Abstract: Introduction

Transcription

1 AVO and Seismic Waveform Inversion in the Plane Wave Domain: Application to Gas Hydrate Data Mrinal K.Sen, Paul L. Stoffa, and Ganyuan Xia Institute for Geophysics The University of Texas at Austin 4412 Spicewood Springs Road Bidg. 600 Austin TX Abstract: AVO analysis has been used with some success in seismic exploration to directly detect the presence of hydrocarbons. AVO inversion essentially implies a least squares fitting of reflection coefficients (seismic amplitude) as functions of source-receiver offsets in the moveout corrected seismograms, assuming that the background velocity is known accurately. Unlike conventional approaches, we carry out the background velocity and AVO inversion in the plane wave (intercept time-ray parameter or T-p) domain. Normal moveout analysis in the plane wave domain results in interval velocity estimates and the T-p data are closer approximations to the plane wave reflection coefficients. Having determined background velocity and fractional changes from an AVO inversion, we carry out a full wave from inversion in which we use full elastic waveform modeling that includes all internal multiples and converted waves. We apply this multi-stage seismic waveform inversion approach to a suite ofcmp gathers from a 2D seismic line collected offshore of the east coast of the United States; a region in which all occurence of gas hydrates has been reported. Gas hydrates have the economic potential of being tapped as a fuel source and also have the potential to act as a greenhouse agent if freed into the atmosphere. In seismic sections, the base of gas hydrate zone is marked by bright, highamplitude relfections, which follow the seafloor topography and are called bottom-simulating reflectors (BSR). BSRs have negative polarity with respect to the seafloor reflection and in a common shot or a CDP gather, the amplitude increases with offset. Our analysis was aimed at deriving a high resolution seismic velocity structure for the gas hydrates and sediments below. At locations where a BSR exists, we identify a low velocity zone that coincides with the BSR. We also identify several thin low velocity zones beneath the BSR, interpreted to be due to the presence of free gas. We compare and contrast our results with the velocity function derived from zero-offset VSP data collected during the ODP drilling Leg at holes 997 located NE of our seismic line. The general trend of the two independent estimates of velocity is in good agreement. The low- P wave velocity zones show no change of shear wave velocity, indicating the presence of free gas. This was confirmed by drilling in the nearby area. However, the VSP-derived velocity model was obtained by the application of smoothing in the traveltime inversion of the VSP data in which only a smooth velocity model was sought. The resulting model shows a nearly 200m thick low velocity zone (continuous free gas) which may have been caused by artifacts due to smoothing. Unlike the VSP model, our result shows several thin low velocity layers. Introduction Estimation of rock properties from remote sensing data such as seismograms remains an active area of research. Most seismic analysis is based solely on traveltime information. However, better constraints on the elastic properties of the subsurface rocks can be obtained by making use of amplitude and waveform information in the seismic traces, in addition to traveltime

2 data. A direct inversion method such as layer stripping (Yagle and Levy 1983, Clarke 1984) suffers from the fundamental limitation that it becomes unstable and the error accumulates with depth. That is why model-based inversion methods (e.g., Sen and Stoffa 1995) have gained popularity in the exploration geophysics community. In model-based inversion (Fig. 1), theoretical or synthetic data (seismograms) are generated for an assumed earth model and compared with the recorded seismograms. If the match is acceptable, the assumed earth model represents the solution. If not, the model is perturbed, the synthetics are recomputed and again compared with the recorded data. This iterative forward modeling procedure is repeated until an acceptable match is obtained between the recorded and synthetic data. Thus inversion is viewed as an optimization process in which a model is sought that best explains the observations. In the first part of the paper, we will review some of the fundamental issues related to seismic waveform inversion and recommend a strategy to improve computational speed while retaining accuracy. The second part of the paper estimates the properties of gas hydrates by making use of the recommended method. Fig 1. A schematic diagram explaining parameter estimation method in Geophysics. IN tghe seismic applications, this would involve generating synthetic seismographs for an assumed earth model and comparing those quantitatively with the field seismograms. The model update procedure is done automatically with the use of optimization methods(local and global) Earth model assumption : ID, 2D or 3D, Acoustic, Elastic, Anisotropic. Data Domian : Offset-time (x,t), plane wave i.e., intercept time-ray parameter (T,p) domain or frequency-wavenumber(f-k) domain. Forward modeling method: Reflectivity (ID), Finite Difference or Ray-theory. Optimization Method : Local optimization (e.g., iterative least squares etc.). Global Optimization (e.g., Simulated Annealing or SA, Genetic Algorithm or GA) or Hybrid Method (Combination of local and global optimization methods). Uncertamtiy Issues: Most seismic waveform inversion problems result in non-unique estimates of model parameters. Thus it becomes important to assess uncertainties in the derived results. A complete description of each of these topics is beyond the scope of this paper. We realize that a true earth model is three-dimensional and anisotropic and the waveform inversion problem is highly nonlinear resulting in error functions that are multi-modal. Therefore, ideally, one should make use of global optimization methods in which each forward model calculation incorporates full waveform 3D anisotropic modeling. Applications based on this approach are computationally prohibitive. We therefore seek methods that are fast and approximate the earth response reasonably well, so that seismic waveform inversion can be applied to seismic lines on a routine basis. We take the following steps towards achieving our goal: Earth Model Assumption: Even though the earth model is truly three-dimensional which may also be anisotropic, we assume that the earth is locally one-dimensional (properties varyig with depth alone) and can be described by compressional wave velocity (a), shear wave velocity (B) and density (p) of rock layers with varying thickness. The Algorithm: Seismic Waveform Inversion Issues and AVO For seismic waveform inversion we must make the following choices: 2 Data Domain: We transform the data from the (x, t) to the (T,p) domain. The plane wave transformation automatically corrects the data for geometrical spreading without having to know the velocity model. For ID earth models, reflec-

3 tion events appear as ellipses. An NMO analysis (which involves flattening of the ellipses) results in interval velocity estimates rather than RMS velocities. Using the ID earth model assumption, amplitude variations in the plane wave transformed data are due to changes in the reflection coefficients with angle (or offset). Thus plane wave data are ideal for AVO analysis, while processing in the (x, t) domain introduces several levels of approximations to generate data required for AVO inversion. The plane wave transformation, however, required recording of large aperture data with fine spatial sampling and careful choices of taper parameters to avoid artifacts from the plane were transfromation. Forward Modeling: For horizontally-stratified earth models, the reflectivity method originally proposed by Fuchs andmuller (1971) and pioneered by Kennett (1983) is ideal for computing full waveform synthetic seismograms that include all multiples and converted waves. The equations of motion and the constitutive relation are first transformed by application of a Fourier- Hankel transformatio, which results in a system of first order ordinary differential equations (ODEs) in depth z, as a function of frequency (CT) and ray-parameter (p). The system of ODEs can be solved for each G) and p by the well known method of propagatro matrics. Kennett s reflection matrix approach is used to design an algorithm that is unconditionally stable. The plane wave ((o,p) responses are summed to generate seismograms in the (x, t)domain because it requires computation of several hundreds of (w, p) seismograms. Rather we transform the field data to the plane wave domain and compare those with plane wave synthetics. NMO, AVO and Optimization : Seismic waveform inversion that involves comparing synthetic seismograms for each trial model with the field seismograms, is a highly nonlinear problem (Sen and Stoffa 1991 ). The objective function is multi-modal and therefore, requires the use of a computationally-intensive global optimization method such as SA and GA (Stoffa and Sen 1991). In order to develop a method that is computationally tractable, we recognize that there are two kinds of attributes that seismic data provide: traveltime and amplitudes. Traveltimes are related to the long period (smooth or slowly varying in depth) variation of the velocity. The relationship between the two is nonlinear. However, the seismic amplitudes are quasi-linearly related to the short period (rapid) impedance changes. The distinct nature of the two kinds of information available from seismic data favours an approach that treats the traveltimes and amplitudes separately, and combines the two to get a starting model- for the final full waveform inversion. A full waveform inversion method based on this approach has been described in detail by Xia et al. (1998 a). The method is described schematically in Figure 2. Our first goal is to find a smooth background velocity that will result in predicted travel Fig 2. The philosophy of multi stage seismic waveform inversion. The seismograms and corresponding velocity model are shown in the right hand panel. The velocity model can be found in two steps. First the background(low frequency) velocity model is found by NMO in the tau-p domain. Then the high frequency perturbations are obtained by AVO inversion. 3

4 times that best match the travel times of primary reflection events. The relationship between the travel time and interval velocity has an exact expression in the intercept time-ray parameter (wp) domain t n (p)=2 å n i=1 Z i q i Where t n is the intercept time of the n th layer,p is the ray parameter, and Z i is the thickness of the i th layer. The vertical slowness, qi, is related to v i the interval velocity of the i th layer, ie., q i = Ö(1-p 2 v 2 i ) The interval velocity as a function of twoway time is usually resolved in a top down fashion (Stoffa et al. 1992). We use the flatness (horizontal alignment) of events after a T-p normal moveout correction as the inversion objective and use a nonlinear optimization method called Very Fast Simulated Annealing (VFSA) (e.g.. Sen and Stoffa 1995) for finding a ID smooth velocity model that NMO-corrects the data the best. Linearized reflection coefficients are derived using the assumption that the contrast in elastic properties at the interface weak. Due to these limitations, a combined model (obtained from the linearized AVO results and the VSFA background velocity estimate) is often not adequate to reproduce all the features observed in the seismograms. Consequently, we recommend using the combined model as a starting model in a full waveform inversion. Our recommended algorithm is described in Figure 3. A detailed description of the algorithm, along with a very realistic synthetic example, can be found in Xia et al. (1998a). The next step is to apply an AVO inversion to estimate the fractional changes in a, R and density p. For this purpose we make use of the following well-known formula for the linearized reflection coefficient (Aki and Richards.o ) of the P-wave Where R is the reflection coefficient of P-wave, (x is the average P-wave velocity, B is the average S-wave velocity, p is the average density, Q is the average of angle of incidence and angle of transmitted P-wave, p is the ray parameter, and Ace, A B and A pare the changes in a, B and p across the interface, respectively. In our application we make use of prior information to relate (x to 6 and a to density p. Often a two-step procedure as described above may be adequate for many applications, However, we identify the following limitations of the linear AVO: AVO analysis makes use of a primaries-only reflection model. Therefore internal multiple reflections and converted waves are not taken into account. Fig 3. Flowchart of the combined inversion algorithm. The inversion consists of three stages: estimating background velocity from travel time, estimating perturbation to the background from amplitude, and combining the results from the first two stages to estimate rock properties from the full waveform data. Finally, we note that such an inversion will result in a best-fit model. However, many more models may explain the data equally well. We can estimate the uncertainties in our answer by a non-linear error analysis based on Gibbs sampler as described in Sen and Stoffa (1996). 4

5 Gas Hydrates Flow restrictions in high-pressure natural gas pipelines led to the first discovery of naturally occurring gas hydrates (Deaton and Frost 1946). Gas hydrates are crystal like solids consisting of water and small molecules of gas (mostly methane) (Stoll and Bryan 1979; Sloan 1990). The following factors control the formation of gas hydrates: Pressure, Temperature, and Gas concentration in the sediments. Hydrates are found in the upper few hundred meters of sediments below the seafloor in continental margins with a high rate of sedimentation in water depths greater than 500 m. The depth at which this occurs marks the lower of the existence of methane as a hydrate. Their presence has been reported in the continental margins of the world s oceans (see Shipley et al for examples of data from different parts of the world). They are primarily identified in seismic sections by the presence of a reflection event with the following properties: High amplitudes in the stacked section. Negative polarity with respect to the sea-floor relection. Increase in amplitude with offset in the prestack data, and Parallel to the seafloor often cutting across the bedding planes. The high amplitude reflection occurring parallel to the seafloor are called Bottom Simulating Reflectors(BSR). The enormous economic potential as a fuel source and the potential as a green house agent if freed into the atmosphere have generated huge interests among the scientific community and industry. Globally, the carbon stored in gas hydrates is estimated to be about 10 4 gigaton, which is of the same order as the current estimate for other fossil fuel deposits (Kvenvolden 1988). The USGS estimate for the area offshore South and North Carolima is more than 1300 trillion cubic feet of methane gas, which is more than 70 times the 1989 gas consumption of the United States. Seismic Velocity of Gas Hydrates Lab measurement (Stoll and Bryan, 1979) established that gas hydrates have a higher com Fig 4: Location map of Carolina Trough area(modified after Verala, 1996). BSR and ODP Leg- 164-Sites are indicated(dillon and Paull, 1983) 5

6 hydrate bearing sediments can lie anywhere within the range km/s. The high velocity is speculated to be causing BSRs, due to the impedence contrast between hydrates and normal sediments with or without free gas. Fig 5. A stack section of line BA-6 from Carolina Trough. Note the bright reflections and the location of BSR. pressional wave velocity and lower thermal conductivity, contrary to the common perception that hydrates have properties similar to the frozen sediments (Stoll and Bryan, 1979). The compressional wave velocity of pure hydrate is believed to be in the range of km/s, while that of the hydrated sediments depends on the hydrate concentration in normal water-saturated sediments and the form of hydrate, i.e., diffuse crystals of solid framework. Assuming that the compressional wave velocity of water saturated sediments lies in the range km/s, that of the It is now well recognized that high resolution estimates of material properties such as compressional wave velocity, etc. are needed to fully characterize the nature and causes of the formation of gas hydrates and to make predictions of gas content (e.g., Wood et al. 1994) Conventional x-t stacking velocity analysis is insensitive to the details of the velocity function. A full elastic waveform inversion is required to estimate in detail the elastic properties from seismic data. Carolina Trough Data: Line 6 We now summarize the results from inversion of seismic data from one seismic lines (Line BA-6) collected along the East Coast of the United States in the Carolina Trough area. Here we apply the multi-stage AVO/seismic waveform inversion method as summarized in an earlier section and described in detail in Xia et al. (1998a). The location of the seismic line is Fig 6. Background velocity model obtained from tau-p NMO analysis. The BSR is marked in the section. Note the smooth increase in velocity with depth above BSR. 6

7 shown in Figure 4. Location of the ODP holes (Leg 164) 994, 995 and 997 are also shown in the diagram. Note that the three holes are close to the Line 6. Detailed description of the data and processing methods are described in Wood et al. (1994) and Xia et al. ( 1998 b) and will not be repeated here. We only mention that care was taken to preserve true amplitude in our (T,p) data are our input to background velocity estimation, AVO and seismic waveform inversion. Figure 5 Shows a stacked section of the line, BA-6, which was acquired in the Blake ridge area where methane hydrates are known to exist. Note the bright event that parallels the seafloor caused by the BSR in the stacked section. The result from the first step of our inversion, i.e., the background (smooth) velocity model is shown in a color display in figure 6. The velocity model shows a general smooth increase in velocity with depth. We note the following features of the derived velocity model: We do not see any noticeable abrupt increase in velocity at the seafloor or anywhere between the seafloor and the BSR. Although background velocity estimates would generally be smooth, any substantial increase (e.g., 1.5 to 3.5 km/s), if present, would be noticeable even in such low frequency estimates. Although we observe an increase in velocity with depth below seafloor, the values do not exceed 1.9 km/s above BSR. For most water depths in this line, hydrates can occur in sediments right underneath the seafloor and continue until the depth of the BSR. We are unable to locate any sharp velocity contrast and thus the top of the hydrate zone cannot be easily identified. We therefore conclude that the hydrate in the sediments, if any, is gradational. We also note that high velocity estimates to the west of CMP 1501 (CMP CMP 1501) are due to artifacts caused by weak reflections. The P-wave velocity in the sediments above the BSR is below 1.9 km/s indicating that the hydrate concentration in the sediments is rather low (less than 1% assuming a velocity of 1.7 km/s of water saturated sediments) since the velocity is closer to that of water saturated sediments. The background velocity model does not answer the question of the cause of the BSR, since these velocities are derived from traveltimes alone and do have the resolution to address the issue. Fig 7. High resolution seismic velocity profile derived at different CDP locations. Note the low velocity zones at and below BSR. 7

8 Figure 7 displays the P-waves velocity profiles (high resolution) derived at ten CMP locations along the line. These were derived from full waveform inversion which involves AVO followed by full waveform modeling that includes all converted waves and internal multiple reflections. These profiles have the following characteristics: Low velocity zones are observed between CMP 1001 and The shallowest and the weakest low velocity zone closely follow the topography of the seafloor and can thus be identified with the BSR. The low velocity zones disappear beyond CMP 1451 (southwest of tile line). There are several thin low P-wave velocity zones below the BSR. The low velocity zones occur over a thick zone in the northeast part of the line (CMP 1001) and gradually decrease in thickness as we move southwest. The thin low velocity zones finally coalesce near CMP 1401, where we observe the brightest amplitude in the seis Fig 8: P-Wave velocity profile derived from VSP at Hole 997(Holbrook et al, 1997) compare this with the velocity profile corresponding to CMP 1001 mic section. All these low P-wave velocity zones show no variation in shear wave velocity and coincide with zones of negative fluid factor, indicating the occurance of free gas (Xia et al. 1998b). The robustness of the low velocity zones was confirmed by a nonlinear error analysis described in detail by Xia et al. (1998b). Comparison with VSP derived velocity model: Figure 8 shows a plot of the P-wave velocity model derived from VSP data collected during Leg 164 at Hole 997 (Holbrook et al. 1997). Notice that above a depth of 400 m below the seafloor(i.e above BSR) there is gradual increase in velocity with depth. The velocity in the hydrated sediment does not exceed 1.7 km/s. This result is consistent with our inversion results. However, Figure 8 shows a very thick low velocity zone (nearly 200m) below the BSR. The velocity model at Hole 997 can be compared without result CMP Unlike the Hole 997 velocity model, we observe several thin low velocity zone due to smoothing applied to the inversion of travel time data. Interpretation of the results Owe results clearly indicate that the BSR is caused by a low velocity zone that is indicative of free gas at the base of hydrates. The hydrated sediments do not show significant increase in the P-wave velocity, indicating that the methane content in the hydrated sediments is rather low. On the other hand, we identify several thin layers of gas below the BSR, which may contain significant amounts of free gas. Estimation of free gas below the BSR would require extensive modeling using a procedure similar to that described in Bangs et al. (1993) combined with full waveform modeling, such as the reflectivity method described here. However, our result suggests that there is a large amount of free gas trapped beneath the BSR and that the hydrate effectively plugs the permeability along the BSR such that it acts as a seal preventing the upward migration of the free gas. The sediments in this region consist mainly of a monotonous sequence of nanno fossil rich clays that were deposited from contour currents at rates varying from 40m/My in the Pleistocene to m/my for the Miocene. 8

9 Pliocene sequence. Bacteria in the sediments may have formed some of the gas but some may be derived from deep strata off the Carolina Trough. ODP drilling at Leg 104 at Sites 994, 995 and 997 found that finely disseminated gas hydrates occupy a minimum of 1% of the sedimentary section between 200 and 450 m below seafloor (Matsumotoet al. 1996). Sites 994,995 and 997 were drilled to mbsf on the Blake outer ridge and penetrated through the predicted depth of BSR into the sediments below. Cores from all three sites were found very gassy and free gas were found dispensed throughout a zone of a few hundred meters thick below the gas hydrate bearing zone. Thus our inversion results are consistent with the drilling discoveries. Discussion and Conclusions We carried out detailed estimates of the seismic velocity structure above and below the BSR along Line BA-6 in the Carolina Trough using a seismic waveform inversion that is staged over spatial frequency. The results from the inversion are very encouraging and can be used in detailed mapping of hydrates and free gas (if any) in a geologic area. Our method, however, makes the assumption of a locally one-dimensional earth model and will therefore fail in areas with complex geologic structures. The interpretation of the results in terms of gas content requires a rock physics model that is based on fluid saturated porous media. Our future work will involve application of waveform inversion of data from the entire region, development of a rock physics model (based on equivalent media theory) appropriate for the geology, estimation of gas concentration and integrated reservoir characterization to aid in future drilling and production plans. Acknowledgements This work was financially supported by the National Science Foundation, grant number OCE We thank Warren Wood, Nathan Bangs, Milo Backus, and Tom Shipley for many helpful discussions. Reference Aid, K and P.G. Richards, 1980,euantitative Seismology, W.H. Freeman and Co. Andreassen, K P.E. Hart, and A. Grantz, 1995, Seismic studies of a bottom simulating reflection related to gas hydrate beneath the continental margin of the Beaufort sea, J. Geophys. Res., 100, 12, Bangs, N.L.B., D.S. Sawyer, and X. Golvovehenko, 1993, Free gas at the base of the gas hydrate zone in the vicinity of the Chile triple junction. Geology, 21, Clarke, TJ., 1984, Full construction of a layered elastic medium from P-SV slant stack data, Geophys. J.R. Astr. Soc., 78, DiUon, W.P., and C.K. PauU, 1983, Marine gas hydiates-n: Geophysical evidence, in Natural gas hydrates: Properties, occurrences, and recovery, Cox, J.L., ed., London, Butterworths, Fuchs, K.and G. MuUer, 1971, Computation of synthetic seismograms with reflectivity method and comparision with observations, Geophys. J.R. Astr. Soc.,23, Holbrook, W.S., H. Hoskins, W.T. Wood, R.A. Steffen, D. Lizarralde, Leg 164 Science Party, 1996, Methane hydrate and free gas on the Blake Ridge from Vertical Seismic Profiling, Science, 273, Hyndman, R. D G.D. Spence, 1992, A seismic study of Methane hydrate marine bottom simulating reflectors, J. Geophy Res., 97, Rven-volden, K.A., 1988, Methane hydrate- a major reservoir of carbon in the shallow geosphere? Chemical Geology, 71, Kvenvolden,K.A andbamard,la., 1983, Gashydratesofthe Blake outer ridge. Site 533 Deep Sea Drilling Project Leg 76, in R.E. Sheridan, F. Gradstein et al (eds.), Init. Rep. Deep Sea Drill. Proj., 76,U.S. Govt. Print. Off., Washington, D.C., Matsmioto, R., C. Paull, and?. Wallace, 1996, 9

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