Seismic Inversion and AVOapplied to Lithologic Prediction Part 6 – AVO Analysis Introduction • In the last section, we looked at the theory of AVO and used the equations to perform forward modeling. • In this section, we will look at real data analysis of AVO anomalies. • We will start by looking at the theory of the intercept and gradient and at a simple example. • We will then look at the classification scheme of Rutherford and Williams and at cross-plotting and how it relates to the ARCO mud-rock line. • Finally, we will consider some processing issues that need to be considered for AVO analysis. 6-2 Intercept/Gradient Analysis Gathers AVO Analysis Intercept Gradient Crossplot Now, we will see how intercept/gradient analysis and crossplotting, the most well known techniques of AVO analysis, can lead to much the same result. The flowchart above shows the 6-3 basic procedure, and we will next look at the theory. The two-term Aki-Richards equation • Intercept/gradient analysis is done with the two-term Aki-Richards equation. Recall that: R( ) A B sin 2 where: 2 2 1 VP VS VS VS 1 VP A RP 4 2 , , B 2 Vp 2 Vp VP VS VP or: 1 2 VP / VP B AD 2(1 D ) ,D . 2 1 (1 ) VP / VP / 6-4 Estimating the intercept and gradient • Step 1 involves converting from offset to angle, for which we need both a velocity model and a relationship between angle and velocity. • Step 2 involves fitting a regression line to the amplitude picks as a function of the sine of the angle squared. • We will assume that the C term is negligible, which assumes we are only recording to an aperture of 30 degrees. • The following slides will illustrate this procedure, 6-5 Converting from offset to angle The slide above shows the difference between constant offset traces and constant angle traces. Notice that to compute constant angle traces we need to move to greater offsets as a function of time. (Western Geophysical) 6-6 Converting from offset to angle Conversion from angle to time can be done very simply using the straight ray approximation (see (1) below), or completely using full ray-tracing. A good compromise between the two is to use the ray parameter approach (see (2) below). (1 ) Straight Ray : tan X X , 2 d Vt0 where X offset , VRMS t0 , 2 t0 2 way time, d depth ( 2 ) Ray Parameter : sin XVINT , 2 tVRMS where VINT Interval velocity , t total traveltime. VRMS RMS velocity . 6-7 Real Data Example • Now let’s look at some real data, and see if it matches the theory. • The next slide shows a group of 2D gathers over a gas zone, in WTVA and color amplitude envelope. Notice the increase in amplitude as a function of offset. • The gas event and the events above and below the gas were then picked and analyzed, as shown in the following three slides. • The slide after that shows a “common offset stack” or “super-gather” over the gathers. The amplitudes have been picked and displayed, to quantify the amplitude increase. 6-8 Seismic Gathers over a Gas Sand (a) A series of corrected CDP gathers over a gas zone. (b) The same gathers, but shown with color amplitude envelope. 6-9 Seismic Gathers over a Gas Sand Here are the picks from the an event above the gas (shown as the red, jagged line), with a gradient/intercept analysis performed on the picks, and the resulting curves annotated on top of the picks (shown as a black 6-10 line). Notice that the amplitudes are decreasing with offset. Seismic Gathers over a Gas Sand Here are the picks from the gas event (shown as the red, jagged line), with a gradient/intercept analysis performed on the picks, and the resulting curves annotated on top of the picks (shown as a black line). Note the strong amplitude increase with offset. 6-11 Seismic Gathers over a Gas Sand Here are the picks from the event below the gas (shown as the red, jagged line), with a gradient/intercept analysis performed on the picks, and the resulting curves annotated on top of the picks (shown as a black line). Note the amplitude decrease with offset. 6-12 Common offset stack from gathers (b) Picks from the trough. (c) Picks from the peak. (a) Common offset stack 6-13 Common Offset Picks as function of sin2 Offset +A +B sin2 Time -A -B (a) Small portion of the common offset stack. (b) Peak and trough picks vs sin2. 6-14 Data Example from the Colony Sand (a) (b) The above figure shows (a) intercept (A) and (b) gradient (B) stacks. This 6-15 is a similar bright spot anomaly to the S-wave example given earlier. Approximate Aki-Richards • Assuming that VP/VS = 2 in the full Aki-Richards equation: 2 2 VS VS VS 1 VP VS 1 1 VP B 4 2 2 Vp 2 Vp VS 2 VP VS VP RP 2 RS , 1 VS where : RP A, RS 2 VS • Thus, the S-wave reflectivity can be estimated as follows from the intercept and gradient: 1 RS A B 2 6-16 Approximate Shuey’s Equation • Assuming that = 1/3 in Shuey’s equation: 1 2 B A D 2(1 D ) 1 (1 )2 1 9 A D 2(1 D ) A 2 2 (2 / 3 ) 4 • Thus, can be estimated from A and B: 4 A B 9 6-17 Hilterman’s Approximation • Hilterman re-arranges Shuey’s equation using the previous approximation. Note that the third term has been dropped in the following equation and we are also assuming a Vp/Vs ratio of 2: R( ) A B sin2 RP 2.25 RP sin2 RP (1 sin2 ) 2.25 sin2 RP cos 2 2.25 sin2 6-18 Equating Shuey and Aki-Richards • In the last few slides, we have seen that: 4 / 9A B 0.5 A B 0.5( RP B ) and: B RP 2RS • Equating the above two approximations, we get: RP RS 6-19 Data Example from the Colony Sand (a) (b) The above figure shows (a) ((A+B)*(4/9)) and (b) Rs ((A-B)/2) stacks. 6-20 Interpreting the previous slide • In the previous slide, note that we have converted from intercept and gradient to both pseudo-RS and pseudo-Poisson’s ratio. How well does this fit the known geology? • First of all, we know there is a gas sand at 630 ms in the centre of the section, and a hard streak just below the gas sand. • Notice that the pseudo-Poisson’s ratio plot shows that we have a class 3 gas sand. • The pseudo-RS plot only responds to the hard streak, and not the gas sand, as expected. • This is also seen in the 3D example on the next slide. 6-21 3D Channel Sand Example (a) Map view of amplitude from 3D channel sand. (b) Pseudo-Poisson’s Ratio over channel sand. 6-22 AVO Cross-plotting AVO cross-plotting involves plotting the intercept against the gradient and identifying anomalies. The theory of cross-plotting was developed by Castagna el al (TLE, 1997, Geophysics, 1998) and Verm and Hilterman (TLE, 1995) and is based on two ideas: (1) The Rutherford/Williams classification scheme. (2) The Mudrock line. 6-23 Rutherford/Williams Classification Rutherford and Williams (1989) derived the following classification scheme for AVO anomalies, with further modifications by Ross and Kinman (1995) and Castagna (1997). The acoustic impedance changes refer to the anomalous layer: Class 1: Large increase in acoustic impedance. Class 2: Near-zero impedance contrast. Class 2p: Same as 2, with polarity change. Class 3: Large decrease in acoustic impedance. Class 4: Very large decrease in acoustic impedance coupled with small Poisson’s ratio change. 6-24 Rutherford/Williams Classification (cont) The Rutherford and Williams classification scheme as modified by Ross and Kinman (1995). 6-25 An example of a Class 1 anomaly (a) Data example. (b) Model example. 6-26 Rutherford and Williams (1989) Angle stacks over class 2 and 3 sands (a) Class 2 sand. (b) Class 3 sand. 6-27 Rutherford and Williams (1989) Class 2p vs class 2 sands Ross and Kinman (1995) suggest creating a near trace range stack (NTS) and a far trace range stack (FTS). For Class 2p: Final Stack = FTS - NTS For Class 2: Final Stack = FTS 6-28 (a) Full stack of a class 2 sand. (b) FTS of a class 2 sand. 6-29 Ross and Kinman (1995) (a) Full stack of a class 2p sand. (a) FTS - NTS of a class 2p sand. 6-30 Ross and Kinman (1995) Class 4 Anomalies • Castagna (1995) suggested that for a very large value of RP, and a small change in Poisson’s ratio, we may see a reversal of the standard Class 3 anomaly, as shown below. Castagna termed this a Class 4 anomaly. Here is a simple example using Shuey’s approximation: 9 G RP , 4 (1 ) If 0.3 and RP 0.1, then G - 0.575 (Class 3) ( 2 ) If 0.1 and RP 0.3 , then G 0.075 (Class 4) 6-31 Class 4 Anomaly Here is Figure 7 from Castagna et al (1998), which illustrates the concept of the Class 4 anomaly in more detail. 6-32 The Mudrock Line • The mudrock line is a linear relationship between VP and VS derived by Castagna et al (1985). The equation is as follows (the plot from their original paper is shown above): VP = 1.16 VS + 1360 m/s 6-33 Intercept versus Gradient • By using the Aki-Richards equation, Gardner’s equation, and the ARCO mudrock line, we can derive a simple relationship between intercept and gradient. Note that: 1 VP A 2 Vp 2 2 VS VS VS 1 VP B 4 2 , 2 Vp VP VS VP Gardner : aV 0.25 P 1 VP 4 VP • If we assume that VP / VS = c, then we can show that: 4 9 B A 1 2 5 c 6-34 Intercept versus Gradient • Now let us use a few values of c and see how the previous equation simplifies. If c = 2, the most commonly accepted value, the gradient is the negative of the intercept (a -45 degree line on a crossplot): 4 9 B A 1 A 5 4 • If c = 3, the gradient is zero, a horizontal line on the crossplot of intercept against gradient: 4 9 B A 1 0 ! 5 9 • Various values of c produce the straight lines (“wet” trends) shown on intercept/gradient crossplots on the next page. 6-35 Mudrock lines on a crossplot for various VP/VS ratios (Castagna and Swan, 1998). 6-36 Intercept / Gradient Crossplots • By letting c=2 for the background wet trend, we can now plot the various anomalous Rutherford and Williams classes (as extended by Ross and Kinman and Castagna et al). • Note that each of the classes will plot in a different part of the intercept/gradient crossplot area. • The anomalies form a rough elliptical trend on the outside of the wet trend. • This is shown in the next figure. 6-37 Gradient Base II P Base II Base I Base III Top IV Intercept Base IV Top III Crossplot showing anomalies Top I “Wet” Trend Top II Top II P Vp 2 Vs 6-38 ARCO example of cross-plotting (a) Cross-plot of well log derived A and B. (b) Cross-plot of seismically derived A and B. Foster et al (1993) 6-39 Intercept / Gradient Crossplots (a) Uninterpreted gas zone (b) Interpreted gas zone 6-40 Seismic Display from Int/Grad Xplots (a) Before interpretation (b) After interpretation 6-41 Problems in Intercept/Gradient Analysis • There are a number of problems that can reduce the accuracy of intercept/gradient analysis and crossplotting: • Noise on the far offsets (i.e. multiples) • Misalignment of events at far offsets • Neglecting the third term in Aki-Richards • Neglecting anisotropic effects • Offset variable phase errors. • We will now therefore have a brief overview of some of the processing issues that need to be considered when processing data with AVO analysis in mind. 6-42 FLOW CHART COMMENTS Raw Shot Gathers Refraction Statics Land or transition data only Amplitude Recovery Surface consistent preferred Noise Attenuation F-X for random noise Parabolic Radon for multiples F-K for Linear noise Residual Statics and NMO DMO / Pre-stack Migration Deconvolution / Phase Correction AVO Analysis A flowchart for AVO processing 6-43 Amplitude Recovery • Amplitude recovery can be done using statistical (surface consistent) or analytical (gain curve) methods. See papers by Gary Yu (Offset-amplitude variation and controlledamplitude processing, Geophysics, 1985, Vol. 50, #12), and Bjorn Ursin (Offset-dependent geometrical spreading in a layered medium, Geophysics, 1990, Vol. 55,#4) • The next slide shows a comparison between an incorrect amplitude recovery on the left and a correct amplitude recovery on the right. Key steps in the proper flow are as follows: – Suppress coherent noise – Restore amplitude loss with offset compensation – Surface consistent amplitude balancing – Partial trace sum – Surface consistent deconvolution – Proper NMO application 6-44 Amplitude Recovery The left slide shows an incorrect amplitude recovery scheme, and the right slide show a correct amplitude recovery scheme, at locations C Yu, 1985 6-45 and B, the gas sands. Noise Attenuation This is an important step since noise amplitudes can be confused with true amplitudes. Three different schemes are recommended: - Common offset stacking for random noise attenuation. - F-K filtering for linear noise attenuation. - Parabolic Radon filtering for multiple attenuation. The next slide shows an example comparing the Parabolic Radon Transform (INVEST) with FK filtering for multiple removal. 6-46 Noise Attenuation Note that the Inverse Velocity Stack (equivalent to the parabolic Radon transform) attenuates the multiples at all offsets. 6-47 Dan Hampson, 1986 DMO/Pre-stack migration This is recommended only in structurally complex areas, as long as an amplitude-preserving algorithm is used (see Black et al, True-amplitude imaging and dip moveout, Geophysics, 1993, Vol. 58, #1) The next slide, taken from Black et al, shows the effect of a non-amplitude preserving DMO algorithm. 6-48 Example of Using Wrong DMO (a) NMO only. (b) Non-amplitude (c) True preserving DMO amplitude DMO (d) (c) - (b) 6-49 Black et al, 1993 Velocity effects of Weak Anisotropy • Tsvankin and Thomsen (“Nonhyperbolic reflection moveout in anisotropic media”, Geophysics, August, 1994) applied Thomsen’s theory of weak anisotropy to reflection moveout for both P and SV waves. Their equation for P-waves is as follows: t X2 t02 A2 x 2 A4 x 4 x 1 V0 t0 where: 2 1 2 A2 , 2 V0 2( ) A4 2 4 . t0 V0 , Thomsen' s parameters . 6-50 o NMO Comparison (to 45 ) NMO Curves NMO/TIV Difference Offset 0 500 1000 1500 60 -0.850 50 -0.900 40 30 Time (msec) -0.800 -0.950 Time (sec) 2000 -1.000 -1.050 -1.100 20 10 -1.150 0 -10 0 -1.200 -20 -1.250 -30 -1.300 500 1000 1500 2000 Offset (m) ( Far = 45 degrees) NMO NMO/TIV NMO/TIV - NMO The effects of applying Dix NMO versus non-hyperbolic NMO in a TIV material. The difference is shown on the right. 6-51 Gulf of Mexico Case Study 1 • As well as the effect of anisotropy on NMO, there are also higher order NMO terms in a layered earth even if the events are not anisotropic. • Unfortunately, it is difficult to tell the two effects apart. • Regardless of the cause, we can do a third order fit to our data and apply the correction. • The case study in the next few slides, from a paper by Chris Ross in the February, 1997 issue of First Break, shows an example from the Gulf of Mexico. 6-52 Gulf of Mexico Case Study 1 The effects of applying Dix NMO versus Non-hyperbolic NMO. C.P. Ross, 1997 6-53 Gulf of Mexico Case Study 1 Top figure shows Dix NMO on real gathers, and bottom 6-54 C.P. Ross, 1997 figure shows non-hyperbolic NMO on real gathers. Gulf of Mexico Case Study 2 • We will now look at a second Gulf of Mexico case study and consider a second approach to dealing with poorly corrected gathers. • This approach will be termed “target-oriented” AVO analysis, since we will pick only the target event. • We will start by looking at the NMO corrected gathers. • We will then improve the signal-to-noise ratio by computing a “super-gather” from the input gathers. • We will perform the rest of the analysis on the “supergather”. 6-55 Gulf of Mexico Case Study 2 The figure above shows the input gathers with the sonic log inserted at Xline 100. Note that the gathers are noisy, and the target event, indicated by the blue line, is badly corrected. 6-56 Gulf of Mexico Case Study 2 The figure above shows a super-gather, or common offset stack, run on the previous gathers using a 3 x 3 mix. The data is cleaner, but the event is still badly corrected. 6-57 Gulf of Mexico Case Study 2 The figure above shows an A+B AVO analysis run on the previous super-gathers, with the anomaly shown below the pick at the well. Despite the poor NMO correction, the anomaly is visible. 6-58 Gulf of Mexico Case Study 2 The figure on the left shows the scaled Poisson’s ratio plot (A+B) averaged over a 30 ms window below the target horizon, using an amplitude envelope attribute. Notice the clear outline of the anomalous zone. However, could we have done better if we had done a better job of NMO? 6-59 Gulf of Mexico Case Study 2 To try to analyze the target horizon correctly, we picked the trough over the target at each gather, using an automatic picking program. Note that some of the long offset picks are miss-picked. 6-60 Gulf of Mexico Case Study 2 The figure above shows a display of the picks below the gathers, where an AVO curve has been fitted. By using a robust fitting method, we have been able to avoid the miss-picks. 6-61 Gulf of Mexico Case Study 2 The figure on the left shows the scaled Poisson’s ratio plot (A+B) from the picked target horizon. Notice the better definition of the anomalous zone when compared back to the standard AVO analysis. Note the reversed scale since we did not need to take the absolute value here. A comparison between the two maps will be shown in the next slide. 6-62 Gulf of Mexico Case Study 2 (a) (b) The figures above show (a) the pseudo-Poisson’s ratio plot from the standard AVO analysis, corrupted by poor NMO, and (b) the targetoriented pseudo-Poisson’s ratio analysis found by picking the horizon. 6-63 Conclusions • In this section, we looked at real data analysis of AVO anomalies. • We started by showing how AVO and multicomponent interpretation are related, based on the analysis of a shallow gas sand. • We then looked at the theory of the intercept and gradient and at a simple gas sand example. • After that, we looked at the classification scheme of Rutherford and Williams and at cross-plotting and how it relates to the ARCO mud-rock line. • Finally, we considered some important processing issues for AVO analysis. 6-64