Unformatted text preview: GPHY 3423 Petroleum Geology and Geophysics Kurt J. Marfurt (University of Oklahoma) Inversion for Acoustic and Elastic Impedance 111 Inversion for Acoustic and Elastic Impedance
After this section you will be able to: Use inversion to integrate a userdefined earth model and synthetic seismograms to `best fit' the measured seismic data, Differentiate and ideally choose between relative, bandlimited, modeldriven, and geostatistical inversion algorithms Relate impedance inversion to deconvolution, and Use elastic inversion effectively as a lithologic indicator. 112 The Acoustic Impedance Attribute
Matrix : Vm, m Porosity Fluid : Vf, f Acoustic impedance = PVelocity x Density
A.I. of a rock is a function of :  Matrix (lithology),  porosity,  the fluid content  Pore pressure  and maybe the shape of the pores! A.I. 1 A.I. 2 A.I. 3 A.I. 4 113 Modeldriven AI inversion is performed in the time domain on post stack migrated data. (Veekan et al, 2002) Hierarchy of acoustic impedance attributes
None (0) Few (12) Near/far angle stacks Normal impedance and scaled Poisson's ratio Fluid factor=RPkRS. Increasing resolution Acoustic/elastic impedance inversion Lambdamurho inversion Neural network well correlation Simultaneous inversion Geostatistical Inversion Regional Prospect Development Characterizatio n Number of wells More (510) Many ( > 10) 114 (Modified after Ross, 2002) Conversion of Reflectivity to Acoustic impedance Disadvantages of interpreting amplitudes
1. Advantages of using acoustic impedance
1. Represents a contrast between layers (relative measurement) Affected by thinbed tuning. Upwardfining and upward coarsening produce subtle amplitude anomalies. Contaminated by noise Not directly measured at the wells Directly represents layer properties such as porosity Removes phase rotations due to tuning, upward fining, and upward coarsening Constrained inversion suppresses noise inconsistent with model Measured at well locations Excellent parameter for geobody visualization 2. 2. 3. 3. 4. 4. 5. Limited value in constructing geobodies 5. 115 (Modified from Duboz et al. , 1998) Inversion for acoustic impedance (wedge model)
0.3 0.4 0.5 0.6 0.3 0.4 0.5 sidelobes! Time (s) `true impedance model' colored seismic synthetic sidelobes! Time (s) variable area seismic synthetic
0.6 0.0 0.1 0.2 0.3 0.4 0.5 Thickness (s) 0.6 0.7 inverted acoustic impedance
0.0 0.1 0.2 0.3 0.4 0.5 Thickness (s) 0.6 0.7 116 (Latimer et al., 2000) Inversion for acoustic impedance (ramp model)
0.0 Z (g/cm3ft/s) 20000 19000 0.1 18000 17000 16000 15000 Time (s) 0.2 14000 13000 0.05 Time (s) 0.3 0.00 +0.05 0.4 117 (Latimer et al., 2000) Impact of low and high frequencies on resolution
Better for calibration to wells! 1080 Hz 10500 Hz 080 Hz (Latimer et al., 2000) 118 Extending the seismic spectrum Amplitude Final inversion spectrum Model band Seismi c band 0 20 40 Frequency (Hz) 60 80 119 (Pendrel and van Riel,2000) Inversion: improvement of vertical resolution
0.95 0 Time (s) 1.00 0
c top i sm i Se Seis mi c bas e Seismic does not reveal reservoir thickening off the horst block Impedance inversion reveals both thickening and reservoir quality Increased resolution improves interpretation confidence 1.05 0 0.95 0 Time (s) 1.00 0 er Inv nt si o op 1.05 0 0. 00 0. 0 00 0.012 0. 4 31100 00 8 Inver s i on bas e Thickness (s) Seismic thickness Inversion thickness 31050 CDP no. 31000 1110 (http://www.eseis.com/Bulletin_PDF/epb300.pdf) Seismic Modeling and Inversion
Subsurface acoustic impedance
Forward Modeling Wavelet Seismic trace with
Seismic trace Wavelet Subsurface acoustic impedance Inversion with 1111 Nonuniqueness in impedance inversion
Seismic data are bandlimited Basically, any one of many 1ft resolution impedance models having the same average (over the distance of a seismic wavelet) can fit the seismic data. The low frequency trend is not measured at all. The interpreter can add any information he or she wishes. Seismic noise can be incorrectly converted to seismic impedance changes This nonuniqueness results in alternative inversion strategies: Favor models that are blocky (sparsespike inversion) Favor components of a usergenerated background model (modeldriven inversion) Examine all possible models that fit the data and userdefined constraints (geostatistical inversion)
1112 Hierarchy of Seismic Inversion
1. Inversion of normalincidence or poststack seismic data  Bandlimited impedance inversion  Sparsespike impedance inversion  Modelbased inversion Cellbased parameterization Stratigraphic parameterization Global optimization  Geostatistical inversion
2. Inversion of prestack seismic data  Sequential commonangle ("elastic") inversion  Simultaneous prestack inversion AVObased Waveequationbased
3. Hybrid inversion 1113 If the impedance profile is smoothly varying and the sampling is sufficiently fine,
Ri = Z i +1  Z i Z i +1 + Z i Impedance Inversion (trace integration implementation) can be approximated by
Ri Z i 2Zi 1 d ln Z i 2 dt ( ) By integrating, we obtain:
ln Z n = 2 R
i =0 n i Finally, we exponentiate to obtain: n 2 Z n = exp Ri i =0 1114 Red Fork horizon slices, Anadarko Basin, USA Bandlimited acoustic impedance Seismic amplitude
1115 (Suarez et al., 2008) Hierarchy of Seismic Inversion
1. Inversion of normalincidence or poststack seismic data  Bandlimited impedance inversion  Extending the bandwidth  Sparsespike impedance inversion  Modelbased inversion Cellbased parameterization Stratigraphic parameterization Global optimization  Geostatistical inversion
2. Inversion of prestack seismic data  Sequential commonangle ("elastic") inversion  Simultaneous prestack inversion AVObased Waveequationbased
3. Hybrid inversion 1116 Flowchart for extending the bandwidth of seismic inversion Migrated seismic data Density logs x Sonic logs Impedance logs Trace integration Bandlimited inversion + Broadband inversion Lowpass filter Lowfrequency model 1117 Bandlimited Inversion 1.0 Addition of low frequency velocity trend from migrationdriven velocity analysis and well logs to the mid frequency component obtained by inversion
2.0 3.0 1118 Images courtesy: ONGC, India Bandlimited Inversion Swan Hills carbonate, Alberta, Canada Porosity Synthethic sonic long (in transit time) generated using the `seislog' process.
1119 (Lindseth, 1979) Hierarchy of Seismic Inversion
1. Inversion of normalincidence or poststack seismic data  Relative acoustic impedance  Bandlimited impedance inversion  Sparsespike impedance inversion  Modelbased inversion Cellbased parameterization Stratigraphic parameterization Global optimization  Geostatistical inversion
2. Inversion of prestack seismic data  Sequential commonangle ("elastic") inversion  Simultaneous prestack inversion AVObased Waveequationbased
3. Hybrid inversion 1120 ModelBased Inversion
1. A geological (impedance) model is first built consistent with the seismic data. A synthetic trace is generated from the model and compared with the equivalent seismic trace. If the difference is small, the model trace is taken as the final solution. If the model trace is significantly different from the equivalent seismic trace, the impedance model is perturbed in terms of reflection time and impedance to yield lateral and temporal impedance changes. The process is repeated iteratively till the difference falls below a set threshold. 2. 3. 4. 1121 Inverse modeling technique
Initial model A.I Synthetic Seismic seismogram trace Residual trace Iteration 1 Iteration 2 Iteration 3
(Veekan et al, 2002) 1122 Time Modelbased inversion objective function
Misfit between modeled data, d(m), and measured data, d0 Minimize the squared error E = [d(m)  d 0 ] + [m  m 0 ] + [m  0]
1123 2 T 1 Cd [d(m)  d 0 ]
Misfit between new model and a priori model T 1 Cm [m  m 0 ] 1 Cm [m  0] T Misfit between smoothness of model and a model that is `perfectly smooth' Classical inversion Start Define initial a priori model, m0, Using horizon picks and AI logs Model seismic, d(m) Calculate d=d(m)d0 Does modeled seismic match measured data? no Output AI model, mi Output residuals d Generate objective function, E2(m) yes Perturb model to obtain E2/m Stop Solve for m Update mi=mi1+ m 1124 Local minimu mA
1 n 2 Objective fucntion, E2 Infeasible solutions Local minimum B Initial model Global minimu m Local minimum C Feasible solutions mj User constra int 1125 User constra int Infeasible solutions Local minimum A
2 6 pdf 8 7 (high T)5 4 3 1 Local minimum C Local minimum B Objective fucntion, E2 Infeasible solutions Initial model Global minimum Infeasible solutions Feasible solutions mj User constraint User constraint 1126 Local minimum A pdf (mid T) 37 1 5 8 4 6 2 Local minimum B Initial model Global minimum Infeasible solutions mj User constraint User constraint Local minimum C Objective fucntion, E2 Infeasible solutions Feasible solutions 1127 Local minimum A pdf (low8T) 7 41 2 5 3 6 Local minimum B Initial model Global minimum Infeasible solutions mj User constraint User constraint Local minimum C Objective fucntion, E2 Infeasible solutions Feasible solutions 1128 Start Define initial a prior model, m0, Using horizon picks and AI logs Decrease mutations or temperature Generate PDF Inversion using simulated annealing or genetic algorithms Choose a random value of mi Model seismic, d(m) Calculate d=d(m)d0 Generate objective function, E2(m) More random models? no Output AI model, mi Output residuals d yes Does modeled seismic match measured data? yes Stop no 1129 ModelBased inversion
Amplitude
D de ow lin nd ea ip tio n Up di High PImpedance (ft/sg/cm3) 28000 26000 24000 water 22000 gas 20000 p water
de lin ea tio n water gas gas Low gas gas 18000 Amplitude Pwave impedance Modelbased inversion discriminates between the gasbearing zones and the nongas zone.
1130
(Russell et al., 2006) Case study
Delineation of a chert deposit Central Basin Platform, west Texas 1131 Impedance inversion applied to a chert deposit 1032 1132 (Ruppel, 2001) Thickbedded chert Chert/carbonate Laminae Major Lithofacies (Good porosity) Brecciated Chert Carbonates 1133 (Fu et al., 2006) Thickbedded Chert, West Texas Spicultic Chert
Sponge Spicules 1134 (Ruppel and Barnaby, 2001) Type logs of WRE (Well "W")
Gamma Porosity
Thickbedded Chert Density Vp Impedance Thirtyone Laminated Chert Laminated chert BEGA
Carbonates BEGB
Laminated Chert BEGC
Thickbedded Chert Laminated Chert 1135 (Fu et al., 2006) Porosity vs. Lithology 0.300 0.250 0.200 Laminated Chert 0.150 & Limestone
0.100 0.050 0.000 Thickbedded Chert Samples 1136 (Fu et al., 2006) Grain Density vs. Lithology
2.75 2.70 2.65 2.60 2.55 2.50
) c / g ( y t s e D n i a r G Limestone Cherts 2.45 Lithofacies Samples
1137 (Fu et al., 2006) Pwave Impedance vs. Lithology
20.00 18.00 Pwave Impedance (km*g/s*cc) 16.00 12.00 10.00 8.00 6.00 4.00
CBS CBS CBS CBP CBS CBS CBBB CBS CB Thickbedded Chert Laminated Chert CLD LM Sample
Dry sample Water satuated 1138 (Fu et al., 2006) Limestone 14.00 Pwave Impedance vs. Porosity (Chert) Chert Impedance versus Porosity
17.00 15.00 Impedance (g*km/cc*s) 13.00 11.00 9.00 7.00 5.00 0% 10% y = 28.86x + 14.94 2 R = 0.9838 y = 27.851x + 15.088 2 R = 0.9826 y = 26.226x + 15.327 2 R = 0.9782 20% 30% Zpd Zpw Zpo Porosity 1139 (Fu et al., 2006) Impedance vs. Porosity Log data & Core measurements
18 17 16 15 14 13 12 11 10 9 8 Impedance (km/s*g/cc) Log data Core data phi>0.1 phi<=0.1 0 0.05 0.1 0.15 Porosity (fraction) 0.2 0.25 1140 (Fu et al., 2006) Typical Synthetic Seismogram (745er)
Marker Gamma Sonic T D RC Wavelet Syn. Seismic Thirtyone BEGC Frame 1141 (Fu et al., 2006) Crossplot Gamma Neutron logs to discriminate lithologies Depth (ft) Shale Thickbedded Chert Neutron Porisity (v/v) Gamma Ray (gAPI) 1142 (Fu et al., 2006) Conventional Seismic Data
X Y Z 300 m Thirtyone BEGC Frame 1143 (Fu et al., 2006) Initial Model for Impedance Inversion
Impedance (km/s*g/cm3) 17 16
1100 W X Y 300 m 15 14 13 Time (ms)
1200 11
Thirtyone 10 9 8 1300 BEGC High vertical resolution Low lateral resolution 1144 Smooth to < 8Hz (Fu et al., 2006) Impedance Inversion Results
W X Y
300 m Impedance (km/sec*g/cc) 17 16 1100 15 14 13 Time (ms)
1200 11
Thirtyone 10 9 1300 BEGC Lower vertical resolution Higher lateral resolution 1145 8 (Fu et al., 2006) Impedance Inversion Results
X Y Z 300 m
Impedance (km*g/s*cc) 17.8 16.6 15.4
Time (ms) 14.3 13.1 11.9 Thirtyone
BEGC Thirtyone 10.7 9.5 8.4 Frame 1146 (Fu et al., 2006) Impedance Inversion Results
A
300 m A' Impedance (km*g/s*cc) 17 16 15 14 13 Thirtyone 11
BEGC 10 9 8 Extract RMS Average Impedance in a 10ms window below BEGC
1147 Frame (Fu et al., 2006) RMS Average Impedance  10ms window below BEGC
High AI Low Artifact of faults Low AI High 1148 (Fu et al., 2006) Most Negative Curvature 3 km Horizon slice along BEGC
1149 Time Slice t = 1222ms
(Fu et al., 2006) Production vs. Curvature Time Slice Large fractures, poor wells!
1150 (Fu et al., 2006) Acoustic impedance calibration Pimpedance (g/cc*ft/s) 1151 Gamma ray (gAPI) (Latimer et al., 2000) Detection of geobodies
AI thresholds determined from calibration step 1152 (Latimer et al., 2000) Detection of geobodies
Geobody thresholds determined by volume of connectivity 1153 (Latimer et al., 2000) Geostatistical inversion
Seismic inversion combined with geostatistical data analysis and modeling is referred to as geostatistical inversion. Geostatistical analysis generates spatial and vertical statistics:
(1) Vertical variograms are generated from wellbore measurements Horizontal variograms are generated from acoustic impedance values taken from the starting impedance model. Such a model could be the impedance model generated by recursive inversion. Steps
(2)
1. 2. 3. 1154
4. Extraction of wavelet by comparing well log reflectivities with seismic traces at well locations. Calculation of synthetic well traces by convolving reflectivities with wavelets. Tying of wells to surrounding seismic tracescorrelation between synthetic and real traces are optimized (tolerance shift of 1 or 2 traces horizontally and 1 or 2 samples in time). Bring in statistical analysis in step 3. Classical Inversion (calculate expected value of AI) Geostatistical Conditional Simulation Geostatistical Inversion 1155 (Dubrule, 2003) 1156 (Dubrule, 2003) Start Geostatistical Inversion Pick an unoccupied grid point at random Use variograms from well data and all previously defined grid points to estimate mean and standard deviation Choose a random AI value that fits mean and standard deviation at current grid point. (local realization) Stop no yes More global realizations? Does seismic match measured data? yes Output AI global realization More grid points? Model seismic no no yes 1157 Geostatistical Inversion 1158 (Dubrule, 2003) Acoustic Impedance Seismic Seismic match improves as the number of local realizations increases! 1159 (Dubrule, 2003) Extending the seismic spectrum using geostatistical inversion
Background model Amplitude Seismic amplitude Geostatistical variogram model 0 50 100 150 Frequency (Hz) 200 250 1160 (Dubrule et al., 2003; Pendrel and van Riel, 2000) Results of geostatistical inversion
One realization Wells are honored by GI Mean Standard deviation Lateral variogram ensures lateral correlation between traces Standard deviation is zero at the wells 1161 (Lamy et al., 1999; Dubrule, 2003) Hierarchy of Seismic Inversion
1. Inversion of normalincidence or poststack seismic data  Relative acoustic impedance  Bandlimited impedance inversion  Sparsespike impedance inversion  Modelbased inversion Cellbased parameterization Stratigraphic parameterization Global optimization  Geostatistical inversion
2. Inversion of prestack seismic data
 Sequential commonangle ("elastic") inversion  Simultaneous prestack inversion AVObased Waveequationbased
3. Hybrid inversion 1162 Hierarchy of Seismic Inversion
1. Inversion of normalincidence or poststack seismic data  Relative acoustic impedance  Bandlimited impedance inversion  Sparsespike impedance inversion  Modelbased inversion Cellbased parameterization Stratigraphic parameterization Global optimization  Geostatistical inversion
2. Inversion of prestack seismic data  Sequential commonangle ("elastic") inversion  Simultaneous prestack inversion AVObased Waveequationbased
3. Hybrid inversion 1163 Sensitivity of finiteoffset data to shear waves Boundary conditions: Continuous displacement, u Continuous stresses, n
^ 1164 Offset (m) Common angle stacks Time (s) 1165 (Barklay et al., 2008) Elastic Impedance
AkiRichards equation V 1 p 1 R() = + 2 V p 2 Vp VV sV s 2 s + 4 2 2 2 V 2 p V Vp p sV 2 Vp 1 2  sin 2 sin + tan 2 V p We define a function which has properties similar to acoustic impedance so that reflectivity can be derived from it. So 1166 Normalized Elastic Impedance One shortcoming of the above EI function is that it dimensionality varies with , and so the values of EI varies appreciably with angle. Because of this, displaying of AI as well as EI logs becomes inconvenient.
Whitcombe (2002) introduced constants (Vp0, Vs0 and 0) in the equation as shown below, where they represent averages of the Vp, Vs and density logs. The average value for the EI logs for the 204/24a2 well, west of Shetland, plotted as a function of incidence angle. The shape of this curve depends on the units in which the data have been specified. In this example, velocities were measured in meters per second and density was measured in grams per cubic centimeter. 1167 Normalized Elastic Impedance
Whitcombe (2002) further shows that if the function is scaled by a factor Vp00, the dimensionality of EI and AI becomes the same. AI and EI (30 degrees) traces for the 204/24a2 well, west of Shetland. (a) The Vpo, Vso, o values have been used appropriate to the start of the log. The AI and EI logs intersect at this point. (b) The Vpo, Vso, o values have been used appropriate to a time of 2150 ms, appropriate to the shales between the pay zones at approximately 2130 and 2180 ms. 1168 Whitcombe (2002) Elastic Impedance EI(30) log curve scaled so that the shale baseline is approximately the same as AI curve shows behavior consistent with class III sands (Tertiary reservoirs, west of Shetlands) 1169 Segment of EI(30) log curve overlain on the inverted 30 degree angle stack. (Connolly, 1999) Elastic impedance
Gaussian curves showing distribution of AI and EI(30) values for three lithologies. Frequency (%) 10000 15000 20000 25000 30000 Frequency (%) 10000 15000 20000 25000 30000 Acoustic Impedance (ft/sg/cm3) Normalized Elastic Impedance at 300 (ft/sg/cm3) Normalized standard deviation
AI Shale Brine sand 1170 Oil sand 0.15 0.12 0.11 EI (30) 0.10 0.08 0.09 (Connolly, 1999) Elastic impedance
7.0*106 Elastic Impedance at 300 Acoustic Impedance 6.5*106 6.0*106 5.5*106 5.0*106 0.4 1.4*10 6 1.3*10 6 1.2*10 6 1.1*10 6 1.0*10 6 0. 4 0. 5 0. 0. 6 7 Oil Saturation 0. 8 0. 9 0.5 0.6 0.7 Oil Saturation 0.8 0.9 Relationship between oil saturation and AI (left) and EI(30) (right) from core sample measurements from the Foinaven Field (west of Shetlands). Evidently, the far offsets are more sensitive to changing saturation than the near ones. 1171 (Connolly, 1999) Angle Impedance
Concept of angle impedance is similar to elastic impedance, but reportedly angle impedance helps in taking the AVO inversion results to physical properties in the form of acoustic. Impedance, and Poisson's ratio and predict about lithology and fluids. Angle impedance is defined as Where Zp= acoustic impedance Zs= shear impedance = angle of incidence C = constantZp exp ([lnZp  2lnZs + C] sin2) Z = 1172 Resnick (1993) Angle Impedance
In the example discussed here the goal was to separate sand from shale and determining fluids in the reservoir. Data from only one well are available. The reservoir is at approx. 2 sec. Steps:
1. Seismic data are processed as angle stacks where average angles of incidence for the three stacks are 10, 20 and 30 degrees. A separate wavelet is estimated for each stack. The three angle stacks are inverted for angle impedance and these are found to be better than seismic data as the wavelet is removed and noise is damped using horizontal continuity. Acoustic impedance, shear impedance and Poisson's ratio were calculated from these impedance volumes. 2. 3. 4. 1173 Input Seismic Data
(10 degrees angle stack)
Well A Gamma ray log 1174 (Espersen et al., 2000) Input Seismic Data
(20 degrees angle stack)
Well A Gamma ray log 1175 (Espersen et al., 2000) Input Seismic Data
(30 degrees angle stack)
Well A Gamma ray log 1176 (Espersen et al., 2000) Well Log Data
Dipole sonic Pwave sonic Density Gamma ray A 0 2 4 2 3 1177 (Espersen et al., 2000) 150 Well Inversion Results Z = Z P exp[( ln Z P  2 ln Z S + C ) sin 2 ]
(10 degrees angle stack) A 1178 (Espersen et al., 2000) Well Inversion Results Z = Z P exp[ ( ln Z P  2 ln Z S + C ) sin 2 ]
(20 degrees angle stack) A 1179 (Espersen et al., 2000) Well Inversion Results Z = Z P exp[ ( ln Z P  2 ln Z S + C ) sin 2 ]
(30 degrees angle stack) A A 1180 (Espersen et al., 2000) Derivation of rock properties
Impedance variation with angle log(v) slop / e~ Intercept AI ~(vP)/ vP
0.0 10 20 0.2 30 0.4 40 ( vP ) 2 R ( ) = cos + sin 2 vP 0.6 50 60 0.8 70 1.0 80 sin2 (deg) 1181 (Espersen et al., 2000) Acoustic impedance
Well Log data Inversion result 2.0 9.0 2.0 1182 4.3 6.7 (106 kg/m2s) 9.0 (Espersen et al., 2000) Poisson's ratio
Well Log data Inversion result 0.00 0.50 0.00 0.16 0.33 0.50 1183 (Espersen et al., 2000) Well log data crossplots to estimate lithology Acoustic impedance Gamma ray color bar Poisson's ratio
1184 (Espersen et al., 2000) Sand Acoustic impedance Resisitivity color bar
Shale Poisson's ratio
1185 (Espersen et al., 2000) Well log data crossplots to estimate lithology
Water sand Oil sand Acoustic impedance Gas sand Shale Probability density functions Poisson's ratio
1186 (Espersen et al., 2000) Time slice 16 ms below top reservoir reservoir
Time slice through the Lithology Cube shows the probabilitiy for lithology and fluids Probability 1187 Oil sand Gas sand Shale Water sand (Espersen et al., 2000) Vertical slice through the Lithology Cube. Probability 1188 Oil sand Gas sand Shale Water sand (Espersen et al., 2000) Inversion for Acoustic and Elastic Impedance
In Summary: Modern acoustic impedance inversion algorithms integrate seismic data, well control, estimations of the source wavelet, and interpreter constraints on structure and lithology in a mathematically rigorous manner Acoustic impedance `deconvolves' the seismic data to remove the source wavelet shape For the above reasons, acoustic impedance has higher resolution than conventional seismic data Of all the attributes, acoustic impedance is one of the most closely tied to rock porosity Elastic impedance and extensions of classical AVO analysis, promise to provide high resolution estimates of lithology and fluid product Geostatistical inversion provides realistic high resolution images that fit both the well statistics, depositional model, and seismic data. 1189 ...
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 Fall '11
 Marfurt
 Optimization, et al., acoustic impedance, Seismic Modeling and Inversion, impedance inversion

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