8/9/2019 The Unreasonable Success of Reflection Seismology

1/3

16

Thm unrmaronabls8UCCrr88 of

rrflmction mmimmoloqyBy FRANKLYN K. LEVIN

Senior Research Scien islExxon Production Research Co.Houston, Texas

T e Nobel Laureate, Eugene Wigner, has often re-marked on the unreasonable successof mathematics inphysics. Why, he has asked, should a discipline basedon consistency of man-m ade rules be so successful indescribing phenomena of the real world? A questionthat intrigues and w orries one of this centurys mo steminent scientists s not one I shall presume to add ress.However, there are shallow asp ects of P rofessorWigners deep inquiry that concern those of us involvedwith developing seismic techniques for geop hysical ex-ploration. In view of the known co mplex ity of real earthsections, why are the simple methods of explorationseismologistsso success ful n p icturing wha t lies beneathour feet?

T he question is not as trivial as it m ust seem to read ersof The Leading Edge. Before reflections were first re-cord ed in the field, m ore than one well-known physicistwas convinced there w as no chance of detectingreflected energy at all. Succ ess s a fine argum ent; signaldetection w as established. Signal process ing and inter-pretation-the path that leads to the depiction of thesubsurface as a geologist sees he subsurface-becameimportant. It is the succe ssof processin g and interpre-tation b ut m ostly processing that w ill co ncern us here.For the first 30 years of reflection seismology mostpractitioners thought of simple subsurfaces and raystraversing those subsurfaces. There were exceptions ofcourse-Frank Riebers Sonograph processedcompletewaveforms and an occasional paper b ased on wavefrontconsiderations was published, but those who were ex-tracting travel times from field record s usually thoug htof energy traveling as rays through homogeneousmaterial, impinging on a plane interface, and returning

to a geophone on the surface.

T hose few corrections that w ere applied to d ata we reray methods. Static corrections assumed rays delayed byamounts that varied with the thickness of the weatheredmaterial at the receiving station. Normal moveout cor-rections assum edrays whose travel times plotted againstsource-to-receiver separations gave hyperbolas.Correction forms for wells shot with o ffset sourceswereset up to handle straight ray paths. Shear waves were ig-nored.Logging, which matured along with reflection seis-mology, showed real earth sections are bedded on scalesas fine as a sheet of paper and as gross as a one-storybuilding. Working in offices in small towns and campsall over the world, geophysicistsknew the real earth wascomplicated but nonetheless were content with an im-aginary earth hom ogeneous down to a few reflectingplanes with a weathered zone to be removed beforemapping began.W ere those interpreting reflection d ata stupid or stub-born? They were neither. Readers of this paper, manyof whom sit down before a computer terminal as theybegin their days wor k, will h ave difficulty conceiving ofa time when data reached interpreters as 12 wiggly traceson long strips of photographic paper, when reflectiontimes were counted off and picks marked by hand, whendata correction meant substituting into equations eval-uated with the aid of tables, logarithms, or hand-cranked calculators.Frequency analysis, perhaps by repeated tracing of awaveform as counters rotated on a sphere,was too labor-ious to be routine. We need not ask why early inter-preters of seismic data assumed simple earth mo dels

GEOPHYSICS: THE LEADING EDGE OF EXPLORATION DECEMBEK 1984

8/9/2019 The Unreasonable Success of Reflection Seismology

2/3

traversedby rays. The ans wer s obvious: nterpretersdid what waspracticalwith the tools available o them.W e should skdifferent questions why did the meth-odsdeveloped y the geophysicalioneers,methods asedon mo dels hat bore only a faint resemblanceo earthsectionsound by logging,work so well? Why did suchobviously rudeapproximationso realityyield map s hatled to reflectionseismology s ecomin ghe most mpor-tant tool of a petroleu m xploratio nist? hy weren t thegrosslyncorrectmodels ong ago ossednto the dustbinof o utmoded echnology nsteadof retainedas he basisof popu lar processesoutinely applied o s eismic ata?

Why did the methods developed bythe geophysical pioneers, methodsbased on models that bore only a faintresemblance o earth sections ound bylogging, work so w ell?1 offer some superficial answ ers.1 also await re-joinders and com ments rom readersmore skilled intheory than I or with deeper physical nsight than Ipossess. eismicwaveleng ths re long, tens of meterslong. As a result, seismic pulses integrate across,average crosshe rapid changes eenby logging ondes.Inhomo geneities mall compa redwith the extent n theearth of a seismic u lsehardly affect the energypassingthem.

I n addition, if the earth section reasonablycan berepresented s consisting f bedsseparated y horizon-tal interfaces, and if source-to-receiver separationsarent large, Dixs 1955 pap er sho wed hat inde edpro-per averaging of velocities and thicknesses ets usreplace he m aterial above a reflectingplane by hom o-geneousmaterial. The resulting ime -distance urve willbe hyperbolic.A poor approximation o reality you say?Certainly apoor approximationbut one good enough o let rapidvelocity analysisand common m idpoint stacking beamon g the m ost powerful of the p rocesses pplied toseismic ata. In detail the model often fails; time-dis-tancedata scatter nd fitting a hyp erbola o them can bea trium ph of faith over sense.Amplitudesdecay morerapidly than geometric preading redicts r vary errati-cally. Still, largestructural rapsare magedwell enoughfor thosewho drill wellseven houghstratigraphicrapsmay be missed.And we ca n justify static corrections,sincewaves, raveling much more slowly n weatheredmaterial than in the rock below , bendnearly vertically.Be fore continuing, et me wiggleon m y hook a b it. Ivebeenusing xpressionso m precise s o shocka carefulreader, expressions uchas reasonablyrepresented,poor approxima tion, good enough , and the like.The list will g row, for when we deal with earth sections,we are involvedwith systemshat range rom thosewell

described y the simplemodelsof early geoph ysicistsosystemspoorly approximated by tho se mod els butsystems till yielding data from which an experiencedinterpretercan deducestructure.Quantitativeconsider-ations, desirableas they are in tech nicalpapers,herewould cloud rather than clarify the discu ssion.The field and processingechniques have touchedupon are memories o someof us and tales old by oldmen o younger eaders f The Leading Edge. Today wehave massive m ountsof data processed ith the mostpowerful com puters that the market offers. Wh atmodelsunderlie he processesoutinely applied n com-puter centers?As mentionedbefore, unlike the wickedwizard n thestory of Alad din , we don t alway soffer new lamp s orold. Static corrections till assum e nergypassing er-tically through he weathering, r if not vertically,at anangle not far from vertical. For com mon midpo intstacking and velocity analysis rays may be tracedthrough airly complexsubsu rfaces, ubsurfaces h erenot a ll interfaces re horizontal planes,but its not un -comm on o fall backon subsurfaceseophysicistsctiveyears ago would recognize.Gaussian eamsoffer oneway to add am plitude information to ray tracing.However, many data processo rs re contentwith planewave reflection coefficients, perhapscoefficients forreflection for plan e nte rfacesseparatingwo solids.When producingsyntheticseismogramsor beddingas detailed as that shownby logs, geophys icistsonteven ray trace. They assu me lanewavesnormally nci-dent on bedsseparated y interfacesas smoothas mir-rors. M ultiple reflectionsmay or m ay not be included,depend ing n an interpreters knowledg e, rejudices, rperhapswhat he learned rom a fortunecookie. Clearly,the foundations or someprocessesommonlyapplied

Unlike the wicked w izard in the storyof Aladdin, we don always offer newlamps for old. Static corrections stillassume energy passing verticallythrough the weathering, or if not ver-tically, at an angle not far from vertical.to seism ic ata are shaky; he modelson which he pro-cesses re based esemble eal earth sections nly in agrosssense.Yet, applicationof the processesroducesdata sections geologists use and use successfully.Wigne rs unreason able successof mathem atics inphysics s matched by the unreason ablesuccess fassumedmode ls n explorationgeophysics.H avehere, then, been no real advancesn the modelsthat b uttress outine seismicdata processing? greatstep forward was taken when g eophysicists egan tomigratedata with w ave equationmethods.Wave equa-tions describehe way elasticwaves ravel n ideal fluidsand solids.Togetherwith initial conditions hat give hestateof the systembefore the sourcewasactivatedan d

GEOPHYSICS: THE LEADING EDGE OF EXPLORATION DECEMBER 1984 17

8/9/2019 The Unreasonable Success of Reflection Seismology

3/3

boundary conditions hat specify the system n as greatdetail as we wish, solutionsof the wave equation shouldreproduce preciselywha t we record in the field. Shouldreproduce precisely, but don t reproducepreciselywhatwe record. Partly we fail becauseof finite resources.Even today there is no comp uter large enough to rou-tinely apply processes ased on the w ave equation forsolids o data from a three-dimensionalseismicsurveyover a complex subsurface. Partly we fail becauseweuse too simple an e quation, an eq uation that ign oresorintroduces incorrectly loss mech anisms, an equationthat doesnt handle correctly the properties of weath-ered material. And partly we fail because we reallycant presc ribeboundary con ditions or treat deviationsfrom the material properties of ideal fluids and so lids.If we were able to specify our subsurface n d etail andknew the physicalpropertiesof every chunk of rock, w ewou ldnt have needed the seism ic survey. Becausewehave limited resources, use equations that are overlysimple, and lack complete knowledgeof earth sections,even wave equation processesmply modelsdiffering inmajor respects rom reality.Those of us who remember seismicdata of 30 yearsago marvel at the beauty of todays fully m igrated, hree-dimensional data sections and time slices. But mar-velous as todays processing is, the processing cannever be perfect, for it is basedon imperfect models. Byany reason able standa rd, the successof reflectionseismology s remarkable but the successs not com-pletely reasonable. C

Franklyn K. Levin obtained his BS in physics rom PurdueUniversityn 1943and hb PhD from the University f W,%consinin 1949.He then oined Carter Oil, now Exxon, wherehe holdsthe highest echnical ositionas senior esearch cienttit.Levinsnumerous papers in Geophysics erited two co-authoredBest PaperAwards.n 1976 he wasSECs Distinguishedec-turer.As oneof theSocietysmostactivemembers, e hasservedon various committees and has been representative at theAmerican Association or the Advancement of Science,andspecialeditor of the SEC Reprint Series,since 1975 and 1977,respectively. n SEC Honorary Membersince1978, Levin willreceive his years Reginald Fessenden ward.

18 GEOPHYSICS: THE LEADING EDGE OF EXPLORATION DECEMBER 1984