SEISMIC FACIES CHARACTERIZATION BY SCALE ANALYSIS

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Goal:¯ Delineate and characterize major reflectors.¯ Develop a common language for lithologic boundaries:seismic ´µ well-dataMeans:¯ Generalize reflector models to capture scaling/sharpness.¯ Estimate the scaling/sharpness.Results:¯ Robust attribute.¯ Sharpness adjusted reconstruction and correction for AVO.¯ Stratigraphical attribute for lithologic boundaries.

Problems¯ seismic amplitudes are difficult to control¯ simplified reflector models miss local texture¯ no common languagegeophysicists ´µ geologistsOpportunities¯ define scale attribute¯ focus on local aspects (boundaries)¯ delineate major singularities

Example4000well-log profileÔ Ñ× ½ ℄30002000100000 1000 2000 3000 4000

ComplexityWell-data are multifractal!Upper sedimentary variability¯ scales different everywhere, i.e. ´Þ · ¡µ ´Þµ ¡ «´Þµ¯ is singular when « ½.¯ singularities are accumulatedIdentify the major singularities!

Local maxima1.5´Üµ10.50−1 −0.8 −0.6 −0.4 −0.2 0 ´µ 0.2 0.4 0.6 0.8 Ü 11.522.5ÐÓ 33.54−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1´µÜ8 ÐÓ WTMML765431.5 2 2.5 3 3.5ÐÓ 2 3 4 2 3 4 2 3 4ÐÓ ÐÓ ÐÓ ´µ

Observed complexity suggestsGeneralized transition¯ generalization of jumps to fractional order onsets «·´Þµ ¸ ¼Þ «´«·½µÞ ¼Þ ¼ « ´Þµ ¸¼Þ «´«·½µÞ ¼Þ ¼¯ allows for a variation of the order/sharpness of the transitions.µ capture local scaling/complexity!

Generalized transitions« ¼Ricker « ¾ ¼ ½℄ Conv. with Ricker20202020404040406060606080808080Þ Ñ℄1001001001001201201201201401401401401601601601601801801801802000 5102000 1 22000 5 102000 5 10

Generalized transitions10−10.1−0.1 010−10.1−0.1 0discontinuity causal gen. trans. anti-causal trans.10550020 40 60 20 40 60 20 40 6020 4020 40 6020 400.1−0.1 00−5−100.1−0.1 020 4020 40 6020 400.1−0.1 00−50.1−0.1 020 4020 40 6020 40

Scaling and seismic reflectivityα=0.001α=0.112α=0.223α=0.334α=0.44550505050501001001001001001501501501501502000 5α=0.5562000 5α=0.6672000 5α=0.7782000 5α=0.8892000 5α=150505050501001001001001001501501501501502002002002002000 50 50 50 50 5Reflectors scale differently for varying order!

Multiscale analysis¯ follow extrema.Ï ´ Þµ ¸ ÅÅÞ Å ´ £ µ´Þµ¯ find order of magnitudeÏ ´ Þµ « as ¼Problem:Seismic data lives on “one” scale!

Post-stack reflectivitygeneralized transitions00stacked Ê ÔÔ 0100100ÐÓÊÔÔ−1−2−3−41 2 3ÐÓ 2002000ÞÑ℄300ÞÑ℄300ÐÓÊÔÔ−1−2−3400400−41 2 3ÐÓ 0500500ÐÓÊÔÔ−1−2−3−1 0 1¡Ô2 4 6 8 10 12 14trace −41 2 3ÐÓ Singularities are “reconstructed” by migration and stacking!

However,Ê ÔÔ´Ô Þµ ´µ ϡ״ ÔÔ´Ôµ ÞµandstackÊ ´Þµ ´µ Ï ½ Ï¡ ×´Þµ¯ stacked reflectivity partly reconstructs the singular part of themedium.¯ reduces noise.Reconstruction remains essentially bandwidth limited!

Monoscale analysisthe methodÏ ¬ ´ ܵ ¸ ¬ ¬1. Find local maxima at one scale.Ü ¬ ´ £ µ´Üµ2. Use maxima onsets to find « at a fixed scale¯ for « ¼ look for min. « for which loc. max. appears,«´ ½ Ü ½ µ Ò Ü Ï ¬ ´ ½ Ü ½ µ ¼¬¯ for « ¼ look for max. « for which loc. max. disappears,«´ ½ Ü ½ µ ×ÙÔ Ü Ï ¬ ´ ½ Ü ½ µ ¼¬

Reconstructionoriginal300020001000200−20200 400 600 800 1000 1200reflectivity200 400 600 800 1000 1200attribute0.5 1 0200 400 600 800 1000 12001reconstructed0.50200 400 600 800 1000 1200

ReconstructionFor each attribute construct the pseudo well:¡ ´Þµ ¡ « ½´Þ Þ µÞ¯ deconvolves¯ does not resolve the smooth part¯ integrated with Zoeppritz inversion

Well example0C pwell−log0Well−log fixed scale attribute analysis2.520020024004001.5600600z [m]8008001100010000.512001200014000 0.5 114000 0.5 1 1.5 2 2.5−0.5

What is it aiming for .....?for the mediumdifferent types of edges α=−0.5−2.7Convolution with Ricker wavelet20202.540402606080801.510010011201201401400.516016001801802002 4 6 8 10 12 142005 10 15−0.5

Reconstruction15 x 106 acoustic impedance well dataζ(x)10501500 1000 1500 2000 2500 3000depth [m]Reconstructed acoustic impedanceζ(x)0.501500 1000 1500 2000 2500 3000depth [m]spatial reflectivity0.5R(x)0−0.5−1500 1000 1500 2000 2500depth [m]

Migration examplemobil data0Selection of the mobil post−stack migrated datasetx 10 840.2320.41time [s]0.60−10.8−21−31.20 5000 10000 15000lateral direction [m]−4

Migration examplemobil data0Fixed scale attribute for post−stack migrated data0.50.200.4−0.5time [s]0.6−1−1.50.8−21−2.5−31.2 −3.50 5000 10000 15000lateral direction [m]

Migration examplemobil data0Selection of reconstructed post−stack migrated dataset0.20.10.40.050.600.8−0.051−0.11.20 5000 10000 15000lateral direction [m]

Well and seismic tie¯ Generate a family of wavelets: ¬ ´Øµ ½ ¬´ Ø µ with ¬´Øµ ¬ ¬Ø ¬ ´Øµ¯ minimize Ê ÛÐÐ Ê ×× Õ whereÊ ÛÐдص ´Ö ÑÓ £ ¬ µ´Øµwith Ö ÑӴص modelled with layercode using the well.¬ can be used in the reconstruction.¡ ´Þµ ¡ « ·¬ ½´Þ Þ µÞ

Wavelet estimationMigrated tracePressure50−50 0.2 0.4 0.6 0.8 1Modelled tracePressure50−50 0.2 0.4 0.6 0.8 1Tie50−50 0.2 0.4 0.6 0.8 1time ×℄Estimated waveletWaveletModelled versus Measured11000.10−0.10 0.1 0.2 0.3 0.4time ×℄0.500 100 200 300 Ö× ½ ℄5000 100 200 300 Ö× ½ ℄

Tie1.4time migrated data plus tie1.51.61.71.8time ×℄1.922.12.22.32.40 10 20 30 40 50trace

Tie1.4Attribute of seismic and tie01.6−0.5−11.8−1.5ØÑ×℄2−2−2.52.2−32.4−3.58.6 8.65 8.7 8.75 8.8 8.85 8.9 8.95ÜÑ℄x 10 4−4

1.4AttributeAttribute of seismic and tiex 10 831.621.81ØÑ×℄202.2−1−22.48.6 8.65 8.7 8.75 8.8 8.85 8.9 8.95ÜÑ℄x 10 4−3

1.4AttributeAttribute of seismic and tie01.51.61.7−0.5−11.8−1.5ØÑ×℄1.92−22.1−2.52.22.32.4−3−3.58.58 8.6 8.62 8.64 8.66 8.68ÜÑ℄x 10 4−4

depth Ñ℄depth Ñ℄depth Ñ℄050100050100050100fining upwards sequence0 1 2 Ôblocky0 1 2 Ôcoarsening upwards0 1 2 ÔÊÊÊFaciesfining upwards210−1−21 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3time ×℄blocky210−1−21 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3time ×℄coarsening upwards0.10.050−0.05−0.11 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3time ×℄

Conclusions and Future plansThe proposed method captures a complementary quantity which¯ is simple and measures the sharpness of edges and reflectors.¯ characterizes the local complexity/texture and frequencycharacteristics¯ is relevant to quantitative geology, lithology and reservoir.¯ is independent of the amplitudes but depends on the variations.¯ is “untouched” by migration/imaging and not dependent onpointwise amplitudes.It is a potential candidate for a common language between well,seismic and reservoir data on the level of (local) texture.

ONLY variations no big boomer!