We P03 02 Locating Scatterers by Non-physical Scattered Waves Obtained by Seismic Interferometry

Transcription

1 We P03 0 Locatg Scatterers by No-physcal Scattered Waves Obtaed by Sesmc Iterferometry U. Harmakaya* (Istabul Techcal Uversty), A. Kasllar (Istabul Techcal Uversty), J. Thorbecke (Delft Uversty of Techology), K. Wapeaar (Delft Uversty of Techology) & D. Dragaov (Delft Uversty of Techology) SUMMARY The vestgato ad detecto of ear-surface structures (such as cavtes, caves, skholes, tuels, meshafts, bured objects, archeologcal rus, water reservor, etc.) s mportat to mtgate geo- ad evrometal hazards. I a former study, we suggested a method based o actve-source sesmc terferometry for locatg the scatterers ad we showed the applcablty of the method a smple model. I our method, we use oly oe source at the surface ad o-physcal scattered waves retreved by sesmc terferometry to estmate the locato of the scatterer. I ths paper, we show the effectveess of the method case of lateral varatos. We use both scattered body ad surface waves to estmate the locato of a corer dffractor ad a scatterer, respectvely, ad we obta very good estmatos. The method s promsg for ear-surface sesmc feld applcatos.

2 Itroducto We use o-physcal scattered body ad surface waves retreved by sesmc terferometry (SI) to estmate the locato of a corer dffractor ad a ear-surface scatterer (such as cavty, cave, tuel, meshaft, bured object, etc.), respectvely. For our method we use actve source SI ad oly oe source at the surface (Harmakaya et al., 01). As we use oly oe source, t s very ulkely that the source s at the statoary pot for retrevg physcal scattered waves. To obta the complete Gree s fucto betwee the recevers whose recorded resposes we cross-correlate, the boudary sources (prmary or secodary) eed to effectvely eclose these recevers (Wapeaar ad Fokkema, 006). Whe the recevers are ot equally llumated from all drectos by the boudary sources, o-physcal arrvals (ghosts) wll appear the SI result (Seder et al., 006; Hallday ad Curts, 009; Hallday et al., 010). Because SI effectvely redatums sources from places away from the scatterers to the target area, the uwated extra effects, due to propagato from the actve-source locatos through possbly laterally chagg medum to the recevers close to the target area, are elmated ad o-physcal ghost scattered waves are retreved. We perform D elastc ftedfferece modellg (Thorbecke ad Dragaov, 011) ad show the effectveess of our method the presece of lateral homogeetes. We obta very good estmatos of the subsurface locato of a corer dffractor ad a scatterer by usg o-physcal scattered S-waves ad Raylegh waves, respectvely. Method I ths study, we use o-physcal scattered body ad surface waves, obtaed from SI, ad verso to estmate the locato of a dffractor or scatterer (Harmakaya et al., 01). SI s appled to the scattered wavefeld obtaed from the sesmc records of the orgal geometry by usg oly oe VS source ad by cross-correlatg the referece trace d (the trace at the vrtual-source posto) wth the rest of the traces, d, whch are preset o the sesmc record. Ths relato s VS d t d t C d d VS. (1) Applcato of Eq. (1) wll elmate the commo travel-path from the source to the scatterer ad wll result the retreval of a o-physcal ghost scattered body or surface waves. To estmate the locato of the dffractor or scatterer, the followg theoretcal ghost travel-tme relato s used, t 1 V r r x 1/ x z z x vs x z vs z. () The relato gves the retreved ghost traveltmes betwee the vrtual source, the scatterer ad the recevers. I Eq. (), V s the wave velocty, s the dex for the recever umbers, vs deote the vrtual source ad x ad z are the locatos of the scatterer the horzotal ad vertcal drecto, respectvely. To fd the locato of the object, the traveltme relato (Eq. ) ad the traveltmes obtaed for each vrtual source locato are used the verso. The olear problem s solved teratvely. The system of equatos for the forward problem s deoted as dgm. The dfferece betwee the observed t obs (retreved), ad the calculated t calc ghost scattered data s deoted by Δd tobs t, the calc ukow model parameters - the x ad z locato of the object - are deoted by the vector m, whle the Jacoba matrx s represeted by G. The damped least-squares soluto of the verse problem s gve terms of Sgular Value Decomposto (SVD) as 1 T mvλ I U d, (3) where V,Λ,U,I ad are the model-space egevectors, the dagoal matrx cotag the egevalues, the data-space egevectors, the detty matrx ad the dampg parameter, respectvely. 1/

3 Cosderg Eq. (3), the verse problem s solved to fd the locato of the object. The ucertates of the estmatos are calculated by the model covarace matrx gve as cov where σ s 1 T m VΛ Λ I V 1 (4) tobs tcalc. m 1 Here, s the umber of observed data, ad m s the umber of model parameters (here m = ). I the followg examples, the ucertates of the estmated parameters are calculated wth 95 % cofdece (1.96σ) ad plotted wth estmated model parametres for each selected vrtual source. Estmato of the Locato of the Objects by the Iterferometrc Ghosts of the Scattered Waves To show the effectveess of the method the presece of lateral homogeetes, the geometry ad the medum parameters of the model gve Fgure 1 are cosdered. (5) Fgure 1 Schematc vew of the scale model (left): the source (star), recevers (tragles) ad scatterer (grey square). A represets the corer of the low-velocty zoe; B1 ad B represet the two terfaces betwee the source ad the recevers. M1 ad M represet the meda havg dfferet veloctes. The modellg parameters are gve the table (rght). The D fte dfferece modellg program of Thorbecke ad Dragaov (011) s used ad the wavefeld show Fgure a s calculated. It should be oted that the startg pot of the coordate system s arbtrarly chose ad t s at the posto of the actual source. Here, we try to estmate both the locato of the scatterer (Fgure 1 grey square) from scattered surface waves (Fgure a Rsc), ad the locato of the dffractor (A Fgure 1) from scattered S-wave (A Fgure a). To obta the scattered wavefeld, a f-k flter s used, whch removed most of the drect Raylegh waves ad drect ad refracted P-waves (Fgure b). SI s appled to the extracted scattered waves by usg Eq (1). I Fgure c-e the retreved ghost scattered surface waves for vrtual-source locatos at recevers 6, 46 ad 55 (9, 49 ad 58 m) are gve, respectvely. The ghost traveltmes are pcked from the maxmum ampltude of the retreved ghost scattered surface waves (red curves o Fgure ce). To fd the locato of the scatterer, the traveltme relato (Eq. ) ad the traveltmes obtaed for each vrtual-source locato (red curves Fgure c-e) are used the verso (Eq. 3). The veloctes are cosdered as kow parameters the verso ad they are estmated from the shot records. The observed ad the calculated traveltmes of the ghost scattered surface waves are plotted Fgure 3a for each vrtual source locato. The tal ad the updated model parameters for each terato are gve Fgure 3b. After eght teratos, the model parameters - the horzotal ad vertcal locato of the scatterer - get closer to the actual values. The ucertates the model parameters are calculated by Eqs. (4-5) ad the results are plotted Fgure 3c for each vrtual-source M1 M Backgrou d Scattere r ρ V p [m/s] V s [m/s] Surface-wave velocty 360 Domat frequecy [Hz] 00 Domat wavelegth [m] 1.80

4 locato ad ther average values. The blue les Fgure 3c deote the mdpot, the upper ad lower bouds of the scatterer. The estmated locatos are wth the sze of the scatterer ad t ca be cocluded that the locato of the scatterer s well estmated. Fgure (a) Shot gather obtaed by fte-dfferece modellg. (b) The scattered wavefeld. (c), (d) ad (e): ghost scattered surface waves retreved by applyg SI to (b) for vrtual-source locatos at recevers 6, 46 ad 55 (9, 49 ad 58 m), respectvely. A: scattered S-wave ad Rsc:scattered Raylegh wave. Fgure 3 (a) Observed ad calculated travel tmes, related to the square scatterer Fgure 1, (b) estmated horzotal ad vertcal locatos of the scatterer for the vrtual sources 6 (blue, 9 m), 46 (brow, 49 m) ad 55 (red, 58 m). (c) Estmated model parameters ad ther 95% cofdece lmts, blue les show the actual mdpot ad the upper ad lower bouds of the scatterer. To fd the locato of the corer dffractor, the scattered S-wave (A Fgure a) s used. The arrvals other tha the scattered S-wave are fltered ad muted out (due to lmted space, ot show here). The remag S-wave scattered feld s used the SI procedure descrbed before. For ths example the vrtual sources 6, 30 ad 34 (9, 33 ad 37 m) are cosdered. The best ft betwee the observed ad calculated traveltmes, the estmated model parameters for each terato ad ther ucertates are gve Fgure 4 a, b ad c, respectvely. It s observed that the locato of the dffractor s well estmated. Cocluso The method proposed for obtag the locato of a ear-surface scatterer by usg traveltmes of o-physcal (ghost) scattered body ad surface waves s appled to a laterally homogeeous model 75th EAGE Coferece & Exhbto corporatg SPE EUROPEC 013

5 to show the effectveess of the method. By cosderg oly oe surface source, the ghost traveltmes of scattered waves retreved from SI are used the verso to fd the locato of the scatterer. Very good estmato of the locato of the dffractor ad the scatterer s obtaed. Fgure 4 (a) Observed ad calculated travel tmes, related to the corer dffractor at A Fgure 1, (b) estmated horzotal ad vertcal locatos of the scatterer for the vrtual sources 6 (blue, 9 m), 30 (brow, 33 m) ad 34 (red, 37 m). (c) Estmated model parameters ad ther 95% cofdece lmts, blue le shows the actual posto of the corer dffractor. Ackowledgemets Ths work s supported by TUBITAK (The Scetfc ad Techologcal Research Coucl of Turkey) wth the project 110Y50 ttled Detectg Near-surface Scatterers by Iverse Scatterg ad Sesmc Iterferometry of Scattered Surface Waves. We gratefully ackowledge ths facal support. The research of D.D. s supported by the Dvso for Earth ad Lfe Sceces (ALW) wth facal ad from the Netherlads Orgazato for Scetfc Research (NWO). We also thak the Colorado School of Mes for provdg the Sesmc U*x (Cohe ad Stockwell, 01) package as ope source software. Refereces Cohe, J.K. ad Stockwell, Jr., J.W. [01] CWP/SU: Sesmc U*x Release No. 43: a ope source software package for sesmc research ad processg. Ceter for Wave Pheomea, Colorado School of Mes. Hallday, D.F. ad Curts, A. [009] Sesmc terferometry of scattered surface waves atteuatve meda. Geophys. J. It., 185, Hallday, D.F., Curts, A., Vermeer, P., Strobba, C., Glushcheko, A., va Mae, D.J. ad Robertsso, J.O.A. [010] Iterferometrc groud-roll removal: Atteuato of scattered surface waves sgle-sesor data. Geophyscs, 75(), A15-A5. Harmakaya, U., Kasllar, A., Thorbecke, J., Wapeaar K. ad Dragaov, D. [01] Estmatg the locato of scatterers by sesmc terferometry of scattered surface waves. Exteded Abstracts of the 74 st EAGE Meetg, Copehage, X008. Seder, R., Wapeaar, K. ad Larer, K. [006] Spurous multples sesmc terferometry of prmares. Geophyscs, 71, SI111-SI14. Thorbecke, J. ad Dragaov, D. [011] Fte-dfferece modelg expermets for sesmc terferometry. Geophyscs, 75, H1-H18. Wapeaar, K. ad Fokkema, J. [006] Gree s fucto represetatos for sesmc terferometry. Geophyscs, 71(4), SI33-SI46.