PAT MEYERS R-WAVE EIGENFUNCTION ANALYSIS [REDUX]

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Andra McDaniel
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1 PAT MEYERS R-WAVE EIGENFUNCTION ANALYSIS [REDUX]

2 EVENT SELECTION EVENT SELECTION Use transient events from Gary/Ross with obvious R-wave regions Choose those r-wave regions by eye, and only use that data. Ground Velocity [m/s] 6 YATES: Frequency [Hz] Radial to Vertical phase Time [s] from :6: Phase

3 EVENT SELECTION 3 EVENTS 8 events Typically 5-8 s or so from each event If you want times and more info, let me know. I have a full table in my thesis

4 ANALYSIS METHOD ANALYSIS PARAMETERS Frequencies:.,.3,.,. Hz FFT segment durations: s Everything is done in the frequency domain using spectrograms Initially, each pixel in spectrogram is a data point f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t

5 ANALYSIS METHOD NORMALIZATION 5 SURFACE STATIONS RADIAL CHANNEL f5,t f5,t f5,t3 f5,t f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t ARBITRARY OTHER CHANNEL SPECTROGRAM f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t f5,t f5,t f5,t3 f5,t f,t f,t f,t3 f,t = NORMALIZATION SPECTROGRAM f3,t f3,t f3,t3 f3,t f,t f,t f,t3 f,t f,t f,t f,t3 f,t FINAL DATA POINTS SPECTROGRAM

6 <latexit sha_base6="futwk+bpma+wvom7rkgq7khvfq=">aaaci3icdvbnswmxem36bfqevqslek9ln3awhueythfatit5rsotsgs9klmrxkv/ixb/ixymixjzxxrbrv9ehjz3gyteueihuhxfxpgxicmp6znznnz8wuls/nllqstp5pdnccylcbmycfgjoklhcvagbrioeyudka+je3oiitnemhgrknekdhdk7xye37sfxsf+kxzzmqxeglrdzxjmy9ctofef8pn/ldxnih8ltpd3gzlc7jq3hebzu6pepwrvytwlkr7lpll3oldgcgegklx/xzfpidijtombkjnjomuxaj/zyfgkgyvedafiqwasmmqv7nmnq7rpggv7fnkh+niy5exvsiwnrhdrvntdcs/veakuzeypjert/xbsmkmjmbhrttdaufysyvwl+fku8wghdbwna3h6l6p7kolzybwmlchaimogrjfuiqeqzedckxosjwckceybn5du6dr+ffefshxngm6vkb5z3drpbm=</latexit> <latexit sha_base6="futwk+bpma+wvom7rkgq7khvfq=">aaaci3icdvbnswmxem36bfqevqslek9ln3awhueythfatit5rsotsgs9klmrxkv/ixb/ixymixjzxxrbrv9ehjz3gyteueihuhxfxpgxicmp6znznnz8wuls/nllqstp5pdnccylcbmycfgjoklhcvagbrioeyudka+je3oiitnemhgrknekdhdk7xye37sfxsf+kxzzmqxeglrdzxjmy9ctofef8pn/ldxnih8ltpd3gzlc7jq3hebzu6pepwrvytwlkr7lpll3oldgcgegklx/xzfpidijtombkjnjomuxaj/zyfgkgyvedafiqwasmmqv7nmnq7rpggv7fnkh+niy5exvsiwnrhdrvntdcs/veakuzeypjert/xbsmkmjmbhrttdaufysyvwl+fku8wghdbwna3h6l6p7kolzybwmlchaimogrjfuiqeqzedckxosjwckceybn5du6dr+ffefshxngm6vkb5z3drpbm=</latexit> <latexit sha_base6="futwk+bpma+wvom7rkgq7khvfq=">aaaci3icdvbnswmxem36bfqevqslek9ln3awhueythfatit5rsotsgs9klmrxkv/ixb/ixymixjzxxrbrv9ehjz3gyteueihuhxfxpgxicmp6znznnz8wuls/nllqstp5pdnccylcbmycfgjoklhcvagbrioeyudka+je3oiitnemhgrknekdhdk7xye37sfxsf+kxzzmqxeglrdzxjmy9ctofef8pn/ldxnih8ltpd3gzlc7jq3hebzu6pepwrvytwlkr7lpll3oldgcgegklx/xzfpidijtombkjnjomuxaj/zyfgkgyvedafiqwasmmqv7nmnq7rpggv7fnkh+niy5exvsiwnrhdrvntdcs/veakuzeypjert/xbsmkmjmbhrttdaufysyvwl+fku8wghdbwna3h6l6p7kolzybwmlchaimogrjfuiqeqzedckxosjwckceybn5du6dr+ffefshxngm6vkb5z3drpbm=</latexit> <latexit sha_base6="futwk+bpma+wvom7rkgq7khvfq=">aaaci3icdvbnswmxem36bfqevqslek9ln3awhueythfatit5rsotsgs9klmrxkv/ixb/ixymixjzxxrbrv9ehjz3gyteueihuhxfxpgxicmp6znznnz8wuls/nllqstp5pdnccylcbmycfgjoklhcvagbrioeyudka+je3oiitnemhgrknekdhdk7xye37sfxsf+kxzzmqxeglrdzxjmy9ctofef8pn/ldxnih8ltpd3gzlc7jq3hebzu6pepwrvytwlkr7lpll3oldgcgegklx/xzfpidijtombkjnjomuxaj/zyfgkgyvedafiqwasmmqv7nmnq7rpggv7fnkh+niy5exvsiwnrhdrvntdcs/veakuzeypjert/xbsmkmjmbhrttdaufysyvwl+fku8wghdbwna3h6l6p7kolzybwmlchaimogrjfuiqeqzedckxosjwckceybn5du6dr+ffefshxngm6vkb5z3drpbm=</latexit> ANALYSIS METHOD SIGNS 6 PHASE MEASUREMENTS For each pixel measure radial to vertical phase Retrograde: assign (+) sign to radial measurement Prograde: assign (-) sign to radial measurement All vertical measurements are negative This is to be consistent with convention in Haney/Tsai paper [] = arctan Z(f) R(f)! [] Haney, M. M., & Tsai, V. C. (5). Nonperturbational surface-wave inversion: A Dix-type relation for surface waves. Geophysics, 8(6), EN67 EN77.

7 ANALYSIS METHOD 7 FINAL STEPS Remove data points with normalized amplitude >.5 Take mean and standard deviation at each depth and each frequency For radial measurements this naturally reduces amplitude in cases R- waves don t dominate question: Should we also reduce Z-amplitude by similar factor (i.e. mean(ampr) / mean( ampr ) Convert standard deviation -> standard deviation of the mean (divide by sqrt(n_points))

8 .5. R measurements, Hz R measurements: mean R measurements: median R measurements: distribution Violin plots Distribution of points at that depth and frequency Amplitude Black bars are 68%.5 intervals Depth [m]. Z measurements, Hz.5..5 Z measurements: distribution Z measurements: median Z measurements: mean Depth [m]

9 <latexit sha_base6="kcqetnfbk6e5lafvukyxhos=">aaacoxicdvfdt9swfhuygncxrrupsohqayirnbcgpqbcceemnqhyignv3kua6cd5ko5vklp/f79jb/g3uxyy6wzushzzfa59bpqlrjtgfyz7xcliy6xlldqrddv3tbfvb9uwsep69bmzpi6ioojnrko5lqw6wykkscxuw3jp9asikll6ouc56yxkjuuxpqbkqzfy/cgx++rph9bkv8ptdkcawldioeodmbywrbqiphovdp3ira8qpcgjjaolwpbtluqsgqmnw59pwu/pw/py/5zwvgob9xu36/cegm7ht5ter5g5u/j/dabhzs+s3sgevgstxqrnph/xfqzirsfrtqztqujjxvzjizalgvsofmsjvsu3rgtgsszkxjljuikphuldnelzugt9vgnkirkjzlidczed9t/ph8suswoj7oltznc8sohufwjbunqz9lrruyguco5oatqafexkhnumsmhl8/hefbpeehf/+ijkcygdfubn5kj9dirourtelurk/wd+vmbtjf7lz9pmrdmdntrxdvcbufclq==</latexit> <latexit sha_base6="kcqetnfbk6e5lafvukyxhos=">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</latexit> <latexit sha_base6="kcqetnfbk6e5lafvukyxhos=">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</latexit> <latexit sha_base6="kcqetnfbk6e5lafvukyxhos=">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</latexit> PARAMETER ESTIMATION 9 BIEXPONENTIAL MODEL Sample over 9 parameters c, a, a, c 3, a 3, a, N vh, v intercept, v slope Use all frequencies at once as data r H (f,z) =(e afz/v + c e afz/v ) +c r Z (f,z) =(e a 3fz/v + c e a fz/v ) N vh +c

10 <latexit sha_base6="kgtrkecom6xcp8d3jvxzukvua=">aaaci3icdvdlsinbfkwzyzv9slm8iwddqvpckagqh6malglehcag6ctsuqx5qdtsymvxn/mrs3ghibsx/ouvhxchmqmfh3puo+juiunmvbslcvfpiwlorf/r85eu3yvrghukylaalepxoqabudkgfkpucjvqfggdiyhk/8yxfoi5phmcpdcn+hctqco5w6luorjvhd3pir78g3cdospljgchpgu9ccnoygjmisfriupfewvumwuz3fj8yd7ex+ons/brtqbzqeeykapkjtne5bhttqwqyxccwpahkuxm3onuigoyp3mqmrfkf9d9ky73dfhpjqb9bpu/drnsxi5qix5jwzrgtjdgozn/erpyx8w3o/ao9mmirazrwgmkczehjtswcdgslrsf6viwduxnivttig8xur/ty58oudarno/mcztiftkmo8qje6rjtsgparfbbskfck8enn/onfpopmkl5x5zyz5b+flff3hpda=</latexit> <latexit sha_base6="kgtrkecom6xcp8d3jvxzukvua=">aaaci3icdvdlsinbfkwzyzv9slm8iwddqvpckagqh6malglehcag6ctsuqx5qdtsymvxn/mrs3ghibsx/ouvhxchmqmfh3puo+juiunmvbslcvfpiwlorf/r85eu3yvrghukylaalepxoqabudkgfkpucjvqfggdiyhk/8yxfoi5phmcpdcn+hctqco5w6luorjvhd3pir78g3cdospljgchpgu9ccnoygjmisfriupfewvumwuz3fj8yd7ex+ons/brtqbzqeeykapkjtne5bhttqwqyxccwpahkuxm3onuigoyp3mqmrfkf9d9ky73dfhpjqb9bpu/drnsxi5qix5jwzrgtjdgozn/erpyx8w3o/ao9mmirazrwgmkczehjtswcdgslrsf6viwduxnivttig8xur/ty58oudarno/mcztiftkmo8qje6rjtsgparfbbskfck8enn/onfpopmkl5x5zyz5b+flff3hpda=</latexit> <latexit sha_base6="kgtrkecom6xcp8d3jvxzukvua=">aaaci3icdvdlsinbfkwzyzv9slm8iwddqvpckagqh6malglehcag6ctsuqx5qdtsymvxn/mrs3ghibsx/ouvhxchmqmfh3puo+juiunmvbslcvfpiwlorf/r85eu3yvrghukylaalepxoqabudkgfkpucjvqfggdiyhk/8yxfoi5phmcpdcn+hctqco5w6luorjvhd3pir78g3cdospljgchpgu9ccnoygjmisfriupfewvumwuz3fj8yd7ex+ons/brtqbzqeeykapkjtne5bhttqwqyxccwpahkuxm3onuigoyp3mqmrfkf9d9ky73dfhpjqb9bpu/drnsxi5qix5jwzrgtjdgozn/erpyx8w3o/ao9mmirazrwgmkczehjtswcdgslrsf6viwduxnivttig8xur/ty58oudarno/mcztiftkmo8qje6rjtsgparfbbskfck8enn/onfpopmkl5x5zyz5b+flff3hpda=</latexit> <latexit sha_base6="kgtrkecom6xcp8d3jvxzukvua=">aaaci3icdvdlsinbfkwzyzv9slm8iwddqvpckagqh6malglehcag6ctsuqx5qdtsymvxn/mrs3ghibsx/ouvhxchmqmfh3puo+juiunmvbslcvfpiwlorf/r85eu3yvrghukylaalepxoqabudkgfkpucjvqfggdiyhk/8yxfoi5phmcpdcn+hctqco5w6luorjvhd3pir78g3cdospljgchpgu9ccnoygjmisfriupfewvumwuz3fj8yd7ex+ons/brtqbzqeeykapkjtne5bhttqwqyxccwpahkuxm3onuigoyp3mqmrfkf9d9ky73dfhpjqb9bpu/drnsxi5qix5jwzrgtjdgozn/erpyx8w3o/ao9mmirazrwgmkczehjtswcdgslrsf6viwduxnivttig8xur/ty58oudarno/mcztiftkmo8qje6rjtsgparfbbskfck8enn/onfpopmkl5x5zyz5b+flff3hpda=</latexit> PARAMETER ESTIMATION BIEXPONENTIAL MODEL A FEW EXPLANATIONS v on the bottom is from dispersion curve Linear for right now (have also also tried power law) Would like to add something different need something that probably levels off at low frequencies. N vh is vertical-to-horizontal ratio at the surface v(f) =v intercept + f v slope

11 <latexit sha_base6="fsafwibx35mrxoizlxruicyakko=">aaacxicjvlljtmwfhxcayipkbbkcwfipolyswghdscdzddoii9wzyhwdxhrnidup6iqsqigt/8aof+ajcjicwvispapzrn3l7xyxwpr3nivfuhjp8pw9q6r/c3g/fujtaspm9juppjsrqtpgftzbvgx5lkjfknl+evqj+yzjxdpktd5mzi/jouehpqbkmh/bqasetyhrislhbenub/enrh8izemyhxtxrwda5wkakt3llwsqzyocjc3x5wysfc3wsarxovlph/6whbycdsqwfnnpekq8j7z9zyevx8ckkcblivdxlpaa/jdb/dsb/yfz7idzi/zaqbvjdnyh6fgtmyprx7o5eb+etx3pahthdnaujolz7xkar6zrfnblfqtqb9gkjnqwblc+ekzysekjvbgjiqmcm/qkdswn3drcbmpvmjhpo9xgqwkltvdszmdgr+lryl9piyhj/cjmuwukbg8jcge6hgjgsugrui6bhepu7goiqaznyeqgnfxwr/bjnvjpevrxdp/vrgh7qj7qitcneahaikobrr65xxnpnvbfndml/sd8qbaq7mdfgn7zfxwude</latexit> <latexit sha_base6="fsafwibx35mrxoizlxruicyakko=">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</latexit> <latexit sha_base6="fsafwibx35mrxoizlxruicyakko=">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</latexit> <latexit sha_base6="fsafwibx35mrxoizlxruicyakko=">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</latexit> PARAMETER ESTIMATION LOG LIKELIHOOD Sum over frequency and depth now. (In the past we re-ran sampling for each frequency) ln p({ĥ, ˆv} ~ )= X f X z hĥ(f,z) rh (f,z; )i ~ H (f,z) + h ˆv(f,z) r V (f,z; ) ~ i V (f,z) C A

12 PARAMETER ESTIMATION PRIOR DISTRIBUTIONS Use Gaussian priors on each parameter informed by: Victor s paper ( a and c ) our data ( N vh ) other measurements (velocity dispersion) (actual values shown in results in a few slides)

13 PARAMETER ESTIMATION 3 FIT RESULTS Amplitude f =. Hz R recovery Z recovery z data r data f =.3 Hz f =. Hz f =.5 Hz f =.6 Hz f =.7 Hz f =.8 Hz f =.9 Hz f =. Hz f =. Hz Depths [m]

14 PARAMETER ESTIMATION PRIOR/POSTERIOR COMPARISON. c Prior Posterior. c. a a. a 3. a N vh.. v slope v intercept

15 <latexit sha_base6="b9ozuioky73gy7fasr7rtyh5=">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</latexit> <latexit sha_base6="b9ozuioky73gy7fasr7rtyh5=">aaadxhicdvjlj9mwehythktdehijaifcdnkebrpbwsixavujlq7ulnfjuueaf7vruufir3odxmiltcwh3l+xyynjcpiyex/tnr9fu379w9uwfcf/dwepu6zmlkrwcshnnoxfhuswoerzteyyzlc5zyqjy3yzxr+t65dbxkwupv/klmelhkztabvriievnhz++sfbrkpsvjehfclrauyposthengzzfmrzsmo8z+pwyiowbvifqut7hr+pjha6npa7gpmda+8evg8wcmvjpviqhkacvtnod7aqdq8wjdaupircjxjid7xqojwnhta/ci5agpuzo/p+skp8vktsgkbbdejtug3b6bqmc7dq9w6djfsmevkkomtzptjegowdqppla8dg7xhy/wohsegljcku7qcwqo9baxs3txnuqz9lln6cmujybdst6353pogkw65gwmuag+mhvqzb9e/zgirsftsmagxt3aufyxhmqixqwy/ecwn9jqsrzcfa5elmrmccvzbwsw5groyjwlmyyhysjelskhcqczebcbnwj/9vmxdynv7aivjcspsqrqsinmvmhdtlipoqix3bdki5jvpbuxgqbewysyf+n5v+dc3tgwut/dnvnb9pnkbn6dl6hszkoxpau3rdfhttbbwcur/l6pdaexcqpws5tdct6998kjp/k</latexit> <latexit sha_base6="b9ozuioky73gy7fasr7rtyh5=">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</latexit> <latexit sha_base6="b9ozuioky73gy7fasr7rtyh5=">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</latexit> RESULTS RESULTS Parameter Mean Error Prior Mean Prior Error c c a a a a N vh v slope v intercept

16 PARAMETER ESTIMATION 6 SOME COMMENTS Making priors larger results in some bi-modal results Not surprising (Daniel has seen something similar) Velocity dispersion curve makes sense Would like to add a better one (maybe 3 parameters?) In the end, I think the MCMC is probably overkill Unless there is a physical model associated with these parameters having specific values, I think from an empirical standpoint it s simpler to state that the space is very degenerate and what we quote are simply effective parameters (continued )

17 PARAMETER ESTIMATION SOME COMMENTS If people are interested in testing/including more models, I d be happy to run the MCMC with that model I can also share the final data points if people are interested.

18 CONCLUSIONS 8 CONCLUSIONS R-WAVE PE What do we want the focus of the paper to be? Separate call? Do we let measurements speak for themselves and include a set of biexponential fit parameters? Would we like to look at some physical models? If so, which ones? I can start putting text into paper. Apologies for not doing that sooner.

19 EXTRAS 9 EXTRAS OTHER DATA METHODS: could use each data point when sampling takes longer. errors would be from pre-event data. need to propagate error in normalization as well. becomes messy, but infrastructure currently exists. could add model for phase estimate distribution of radial to vertical phase on surface use this to generate a likelihood for R-wave phase at depth

qualitative fits were similar for eigenfunctions; below are results

20 VELOCITIES REDOING THIS ANALYSIS WITH A POW Comparison of velocities powerlaw velocity dispersion used instead of linear qualitative fits were similar for eigenfunctions; below are results from Daniel, Michael and myself for the different velocity measurements we ve done.

21 SEISMIC RADIOMETER APPLYING EIGENFUNCTION TO SEISMIC RADIOMETER We can apply this to the radiometer all maps show propagation direction Microseism measurements from Michael/Jan [I used ~ hours instead of full day to speed things up] Noisy day consistent with R-waves Quiet day mixed-wave content.5 Hz source Future average coherences for mine blasts from roughly same direction Using injections, I ve found that amplitude recoveries can be suspect, but direction information (even for multiple injected sources) is generally reliable. I m still checking the units. There s a chance I m missing a (/( * pi * f))^ in all of these!

22 RADIOMETER RUNS MICROSEISM (NOISY DAY) Indicates wave propagating in westward direction 6 Power [m ] 5 Histogram of pixels 6 S median( S )

23 6 6 5 S.5..5 median( S ) 6 6 Histogram of pixels 6 Histogram of pixels 6.5 S median( S ) P/S/R -WAVES NOISY DAY vr=3.5 km/s, vp = 7km/s, vs=5km/s..5 S median( S ) Power [m] Power [m]. 6 S median( S ) Histogram of pixels 6 Histogram of pixels Power [m] Power [m]

24 TEXT 5 Histogram of pixels Histogram of pixels 5 5. S.5 S median( S ) median( S ) 5 Histogram of pixels 5 Histogram of pixels 5 Power [m] Power [m] 5 Power [m] 5 Power [m] 5 S median( S ) P/S/R -WAVES QUIET DAY vr=3.5 km/s, vp = 7km/s, vs=5km/s 5 S median( S )

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sha_base6="rmfepljpfn6hhygwevflqdc7l=">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</latexit> MICROSEISM MAP POWER COMPARISONS NOISY DAY Wave type Total map power [m ] R.9 P.59 3 S h. 3 S v Total Body. QUIET DAY Wave type Total map power [m ] R 9.93 P 9.3 S h 5.3 S v.6 3 Body waves.7 3

26 7 3 3 Histogram of pixels Histogram of pixels S.5 S median( S ) median( S ) 7 Histogram of pixels Histogram of pixels Power [m] 3 5 S median( S ).5 HZ SOURCE vr =.8 km/s, vp = 6 km/s, vs = 3.5km/s 5 S median( S ) 5 Power [m] Power [m] 7 Power [m]

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28 CONCLUSIONS CONCLUSIONS Hoping to run on a few more interesting frequencies Maybe convert these into NN measurements Try MCMC sampling, which could naturally give uncertainties.

PS User Guide Series Utility

PS User Guide Series Utility PS User Guide Series 2015 Utility Prepared By Choon B. Park, Ph.D. January 2015 Table of Contents Page 1. Overview 2 2. Format SEG-2 Files 5 3. Format TEXT data 7 4. Make Common Seismic Gathers 9 5. Make