AVO地震資料的解釋

1、AVO地震資料的解釋AVO地震資料的解釋IntroductionIn our previous section on rock physics we discussed fluid effects on P and S-wave velocity, and density.We then looked at post-stack inversion, its advantages and limitations.Next, we considered the recording of S-wave data.In this section, we will first review the b

2、asic principles of AVO and show its relationship with P and S-wave velocity.We will then look at the AVO response of two simple models, one wet and one gas-saturated.We will then look at various AVO modeling schemes, including full wave equation modeling and anisotropic modeling.2IntroductionIn our

3、previous se“Bright spots”Recall that in the section on inversion, we showed the “bright spot” shown above, and pointed out that in the 1970s this would have been interpreted as a gas sand.3“Bright spots”Recall that in tThe AVO methodBut “bright spots” can be caused by lithologic variations as well a

4、s gas sands. This lead geophysicists in the 1980s to start looking at pre-stack seismic data. The amplitude increase with offset shown here is an example of a Class 3 sand, as we will discuss later.4The AVO methodBut “bright spotReflected P-wave = RP(q1)Reflected SV-wave = RS(q1)Transmitted P-wave =

5、 TP(q1)Incident P-waveTransmitted SV-wave = TS(q1)VP1 , VS1 , r1VP2 , VS2 , r211122Consider the interface between two geologic horizons of differing P and S-wave velocity and density and an incident P-wave at angle q1. This will produce P and S reflected and transmitted waves, as shown above.Mode Co

6、nversion5Reflected Reflected TransmitteBut how do we utilize mode conversion? There are actually two ways:(1) Record the converted S-waves using three-component receivers (in the X, Y and Z directions). This was discussed in the last chapter.(2) Interpret the amplitudes of the P-waves as a function

7、of offset, or angle, which contain implied information about the S-waves. This is called the AVO (Amplitude versus Offset) method.In the AVO method, we can make use of the Zoeppritz equations, or some approximation to these equations, to extract S-wave type information from P-wave reflections at dif

8、ferent offsets. Utilizing Mode Conversion6But how do we utilize mode conThe Zoeppritz EquationsZoeppritz derived the amplitudes of the reflected and transmitted waves using the conservation of stress and displacement across the layer boundary, which gives four equations with four unknowns. Inverting

9、 the matrix form of the Zoeppritz equations gives us the exact amplitudes as a function of angle:7The Zoeppritz EquationsZoeppriThe Aki-Richards EquationThe Aki-Richards equation is a linearized approximation to the Zoeppritz equations. The initial form (Richards and Frasier, 1976) separated the vel

10、ocity and density terms:where:8The Aki-Richards EquationThe AWiggins version of Aki-RichardsA totally equivalent form was derived by Wiggins. He separated the equation into three reflection terms, as follows:where:9Wiggins version of Aki-RicharTo see why the A term in the linearized approximation is

11、 approximately equal to the zero-offset reflection coefficient, recall that in Part 2 we showed that:Reflectivity approximationThis leads to:10To see why the A term in the lFattis version of Aki-RichardsAnother equivalent form was derived by Fatti et al. They separated the equation into three reflec

12、tion terms, as follows:11Fattis version of Aki-RichardA Summary of the Aki-Richards Eq.All three forms of the Aki-Richards equation consist of the sum of three terms, each term consisting of a weight multiplied by an elastic parameter (i.e. a function of VP , VS or r). Here is a summary:Note that th

13、e weighting terms a, b, c and d, e, f contain the squared VP/VS ratio as well as q. However, in the Wiggins et al. formulation, this term is in the elastic parameter B.EquationWeightsElastic ParametersAki-RichardsWiggins et al.Fatti et al.12A Summary of the Aki-Richards A physical interpretation of

14、the three equations is as follows:Since the seismic trace consists of changes in impedance rather than velocity or density independently, the original form of the Aki-Richards equation is rarely used.The A, B, C formulation of the Aki-Richards equation is very useful for extracting empirical informa

15、tion about the AVO effect (i.e. A, which is called the intercept, B, called the gradient, and C, called the curvature) which can then be displayed or cross-plotted. Explicit information about the Vp/Vs ratio is not needed in the weights.The Fatti et al. formulation gives us a way to extract quantita

16、tive information about the P and S reflectivity which can then be used for pre-stack inversion. The terms RP0 and RS0 are the linearized zero-angle P and S-wave reflection coefficients.Physical interpretation13A physical interpretation of tLet us now see how to get from the geology to the seismic us

17、ing the second two forms of the Aki-Richards equation. We will do this by using the two models shown below. Model A consists of a wet, or brine, sand, and Model B consists of a gas-saturated sand.Wet and Gas Models(a) Wet model(b) Gas modelVP1,VS1, 1VP2,VS2, 2VP1,VS1, 1VP2,VS2, 214Let us now see how

18、 to get fromIn the section on rock physics, we computed values for wet and gas sands using the Biot-Gassmann equations. The computed values were: Wet: VP2 = 2500 m/s, VS2= 1250 m/s, 2 = 2.11 g/cc, s2 = 0.33 Gas: VP2 = 2000 m/s, VS2 = 1310 m/s, 2 = 1.95 g/cc, s2 = 0.12 Values for a typical shale are:

19、 Shale: VP1 = 2250 m/s, VS1 = 1125 m/s, 1 = 2.0 g/cc, s1 = 0.33This gives us the following values at the top of the sand/shale zone: Model ValuesWet Sand:Gas Sand:15In the section on rock physicsExercise 4-1Compute the intercept, A, the gradient term, B, and the curvature, C, for the top and base of

20、 both the wet model and the gas model, given the parameters on the previous page. Note that the base values are the negative of the top due to symmetry:Wet Model Top:A =B =C =Gas Model Top:A =B =C =Wet Model Base:A =B =C =Gas Model Base:A =B =C =16Exercise 4-1Compute the intercExercise 4-2For both t

21、he next exercise and a later exercise on anisotropy effects in AVO, you will need to compute the following trigonometric functions of four angles. Compute them here for later use.sin2qtan2qsin2q*tan2q17Exercise 4-2For both the next Exercise 4-3Using the A, B, and C terms for the wet and gas models t

22、hat were computed in Exercise 1, work out the values for R(q) at angles of 0o, 15o, 30o, and 45oin the table below. Then, plot the results on graph paper, with and without the third term, as a function of .Top:Base:18Exercise 4-3Using the A, B, anWet Model AVO Curves0.0RP(q)q0.10.2- 0.1- 0.210o20o30

23、o40o50o19Wet Model AVO Curves0.0RP(q)q0Gas Model AVO Curvesq0.0RP(q)0.10.2- 0.1- 0.210o20o30o40o50o20Gas Model AVO Curvesq0.0RP(q)0Wet Model AVO Curvesq0.0RP(q)10o20o30o40o50o0.10.2- 0.1- 0.2Wet Sand BaseWet Sand Top21Wet Model AVO Curvesq0.0RP(q)1Gas Model AVO Curvesq0.0RP(q)10o20o30o40o50o0.10.2-

24、0.1- 0.2Gas Sand TopGas Sand Base22Gas Model AVO Curvesq0.0RP(q)1This figure on the right shows the computed AVO curves for the top and base interfaces of the gas sand using all three terms (A, B, and C) in the Aki-Richards equation, and then only the first two terms (A and B). Note the deviation of

25、 the two above 25 degrees.Gas Model AVO Curves23This figure on the right showsThis figure on the right shows the computed AVO curves for the top and base interfaces of the wet sand using all three terms (A, B, and C) in the Aki-Richards equation, and then only the first two terms (A and B). Note the

26、 deviation of the two above 25 degrees.Wet Model AVO Curves24This figure on the right showsParameters for ABC and Fatti eqs.Her is a comparison of the results from the ABC and Fatti equations for the top of the sands (because of symmetry in this example, the base of sand values are simply these valu

27、es multiplied by -1):Gas Sand:Wet Sand:Note that A and B have the same polarity for the gas sand and opposite polarity for the wet sand, whereas RP0 and RS0 have opposite polarity for the gas sand and the same polarity for the wet sand. The reason for this will be clear later.25Parameters for ABC an

28、d Fatti eAki-Richards valuesHere are computed values for the ABC and Fatti versions of the Aki-Richards equation at angles of 0, 30 and 60 degrees: 0o Gas30o Gas60o Gas0o Wet30o Wet60o Wet1st Term2nd Term3rd Term2nd Term3rd Term1st TermRP(q)ABC MethodFatti MethodAngle/ Sand-0.0710.079-0.0710.0790000

29、0000-0.0710.079-0.1370.064-0.071-0.0710.0790.079-0.060-0.006-0.095-0.0426x10-5-0.0200.0050.106-0.040-0.002-0.181-0.385-0.133-0.285-0.1250.025-0.0600.1190.318-0.119-0.0610.13826Aki-Richards valuesHere are coThere was a lot of information in the last slide, but the key points are:The individual terms

30、in each approach are different, but the sum is always identical.For an angle of zero degrees, the second two terms in both methods are equal to zero, and the scalar on the first term in the Fatti method is equal to one.In the ABC method, the first term is always the zero offset reflection coefficien

31、t, but this is true only at zero angle in the Fatti method.The third term makes less of a contribution to the sum in the Fatti method than in the ABC method.The next slides will show the results at all angles.Summary of the ABC and Fatti methods27There was a lot of informationThis figure on the righ

32、t shows the AVO curves computed using the Zoeppritz equations and the two and three term ABC equation, for the gas sand model.Notice the strong deviation for the two term versus three term sum.Note: On the next four plots, the curves have been calculated as a function of incident angle and scaled to

33、 average angle.Zoeppritz vs ABC Gas SandZoeppritzABC method:two termABC method:three term28This figure on the right showsThis figure on the right shows the AVO curves computed using the Zoeppritz equations and the two and three term ABC equation, for the wet sand model.Again, notice the strong devia

34、tion for the two term versus three term sum.Zoeppritz vs ABC Wet SandZoeppritzABC method:two termABC method:three term29This figure on the right showsThis figure on the right shows the AVO curves computed using the Zoeppritz equations and the two and three term Fatti equation, for the gas sand model

35、.Notice there is less deviation between the two term and three term sum than with the ABC approach.Zoeppritz vs Fatti Gas SandZoeppritzFatti method: two termFatti method: three term30This figure on the right showsThis figure on the right shows the AVO curves computed using the Zoeppritz equations an

36、d the two and three term Fatti equation, for the wet sand model.As in the gas sand case, there is less deviation between the two term and three term sum than with the ABC approach.Zoeppritz vs Fatti Wet SandZoeppritzFatti method: two termFatti method: three term31This figure on the right showsThis f

37、inal computed synthetic seismogram is shown above on the right, where the log curves are on the left. Notice that the sand is thin enough that the wavelets from the top and bottom of the layer “tune” together.The final synthetic seismogram32This final computed synthetic Ostranders Paper Ostrander (1

38、984) was one of the first to write about AVO effects in gas sands and proposed a simple two-layer model which encased a low impedance, low Poissons ratio sand, between two higher impedance, higher Poissons ratio shales. This model is shown in the next slide. Ostranders model worked well in the Sacra

39、mento valley gas fields. However, it represents only one type of AVO anomaly (Class 3) and the others will be discussed in the next section.33Ostranders Paper Ostrander (1Ostranders ModelOstrander (1984) wrote the classic paper on AVO. His model is shown above. Notice that the model consists of a lo

40、w acoustic impedance gas sand encased between two shales34Ostranders ModelOstrander (19Synthetic from Ostranders Model(a) Well log responses for the model.(b) Synthetic seismic.Notice that Ostranders model produces an increase in amplitude on the pre-stack synthetic gather. 35Synthetic from Ostrande

41、rs ModAVO Curves from Ostrander (a) Response from top of model to 45o. (Note that the transmitted P-wave amplitude is shifted to plot within the data range).(b) Response from base of model to 45o. 36AVO Curves from Ostrander (a) Ostranders case study - stackOstranders case study is from the Sacramen

42、to basin. The stack above has “bright spots” at locations A, B, and C, but only A and B are due to gas. 37Ostranders case study - stackOstranders case study Supergathers from locations A, B, and C. Note that locations A and B show amplitude increases with offset but C does not.(A)(B)(C)38Ostranders

43、case study SupergaShueys EquationShuey (1985) rewrote the Aki-Richards equation using VP, , and , writing the basic form the same way:Only the gradient is different than in the Aki-Richards expression, and is given by:39Shueys EquationShuey (1985) rShuey vs Aki-Richards In this course, we have been

44、using a modeled gas sand and wet sand example. Using Shueys equation for this example, we get the following comparison with the answers in exercise 6-1: B (Aki-Richards) B (Shuey) Gas Sand Top: -0.242-0.252 Wet Sand Top: -0.079-0.079Why do we get the same values in the wet case but not in the gas ca

45、se?40Shuey vs Aki-Richards In this This figure showsa comparisonbetween the Aki-Richards and Shuey equationsfor the gas sand we just considered.Shuey vs Aki-Richards 41This figure showsShuey vs Aki-Multi-layer AVO modelingMulti-layer modeling in the consists first of creating a stack of N layers, ge

46、nerally using well logs, and defining the thickness, P-wave velocity, S-wave velocity, and density for each layer.You must then decide what effects are to be included in the model: primaries only, converted waves, multiples, or some combination of these.42Multi-layer AVO modelingMulti-The Possible M

47、odelled EventsThe following example, taken from Simmons and Backus (AVO Modeling and the locally converted shear wave, Geophysics 59, p1237, August, 1994), illustrates the effect of wave equation modeling. The figure above shows the modelling options.43The Possible Modelled EventsThThe Oil Sand Mode

48、lSimmons and Backus used the thin bed oil sand model shown above.44The Oil Sand ModelSimmons and Response to various algorithms(A) Primaries-only Zoeppritz, (B) + single leg shear, (C) + double-leg shear, (D) + multiples,(E) Wave equation solution, (F) Linearized approximation.Simmons and Backus (19

49、94)45Response to various algorithmsPrimary and Converted WavesSimmons and Backus (1994)Zoeppritz, primaries onlyZoeppritz, primaries + single leg conversionsAki-Richards, primariesSingle leg conversions46Primary and Converted WavesSimLogs from a real data exampleThe logs shown above come from a real

50、 data example in the Colony sand that we will look at in the next section.47Logs from a real data exampleTModels from a Real Data Example(a) Full elastic wave.(b) Zoeppritzequation.(c) Aki-Richardsequation.48Models from a Real Data ExamplAVO ModelingBased on AVO theory and the rock physics of the re

51、servoir, we can perform AVO modeling, as shown above. Note that the model result is a fairly good match to the offset stack. P-waveDensityS-wavePoissons ratioSyntheticOffset Stack49AVO ModelingBased on AVO theorAnisotropy and AVOSo far, we have considered only the isotropic case, in which earth para

52、meters such as velocity do not depend on seismic propagation angle.In the next few slides, we will discuss anisotropy, in particular the case of Transverse Isotropy with a vertical symmetry axis, or VTI.We will then see how anisotropy affects the AVO response.Finally, we will look at this effect on

53、our original model50Anisotropy and AVOSo far, we hIsotropic versus anisotropic velocityAs mentioned, in an isotropic earth P and S-wave velocities are independent of angle.VTI velocities depend on angle, as shown below for three different angles:VP(0o)VP(45o)VP(90o)VTI can be extrinsic, caused by fi

54、ne layering of the earth, or intrinsic, caused by particle alignment as in a shale.51Isotropic versus anisotropic vVelocities for weak anisotropyAlthough the equations for full anisotropy are quite complex, Thomsen (1986) showed that for weakly anisotropic materials the velocities can be written as

55、follows, where e, d, and g are called Thomsens parameters. Note that, for AVO and converted wave studies, we are only interested in the first two velocities and constants. Note also that VSV(0o) = VSH(0o):52Velocities for weak anisotropyThomsens ParametersThomsens constants are simply combinations o

56、f the differences between the P and S velocities at 0o, 45o, and 90o. The following relationships can be derived quite easily using the velocities in the previous slide:In the next slide, we will look at VP and VSV as a function of angle for different values of d and e. (As mentioned, VSH will not b

57、e used in AVO).53Thomsens ParametersThomsens Group angle versus phase angleFor anisotropic velocities, it is important to note the difference between the phase angle q, which is computed normal to the seismic wavefront, and the group or ray angle f, along which energy propagates. Most of the angles

58、we will discuss are phase angles. This is illustrated below. zxWavefrontRayWavefrontNormalGroup angle versus phase angleAnisotropic P and SV VTI velocities(a) VTI medium with d = 0.2 and e = 0.2. (b) VTI medium with d = 0.1 and e = 0.2. (a) VTI medium with d = 0.2 and e = 0.1. 55Anisotropic P and SV

59、 VTI velocExerciseUsing the above P-wave velocity curve, compute the values for d and e.56ExerciseUsing the above P-waveAVO and Transverse IsotropyThomsen (1993) showed that a transversely isotropic term could be added to the Aki-Richards equation using his weak anisotropic parameters d and e, where

60、 Ran(q ) is the anisotropic AVO response and Ris(q ) is the isotropic AVO response. Ruger (2002) gave the following corrected form of Thomsens original equation:57AVO and Transverse IsotropyThoTypical values for anisotropyTypical values for delta, epsilon, and gamma were given by Thomsen (1986). Her