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
Background:
Rayleigh Calibration of Pressure-Acceleration Transfer Functions, Plane Wave Assumption:
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 pressureacceleration 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.
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]
a.
b.
c.
d.
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].
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.
Rayleigh Calibration, Assuming Elliptic Polarization (Spahr Webb, Pers. Comm.):
Filloux[8]
The “static assumption” of
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
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.
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.
Figure 1. Left: Marine Observations of Anisotropy Near Aotearoa (MOANA) stations
and bathymetry. 30 broadband OBS and DPG were deployed from 2009-2010.
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.
Figure 8. Same as Fig 8 but with compliance values corrected using the Rayleigh calibration.
Note the improved agreement between compliance and dispersion data.
Conclusions:
Seafloor Compliance and Infragravity Noise Removal:
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 Vc. 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.
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
• The resulting correction can be applied directly to seafloor
measurement site. Compliance η and an estimate of uncertainty ε are obtained from acceleration and pressure PSDs (Sa , Sp) compliance measurements.
and their coherence (γ) according to[1]:
• Following the method of Webb, the wave-vector r where c >> α
provides a direct functional mapping between the P/A transfer function
Note that compliance is inversely proportional to the calibration transfer functions, so the correction can be directly applied to
and short-period Rayleigh phase velocities.
compliance measurements.
a.
Figure 3. Nominal OBS acceleration (top) and DPG (bottom) responses from Scripps.
• Teleseismic Rayleigh wave transfer functions provide a convenient
constraint on relative calibration of DPG/OBS.
b.
c.
d.
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 )
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.html
[5] H. Haario et al. DRAM: Efficient adaptive MCMC. Statistics and Computing, 16: 339-354, 2006, 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.