#### Transcript Q factor estimation for seismic data with localized phase space method

Q factor estimation for seismic data with localized phase space method Jinghuai Gao Institute of Wave and Information Xi’an Jiaotong University, China Outline 1. Why we need to estimate the Q ? 2. Methods and challenges 3. WEPIF principle 4. WEPIF methods and applications 5. Conclusions 2 Why we need to estimate the Q ? Seismic waves propagating through the earth suffer attenuation and dispersion due to the viscosity of the media (Ricker, 1953; Futterman, 1962; Kneib and Shapiro, 1995). Seismic attenuation is usually quantified by the quality factor Q. 3 Measurements in both the field and the laboratory demonstrate that Q is associated with factors such as physical properties of rocks, types of fluids, and saturation of fluids (Winkler and Nur, 1982; Sheriff and Geldart, 1995). Thus, Q is a diagnostic tool for reservoir characterization and hydrocarbon detection (Toksöz et al., 1979; Frisillo and Stewart, 1980). Q is very important when interpreting the effects of AVO, improving the resolution of seismic imaging, and advancing the study of material properties. Methods and difficulties Approach 1:Time-domain methods: pulse amplitude decay, pulse rising time, pulse broadening. Problem: amplitude information of seismic pulses is often influenced by scattering, geometric spreading, and other factors. 5 Methods and difficulties Approach 2: Fourier-frequency domain methods: logarithm spectral ratio (LSR), centroid frequency shift (CFS), peak frequency shift methods. Problem:To properly select the window function and window length (Harris, 1978) is difficulty. Approach 3:Instantaneous frequency (IF) methods Tonn (1991), Barnes (1991 and 1993), and Engelhard (1996) obtained the relationship between the measured instantaneous spectra and seismic attenuation. Assuming that the source wavelet is an idealized band-pass wavelet, Barnes (1991) derived the relation between Q and IF variations of seismic waves, establishing a new approach for Q estimation. Problem: These reletionships are qualitative or implicit and cannot be used to estimate the Q. In this work, we further develop Barnes’s work (Barnes, 1991), and propose a method for estimating Q based on our new development. WEPIF-method principle Definition: Instantaneous frequency at the wavelet envelope peak is called WEPIF 80 source 60 40 Receiver 1 0 Receiver 1 20 0 t=0 80 -20 -40 z -60 10 20 Receiver 2 Z 30 40 50 60 70 80 40 z P(c, , z, Q) 60 0 20 Receiver 2 0 t -20 A slab -40 -60 0 10 20 30 40 50 60 70 80 9 Propagator Considering a one-way plane wave propagating in a homogeneous anelastic medium with a frequencyindependent Q, the propagator is as follows: i z z P(c, Q, z, ) exp c ( ) 2 c ( ) Q where , z denotes the travel-distance, c(ω) the phase velocity, Q is the quality factor in the medium. Source wavelet We assume that the source wavelet and seismic wavelet can be approximated in the frequency domain by Uˆ (0, ) A 4 2 1/ 4 ( )2 exp i 2 2 (2) where, σ is the modulating frequency, A and φ are the amplitude and phase factor, δ is the energy decay factor. At Z 0 the seismic wavelet recorded by receiver 1 can be approximated by Uˆ (0, ) A 4 2 1/ 4 ( )2 exp i . 2 2 (2) At Z z the seismic wavelet recorded by receiver 2 is Uˆ ( z, ) P(c, Q, z, )Uˆ (0, ) 2 z z 4 A exp i 2 2Qc c 1/4 (3) In order to find the relation between Q and the EPIF, we first discuss the EPIF of a seismic wavelet. For a constantphase wavelet propagated for time τ= z/c through a homogeneous anelastic medium, its EPIF is exactly equal to the average Fourier frequency weighted by its amplitude spectrum. f p ( ) 0 f Uˆ ( , f )df 0 Uˆ ( , f )df (4) Using eq.(4 ), we get the EPIF of the source wavelet : 2 2 2 exp 2 4 2 2 2 f p (0) 2 0 2 exp 2 f 2 2 2 (5) df and the EPIF of the wavelet at τ : 2 2 2 exp 2 4 2 2 4 Q f p ( ) 2 2 2 2 4 Q 0 exp 2 f 2 4 Q df 2 (6) We apply Taylor series expansion to Eq.6, and obtain the approximate expression ,Eq.7, with its error estimation, based on analyzing the characteristics of the seismic wavelets which are extracted from zero-offset VSP data and poststack seismic data, and investigating the ranges of the Q-factor in various media. 15 Q 2 2 1 D 2 4 f p (0) f p ( ) 1 2 2 2 D exp 2 2 I1 4 I1 2 (2 ) (7) 2 1 ( x) 2 t2 exp 2 dt x (Jinghuai Gao, et al, 2011, Journal of Computational Acoustic, Vol. 19,No.2) IF extraction Conventional method s(t ) s (t ), sc (t ) s(t ) is (t ) H * * sc is the complex signal of analyzed signal ds (t ) ds (t ) s (t ) s (t ) 1 dt dt f (t ) 2 e(t ) em e(t ) s 2 (t ) s2 (t ) (8) 18 Nosy signal soft threshold, hard threshold Extracting IF of a noisy signal in wavelet domain Step 1: Choose a proper basic wavelet g(t) and transform the signal s(t) into the wavelet domain. The wavelet transform of s(t) is defined as (Mallat, 1999): 1 t b S b, a s(t ) g dt a a (9) Step 2: Determine the range Ω of the energy distribution of the useful contents of the signal s(t) in the wavelet domain. Step 3: Compute the analytic signal sc (t ) of the s(t) in Ω,let sI(t) represent the imaginary parts of sc (t ) : 1 sc (t ) Cg da S t, a a (10) Step 4. Calculate the IF using eq.(8) by replacing s*(t) with sI (t ) Im(sc (t )). 22 Testing Wavelet-Dependence Infinite viscoelestic medium, zero-offset VSP record The shape of four different seismic wavelet Receiver Depth A slab The source and the first receiver are located at the same localization The first three wavelet have constant-phase, and the last wavelet is Ricker wavelet. Wavelet-Dependence Trace number The Q estimated by the four methods when the parameter of the wavelet is 0.65. The interval between adjacent two traces is 5m. Wavelet-Dependence Trace number The Q estimated by the four methods when the parameter of the wavelet is 0.5 Wavelet-Dependence WEPIF LSR CFS PFS Trace number The Q estimated by the four methods when the parameter of the wavelet is 0.35 26 Wavelet-Dependence testing tracenumber The Q estimated by the four methods when the wavelet is Ricker 27 WEPIF methods and applications-VSP Data Figure 1. Forming the slabs for zero-offset VSP data. 28 Calculation procedure a) Split the medium into slabs with thicknesses equal to the space between two successive VSP geophones; b) Approximate the direct wave at the top of the ith slab by a constant-phase wavelet and determine its energy decay factor δi and modulated frequency σi; then calculate ratio ηi = σi /2 πδi c) Calculate the instantaneous amplitude (IA) of the direct waves at the top and bottom of the ith slab, respectively, pick their envelope-peak and determine the traveltime τi in the ith slab; d) e) f) g) Calculate the IF of the direct waves recorded at the slabtop (denoted by ft(t) ) and the slab-bottom (denoted by fb(t) ) Pick the EPIFs of direct waves with fp(0)= ft(tt) and fp(τi ) = ft(tb), then compute the EPIF variation by fp(0)- fp(τi ) the ith slab. Insertσi , δi , ηi and fp(0)- fp(τi ) into eq.(7) and compute the Q-factor for the ith slab. For all slabs, loop from step (b) to (f) until the Q-factor of the last slab is obtained. Examples of Synthetic VSP data b) 0 density: 2.0 g/cc c=1.0 km/s Q=30 Depth (m) source layer 1 200 density: 2.5 g/cc c=1.25 km/s Q=60 layer 2 400 Depth (m) a) density: 3.0 g/cc c=2.0 km/s Q=100 layer 3 600 geophones 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 440 480 520 560 600 0 50 100 150 200 250 300 Time (ms) Figure 3. 3-layer depth model (a) and synthetic seismograms (b). Depth (m) 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 -50 T rue Q LSR CFS CFS WEP IF LSR WEPIF CFS LSR WEPIF -25 0 25 50 75 100 125 150 Q Figure 4. Theoretical Q-factors (black line). Estimated Q-factors from the synthetic VSP data using the LSR method (green line), the CFS method (blue line), and the WEPIF method (red line). Real zero-offset VSP data with six levels c) a) 3380 3380 3400 3400 3420 3420 3440 3440 3460 3460 b) 3380 3380 LSR 3420 3440 3460 T arget reservoirs 3420 3440 3460 3480 3480 -10 800 Depth (m) Depth (m) Depth (m) CFS WEPIF 3400 3400 850 900 950 1000 1050 1100 1150 1200 Time (ms) 0 10 20 Q 30 40 3480 0 100 GR (API) 200 3480 170 230 290 350 AC (us/m) Figure 5. (a) One-shot zero-offset VSP data with six levels, (b) Q-factors estimated by the LSR (black solid line), CFS (green solid line), and WEPIF methods (red line: IF calculated with Hilbert transform method). The GR and AC logs are given in (c). The depth ranges of target reservoirs are indicated by blue crosses in (b) WEPIF methods and applicationsPoststack Data Figure 2. Forming the slabs for poststack reflection seismic data and finding the EPIF: (a) CDP trace, (b) IA of (a), (c) IF of (a), and (d) EPIF. 34 Example of Real reflection seismic data Known Excellent Clastic Reservoirs Known prediction No gas Known Motivation How do we Identify Excellent Clastic Reservoirs Moderate Clastic Reservoirs Poor Clastic Reservoirs ? 37 WEPIF methods and applications-Prestack Data Response of seismic waves for the gas-bearing reservoir and gas-not bearing reservoir Criterion for distinguishing three classes reservoir 38 Wave field from the complex reservoir Laterally inhomogeneous media 4800m Source Receiver 2500m Vp=4600m/s Q=100 600m 100m Vp=4500m/s Q=80 Vp=4200m/s Q=20 Vp=4500m/s Q=80 Vp=4600m/s Q=100 Total 280 shot records with 20m space interval Partially stacked seismic dada A Q=20 B A A B B Q=20 Q=20 Partial stacked profiles for small（top-left）、medium（top-right）、wide（bottom）angle gathers QVA (Q versus angle) attenuation Small-angle Mid-angle Wide-angle Well apparent absorption versus prestack angles Excellent Clastic Reservoirs Class Ⅰ Small angle: strong absorption Wide angle: weak absorption Moderate Reservoirs Class Ⅱ The attenuation estimated for the Partially stacked profile from the small, medium and wide angle Small angle: moderate absorption Wide angle: weak absorption Poor Reservoirs Class Ⅲ Small angle: none absorption Wide angle: none absorption Testing the Criterion Zh10 10.6 104 m3 /Day 召33 Zh17 1.1104 m3 /Day 召17 E 小角度吸收 Small- angle 大角度吸收 The most advantageous gas-bearing Apparent attenuation profiles for S061292 Wide -angle The apparent attenuation of the small-angle profiles near the two wells, Well zhao10 and well zhao17, is strong. But in the wide-angle profiles, apparent attenuation near well zhao 10 and zhao 17 is very different. The former is weak , but the latter is still strong. Our criterion state that the well zhao 10 has an advantage over the zhao 17. Gas well testing productivity shows that well zhao10 has good gasbearing ,the output is ten times as much as well zhao17. Testing the Criterion Apparent attenuation in small-angle is stronger than wide-angle . Our criterion states that the well belong to ClassⅠ. Well-drilling-results: Su46 drills across a thickness of 24m for sands of He8, well log reveals ClassⅠ, Gas well testing productivity is 5.4 104 m3 /Day . SD46 Small angle Medium angle Wide angle Apparent attenuation profiles (S077003) E Apparent attenuation profiles(S076272 ) 鄂20 N Small angle Wide angle Apparent attenuation in small-angle is stronger than that in wide-angle, but the difference of them is not larger. For this case, our criterion states the well is Class Ⅱ. Well-drilling-results: Well E20 drills across a thickness of 18.1m for sands of He8，well log reveals Class Ⅱ, Gas well testing productivity is 2.5 104 m3 /Day . . S60 SE Small angle Medium angle Wide angle Absorption attenuation profiles ( L051735 ) Well-drilling-results: Well Su60 is water well（25m3/d), not gas. The apparent attenuation is more stronger in small-angle than that in the wide-angle. In this case, our method does not give an identification. Pre-drilling-prediction:The apparent attenuation profiles show that the absorption at small-angle is strong ,but the apparent attenuation at wide-angle is weak. Based on our criterion, the well has good Physical Properties and gas-bearing, and it belongs to Class Ⅰ. Well-drilling-results: Su172 drills across a thickness of 23.6m for sands of He8，well log revealed that it belong to Class Ⅰ. Gas well testing productivity is 4.14 104 m3 /Day E Su172 Small angle Attenuation at small angle in He8 Wide angle Absorption at wide angle in He8 Absorption attenuation profiles (L076763 ) Field result in angle domain –prediction before drilling As the angle increases, the absorption is weak. It is predicted as Class Ⅰby post-stack. But it is predicted as Class Ⅱby pre-stack data. Drilling-result shows that the reservoir belong to Class Ⅱ. S134 Small angle Attenuation at small angle in H8 Medium angle Attenuation at medium angle in H8 Wide angle Attenuation at Wide angle in H8 Absorption attenuation profiles(L 051735 ) SE Results Workload for processing: 13 lines, total 831km Workload for prediction： 55 wells Testing:26 wells(Correct rate of 70%) Predict before drill: 29 wells (Correct rate of 69%) 5 Conclusions We propose the WEPIF method for estimating Q. A test using synthetic VSP data shows that the WEPIF method is more stable, more convenient for selecting parameters, and less sensitive to the interference from interface reflections than the LSR and CFS methods. The results, in which the WEPIF method is used for zero-offset VSP data and post-stack seismic data, show that this method is valid and has great potential for seismic attenuation estimation and gas reservoir characterization. The Q analyzing method for pre-stack multi-angle partially stack profile can be used to identify the ClassⅠ, Class Ⅱand Class Ⅲ of reservoir which can not be done with post-stack data. 50