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Rayleigh Calibration of Pressure-Acceleration Transfer Functions, Plane Wave Assumption: A Rayleigh wave at the seafloor exerts a force on a water column of depth H equal to its mass (ρH) times the seabed acceleration. For acceleration periods much larger than the quarter-wave resonance period of the water column, the transfer function between seafloor pressure and acceleration should be described by P/A=ρH. [8] Rayleigh Calibration, Assuming Elliptic Polarization (Spahr Webb, Pers. Comm.): The “static assumption” of Filloux [8] above is valid only at wavelengths long enough to displace the entire water column. At shorter periods this is no longer the case and the phase velocity of Rayleigh waves must be accounted for. [8] Solving the acoustic wave equation in the frequency domain for coupled upward and downward propagating waves at phase velocity with a vertical wave-vector yields a transfer function described by: Thus the transfer function still converges to ρH at periods where c >> α, but is now dependent on phase velocity at shorter periods. Seafloor Compliance and Infragravity Noise Removal: Ocean surface wave energy in the infragravity band (0.002-0.02Hz) can propagate to the seafloor and produce a time-varying pressure load. The transfer function between displacement and pressure fields measured on ocean-bottom seismometers and differential pressure gauges (DPGs) is known as the seafloor compliance and depends strongly on the shear structure beneath the measurement site. Compliance η and an estimate of uncertainty ε are obtained from acceleration and pressure PSDs (S a, S p ) and their coherence (γ) according to [1] : Note that compliance is inversely proportional to the calibration transfer functions, so the correction can be directly applied to compliance measurements. Using Rayleigh Calibration to Improve Sediment Characterization: The shallow velocity sensitivity of compliance makes it an ideal complement to deeper-focused seismic studies. Results from a joint Monte Carlo analysis of seafloor compliance and Rayleigh phase velocity dispersion [9] are shown below. The algorithm follows the method of Haario et al. [5] and forward modeling is performed using the code of Crawford [4] and Herrmann [2]. Conclusions: Teleseismic Rayleigh wave transfer functions provide a convenient constraint on relative calibration of DPG/OBS. The resulting correction can be applied directly to seafloor compliance measurements. Following the method of Webb, the wave-vector r where c >> α provides a direct functional mapping between the P/A transfer function and short-period Rayleigh phase velocities. Figure 6. (a) Schematic of seafloor loading from infragravity waves. (b) 24-hour pressure and displacement timeseries filtered to the infragravity band showing the relationship between forcing and seafloor motion. (c) Coherence, raw data and compliance for the same data segment. (d) Compliance can also be used as a filter to remove infragravity energy from long-period seismic data following the method of [3]. (from Fan-Chi Lin ) Background: The Cox/Webb Differential Pressure Gauge (DPG) [7] is a standard instrument deployed by the NSF-funded Ocean Bottom Seismic Instrument Pool (OBSIP). The ocean-bottom pressure recordings provided by DPGs are useful in characterizing sediment thickness and shear velocity using the seafloor’s response to loading from long-period ocean surface waves (seafloor compliance). Seafloor compliance measurements are highly sensitive to uncertainties in the DPG’s amplitude and low-frequency response calibration. A method is presented here to calibrate the pressure- acceleration transfer function using teleseismic Rayleigh wave arrivals from 10-30s period. The effect of this calibration on compliance-derived shear velocity models is also examined. Figure 1. Left: Marine Observations of Anisotropy Near Aotearoa (MOANA) stations and bathymetry. 30 broadband OBS and DPG were deployed from 2009-2010. Figure 2. At left, a Scripps OBS package including a Cox/Webb DPG. At right, a schematic of the DPG taken from Cox, Deaton and Webb 1984. [7] The strain gauge T measures the difference between ocean pressure admitted through diaphragm R and pressure in the reference chamber V c. Capillary leak L allows the instrument to equilibrate to ambient ocean pressure over a certain characteristic time (~1200s). Nominal OBS and DPG Responses: The nominal pole-zero instrument responses were deconvolved from the data and the vertical OBS response was differentiated to acceleration for analysis. Figure 3. Nominal OBS acceleration (top) and DPG (bottom) responses from Scripps. In-Situ Calibration of Differential Pressure Gauges at OBS Stations off New Zealand Justin S. Ball [1], Anne F. Sheehan [1], Fan-Chi Lin [2] and John Collins [3] [1] CIRES and the Dept. of Geological Sciences, University of Colorado, Boulder [2] California Institute of Technology [3] Woods Hole Oceanographic Institution References: [1] W. Crawford, S. Webb, and J. Hildebrand. Seafloor compliance observed by long-period pressure and displacement measurements. J. Geophys. Res, 96(10):16151–16160, 1991. [2] R.B. Herrmann and C. J. Ammon. Surface waves, receiver functions and crustal structure. Computer Programs in Seismology, v. 3.30. St. Louis University, 2004. http://www.eas.slu.edu/People/ RBHerrmann/CPS330.html [3] S.C. Webb and W.C. Crawford. Long period seafloor seismology and deformation under ocean waves. BSSA. 89(6): 1535-1542, 1999. [4] http://www.ipgp.fr/~crawford/Homepage/Software.htmlhttp://www.ipgp.fr/~crawford/Homepage/Software.html [5] H. Haario et al. DRAM: Efficient adaptive MCMC. Statistics and Computing, 16: 339-354, 2006, http://helios.fmi.fi/~lainema/mcmc/http://helios.fmi.fi/~lainema/mcmc/ [6] J. Stachnik et al. Amphibious Rayleigh wave ambient noise tomography, South Island, New Zealand. In Preparation. [7] C. Cox, T. Deaton and S. Webb. A deep sea differential pressure gauge, J. Atmos. Oceanic Technol., 1(3), 237-246, 1984. [8] Filloux, J. H., Pressure fluctuations on the open ocean floor off the Gulf of California: Tides, Earthquakes, Tsunamis, J. Phys. Oceanogr., 13, 783-786, 1983. [9] Ball, J.S., A. F. Sheehan, J. C. Stachnik, and J. A. Collins, A joint Monte Carlo inversion of seafloor compliance, receiver functions and Rayleigh wave dispersion at OBS stations off New Zealand, Abstract OS41D-1759, Fall 2012 Meeting of the American Geophysical Union Meeting, 2012. Acknowledgements: The authors wish to thank Wayne Crawford, Eleanor Willoughby, Spahr Webb, Peter Molnar, Julien Chaput and John Collins for graciously providing their code and guidance. Software from the IRIS consortium, GMT project, Robert Herrmann and Chuck Ammon were instrumental in this work. Support was provided by NSF EAR-0409835. b.a.c.d. Figure 8. Same as Fig 8 but with compliance values corrected using the Rayleigh calibration. Note the improved agreement between compliance and dispersion data. a.b. c. d. Figure 4. Left: a teleseismic Rayleigh wave arrival recorded by instrument NZ16. Acceleration shown at top and pressure at bottom. Middle: pressure and (scaled) acceleration PSDs used to calculate transfer functions. Right: pressure-acceleration transfer function for the same event corrected to the value of ρH shown in red. The measured correction coefficient is a factor of ~6. Figure 7. Left: results from a Monte Carlo inversion of uncalibrated seafloor compliance and Rayleigh phase velocity dispersion (from Fan-Chi Lin’s analysis). Right: Starting (black) and resulting (red) velocity models. Note the large disagreement between compliance and dispersion data. Figure 5. Left: Phase velocity dispersion at NZ16 from ballistic and ambient noise measurements. Right: Calibration results incorporating these phase velocities (mapped to blue crosses via r) into the elliptically polarized solution above. The calibration correction coefficient is now a factor of ~5.

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