1. Geology 6600/7600 Signal Analysis 03 Dec 2013 © A.R. Lowry 2013 Last time: Deconvolution in Flexural Isostasy Surface loads can be solved from observed gravity and topography provided ~  (z), flexural rigidity and internal load depth z l are known a priori: In contrast to Tharsis, western US topography appears to be supported significantly by dynamic (i.e., sublithospheric) buoyancy Estimation of flexural rigidity D still relies on sometimes- questionable assumption of uncorrelated loading, so future analysis should use seismic constraints

2. Deconvolution of source & receiver terms from distant earthquakes: Recall that a seismogram represents a convolution of the source-time function s(t) with the Earth system response h(t) and the seismometer response i(t) : For imaging applications we would like to remove the source and receiver terms and just look at the Earth response. One approach to doing this is to isolate the impulse response to phase-conversions at impedance boundaries using teleseismic receiver functions Nov 30 Little Cottonwood Creek seismogram for M5 earthquake in S Mexico… P S Rayleigh

3. In the most commonly-used approaches to seismic receiver function analysis (e.g., Ammon, BSSA 1991; Ligorria & Ammon, BSSA 1999) the horizontal (E, N) components of a three-component seismogram are rotated into radial and transverse directions based on back-azimuth to the source event: For a teleseismic event arriving rays are near-vertical, so the vertical component contains predominantly P-wave particle motion (with a small contribution from SV) and the radial horizontal component contains predominantly SH motion (with a small contribution from P). In an idealized (1D, isotropic) Earth, the transverse contains motion neither from primary P or converted (polarized) S! N E Transverse Radial P S Vertical

4. Both vertical & radial components are convolved with the same source-time function and instrument response for each different phase that comes in: Here, k represents each of N phases that originated as a P wave and, after conversion, arrived as an S wave: (Ammon, BSSA 1991)

5. Thus the source and instrument response are removed from the time series by (frequency domain) division of the radial by vertical components. The resulting impulse response function is called the receiver function: (Ammon, BSSA 1991)

6. Receiver Function Estimates of Crustal Thickness: PPsPs Delay Time Deconvolve source-time function to get impulse response of phases converted at impedance boundaries Delay time between phase arrivals depends on crustal thickness and relative velocities of P & S phases EARS uses iterative time-domain deconvolution [Ligorria & Ammon, BSSA, 1999]: well-suited to automation PPsPs Crust Mantle

7. PPsPsPpPs PpSs PsPs Contribution of crustal thickness ( H ) versus v P /v S ratio ( K ) to delay time is ambiguous… Resolve using reverberations, which have differing sensitivity to H and K PPsPsPpPsPpSsPsPsPsPs

8. Ps PsPs PpSs & PpPs Crustal thickness ( H ) & v P /v S ratio ( K ) parameters that predict the observed phase delay times intersect at a point in parameter space PPsPpPs PpSs PsPs H–K Stacking: [Zhu & Kanamori, JGR, 2000]

9. Ps PsPs PpSs & PpPs Method stacks observed amplitudes at delay times predicted for converted Ps phase and reverberations. Max stack amplitude ideally reveals crustal thickness & v P /v S ratio. H–K Stacking: [Zhu & Kanamori, JGR, 2000] PPsPpPs PpSs PsPs (EARS H–K stack for station COR) [Crotwell & Owens, 2005]

10. The Moho is not the only lithospheric impedance contrast… And crustal thickness is not constant The Problem: (EARS H–K stack for station TA.P10A)

11. Despite outliers and other issues, crustal thickness & v P /v S have statistical properties consistent with a fractal surface… Crustal Thickness ( H ) v P /v S Ratio ( K ) Root Variogram H (km) Root Variogram K

12. Station TA.O09A (Central Nevada) Variograms can be used to estimate a “most likely” crustal thickness and v P /v S ratio via optimal interpolation from nearby sites.

13. Station TA.O09A (Central Nevada) And search for a “most likely” model with uncertainties. Can also model gravity predicted for each H & K at the site…

14. Station TA.O09A (Central Nevada) Gravity Model Likelihood Filter Optimal Interp. Likelihood Filter Combined

15.  Unlikely stack amplitude maxima are downweighted using likelihood statistics Station TA.O09A (Central Nevada)