversion that it is limited by the search bounds imposed on the model. It may be that the amplitude is enhanced by
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READING ET AL.: S-WAVEVECTOR RECEIVER FUNCTION
superposition effects produced by interfingering of low and high velocities at the Moho interface [Helffrich and Stein, 1993] which are not resolved in this model. WS03 shows a very significant improvement. The low-amplitude Moho conversion was not fitted (Figure 4c, iii) by the inversion algorithm using the standard, radial receiver function but has been successfully fitted and a structure determined (Figure 4c, iv) using the S-wavevector receiver function. Although the record for WS03 has a low signal-to-noise ratio, the pulse at just less than 5 seconds is a known feature of records from this region [Reading and Kennett, 2003] and the main features of the structures determined for WS03 are therefore due to signal rather than noise. Tests on synthetic S-wavevector receiver functions (compared with radial receiver functions for the same model, both with added noise) also show a faster, improved misfit reduction in the same number of iterations.
4. Applications [ 12 ] The determination of seismic structure from S-wavevector receiver functions has most significant applications where 1-D structure is to be determined beneath a single station in three different cases. 1) Where the Moho and/or other important features of the crust are gradational or show a low contrast in seismic impedance, 2) where the signal-to-noise level is low, either due to a paucity of recorded events or due to local conditions at the station and 3) where the exact nature of a converting interface is the subject of the study. [13] In case 1, gradational or low-contrast structures will give rise to low amplitude features of the receiver function which may not yield to an inverse approach using radial receiver functions. The S-wavevector method allows the Neighbourhood Algorithm, and in principle any adaptive Monte Carlo-style inverse approach, to focus on those parts of the receiver function waveform which are of most interest. This opens up more locations to analysis provided a 1-D approximation is appropriate. In coping with a low signal-to-noise ratio, case 2, there can be never be a substitute for good station sites and long deployment durations. The S-wavevector method, nonetheless, provides a means of determining structure beneath the minority of stations (typically 5 – 25%) in any field experiment which may have reduced recording durations or unexpected signalto-noise problems. Finally, case 3, if the exact nature of an interface is under investigation, the S-wavevector receiver function method is very powerful because the full S signal is extracted. [14] The least-squares misfit function used in the inversion of radial receiver functions is conceptually more appropriate in the inversion of S-wavevector receiver functions since disproportionate weight is no longer given to the high-amplitude P-pulse. Additional potential benefits of the PSH approach include the analysis of S-coda receiver functions as well as the P-coda receiver functions most
commonly studied. Comparing the relative amplitudes of the S and H-wavevector receiver functions would allow a better-posed determination of the influence of dipping structure and anisotropy. [15] Inversion of S-wavevector receiver waveforms is a promising development of a widely used method in broadband seismology: allowing more flexible, more efficient, and more detailed experimental determinations of seismic structure. [16] Acknowledgments. We thank technical, research and field staff from RSES for their efforts during the WACRATON experiment (including WT08 and WS03). The manuscript was improved by critical comment from two anonymous referees.
References Agostinetti, N. P., F. P. Lucente, G. Selvaggi, and M. Di Bona, Crustal structure and Moho geometry beneath the Northern Appennines (Italy), Geophys. Res. Lett., 29(20), 1999, doi:10.1029/2002GL015109, 2002. Ammon, C. J., The isolation of receiver effects from teleseismic P waveforms, Bull. Seism. Soc. Am., 81, 2504 – 2510, 1991. Ammon, C. J., and G. Zandt, Receiver structure beneath the southern Mojave block, California, Bull. Seism. Soc. Am., 83, 737 – 755, 1993. Bannister, S., J. Yu, B. Leitner, and B. L. N. Kennett, Variations in crustal structure across the transition from West to East Antarctica, Southern Victoria Land, Geophys. J. Int., in press, 2003. Betts, P. G., D. Giles, G. S. Lister, and L. R. Frick, Evolution of the Australian Lithosphere, Aust. J. Earth Sci., 49, 661 – 695, 2002. Cassidy, J. F., Numerical experiments in broadband receiver function analysis, Bull. Seism. Soc. Am., 82, 1453 – 1474, 1992. Dahl-Jensen, T., et al., Depth to Moho in Greenland: Receiver-function analysis suggests two Proterozoic blocks in Greenland, Earth Planet. Sci. Lett., 205, 379 – 393, 2003. Goleby, B. R., et al., Crustal structure and fluid flow in the Eastern Goldfields, Western Australia: Results from the AGCRC’s Yilgarn Deep Seismic Reflection Survey and Fluid Flow Modelling Projects, Aust. Geol. Surv. Org., Record 2000/34, 2000. Helffrich, G. R., and S. Stein, Study of the structure of the slab-mantle interface using reflected and converted seismic waves, Geophys. J. Int., 115, 14 – 40, 1993. Kennett, B. L. N., The removal of free surface interactions from threecomponent seismograms, Geophys. J. Int., 104, 153 – 163, 1991. Kind, R., G. L. Kosarev, and N. V. Petersen, Receiver functions at the stations of the German Regional Seismic Network (GRSN), Geophys. J. Int., 121, 191 – 202, 1995. Langston, C. A., Structure under Mount Rainier, Washington, inferred from teleseismic body waves, J. Geophys. Res., 84, 4749 – 4792, 1979. Reading, A. M., B. L. N. Kennett, and M. C. Dentith, Seismic structure of the Yilgarn Craton, Western Australia, Aust. J. Earth Sci., 50, 427 – 438, 2003. Reading, A. M., and B. L. N. Kennett, Lithospheric structure of the Pilbara Craton, Capricorn Orogen and northern Yilgarn Craton, Western Australia, from teleseismic receiver functions, Aust. J. Earth Sci., 50, 439 – 445, 2003. Sambridge, M. S., Geophysical inversion with a neighbourhood algorithm. I. Searching a parameter space, Geophys. J. Int., 138, 479 – 494, 1999. Shibutani, T., M. S. Sambridge, and B. L. N. Kennett, Genetic algorithm inversion for receiver functions with application to crust and uppermost mantle structure beneath Eastern Australia, Geophys. Res. Lett., 23, 1826 – 1832, 1996. Vinnik, L. P., Detection of waves converted from P to SV in the mantle, Phys. Earth. Planet. Inter., 15, 39 – 45, 1977.
A. Reading, B. Kennett, and M. Sambridge, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia. (
[email protected])
