1. Numerical Investigations of Seismic Resonance Phenomena in Fluid-Filled Layers Hans F. Schwaiger and David F. Aldridge Geophysics Department Sandia National Laboratories Albuquerque, New Mexico, USA Seismological Society of America 2008 Annual Meeting Sante Fe, New Mexico April 16-18, 2008 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2. Numerical Algorithm –Features and limitations Problem formulation Preliminary results Conclusions and ongoing work Outline

3. 1-D Layered Model –N layers, 2 half-spaces –Homogeneous, isotropic, anelastic –Welded interfaces between layers Layered Earth Model interface depth x y z 1 2 n-1 n n+1 N N+1 0 layer # 2 3 n-1 n n+1 N N+1 1 interface # z2z2 z3z3 z n-1 znzn z n+1 zNzN z N+1 z1z1...

4. Solution Strategy –Fourier transform x, y, t to k x, k y,  –Obtain analytic solution for layers –Apply interface conditions –Solve for coefficients a, b, c, d, e, f –Inverse FFT back to x, y, z, t Numerical Algorithm interface depth x y z 1 2 n-1 n n+1 N N+1 0 layer # 2 3 n-1 n n+1 N N+1 1 interface # z2z2 z3z3 z n-1 znzn z n+1 zNzN z N+1 z1z1...

5. Cartesian Coordinates –Enables use of 2D FFT (FFTW)‏ –Advantageous for eventual inclusion of anisotropy Global matrix approach –Solved by LU decomposition (Lapack)‏ Uses layer-local coordinates –Allows arbitrary number of layers Allows both force and moment point sources Top surface can be specified as stress-free Algorithm Features

6. Variation of material properties limited to 1-D Thickness of individual layers is limited Solution is periodic in x, y and t Algorithm Limitations

7. Rectangular spectrum of attenuation mechanisms –Attenuative, dispersive wave propagation –Characterized by 8 parameters per layer: Anelastic Geological Layers ,  lo,  hi,  ref V p (  ref ), Q p (  ref )‏ V s (  ref ), Q s (  ref )‏ High Q mediumLow Q medium

8. Example Synthetic Seismograms 300 m V P = 350 m/s V S = 1 m/s ρ = 1 kg/m 3 V P = 2000 m/s V S = 1500 m/s ρ = 2200 kg/m 3 V p = 3500 m/s V s = 2100 m/s ρ = 2400 kg/m 3 RayleighHead Waves Multiples PPPP 3P+1S 2P+2S 1P+3S SSSS PP Amplitude scale: x4 SS PS+SPPS+SP Amplitude scale: x1 Air overlying earth model Full solution Difference solution

9. Problem Geometry V P = 3500 m/s V S = 2020 m/s ρ = 2400 kg/m 3 V P = 1500 m/s V S = 1 m/s ρ = 1000 kg/m 3 V P = 350 m/s V S = 1 m/s ρ = 1 kg/m 3 Fluid layer 20 m d Sources: Fx, Fz, E, Torque Receivers: Vx, Vz 200 m Water: Air:

10. Problem geometry Reverberations Direct Arrival Top-bed reflection Intra-bed multiple

11. Seismic Source Wavelet: Berlage Berlage wavelet characteristics: causal high-frequency content

12. Fz / Vz Responses (20 Hz Berlage Wavelet) Half-space 5 m Water layer5 m Air layer Z = 2.5 m Z = 7.5 m Z = 12.5 m Z = 17.5 m Z = 22.5 m Z = 27.5 m Source depth

13. Spectra: Fz / Vz (Direct wave subtracted)

15. Spectra: Fz / Vz (Source in layer)

16. Spectra: E / Vz (Direct wave subtracted)

18. Spectra: E / Vz (Source in layer)

19. Torque Source Spectra (z = 10 m) 5 m Air layer 20 Hz Berlage Source depth z = 10 m

20. Fz / Vz Traces (50 Hz Berlage Wavelet) Half-space 5 m Water layer5 m Air layer Z = 2.5 m Z = 7.5 m Z = 12.5 m Z = 17.5 m Z = 22.5 m Note: Direct wave subtracted

21. Spectra: E / Vz (Direct wave subtracted)

23. Spectra: E / Vz (Source in layer)

24. Orientation Dependence on Force Source 5 m Air layer Source depth z = 22.5 m

25. Receiver spectrum is dominated by reverberations in the layer containing the source –No significant generation of reverberations in fluid layer when source is in overburden Some sources are more effective than others in generating reverberations –Explosion sources are efficient at generating reverberations –Frequency of reverberations from force sources are angle dependent –Torque sources are inefficient Reverberations are stronger in air layers than water layers Investigation of magma-filled layers are underway Conclusions and Ongoing Work

26. Spectra: Fz / Vz (Direct wave subtracted)

28. Spectra: Fz / Vz (Source in layer)