Estimation of AVO attributes sensitivity to velocity uncertainty using forward modeling: a progress report

We investigate the sensitivity of AVO attributes to uncertainty in migration velocity in a synthetic dataset. The synthetic data was built using a earth model with typical rock properties from a real North Sea turbidite field. The model includes a thick overburden layer with complex velocity anomalies. We examine the sensitivity of AVO response due to the presence of this complex layer and quantify the influence of migration velocity errors in the AVO signature. Results show that AVO gradient attribute is more sensitive to velocity errors than AVO intercept attribute. For velocity errors up to 5% we see a maximum of AVO intercept errors of 34%, whereas for velocity errors of only 1%, the inversion of AVO gradient attribute has an error of 185%. Further work is needed to evaluate the influence of observed boundary artifacts on these results. INTRODUCTION The variation of seismic reflection coefficients with offset can be used as a direct hydrocarbon indicator (Ostrander, 1984; Swan, 1993), which is supported in the AVO analysis theory. AVO analysis requires previous prestack migration of the data, and velocity estimation is a key factor for this imaging problem. Velocity estimation affects the AVO response because it modifies the position of the events and the resulting amplitude values (Grubb and Tura, 1997). Because of the difficulty of estimating velocity models in complex areas, it is important to understand the sensitivity of AVO attributes to variation in velocity models. Mora and Biondi (1999) explore the relationship between velocity uncertainty and AVO-related seismic attributes using a real dataset. A conclusion from that work is that is important to investigate this problem using a synthetic model that allows more control over the data, which is needed to obtain a quantitative measure of the uncertainties. In this work we do seismic modeling using typical rock properties from a real North Sea turbidite field. As is mentioned in (Avseth et al., 1999), this field has been problematic because of complex sand distribution and non-reservoir sand anomalies. Two of the three most recent exploration wells failed to encounter reservoir sands in locations where poststack seismic amplitudes indicated reservoir sands. Avseth et al. (1999) suggest that AVO analysis in this field can help to discriminate sands from other lithofacies. However, because of the presence of 1email: [email protected], [email protected] 205 206 Mora & Biondi SEP–103 complex velocity anomalies in the overburden, it is desirable to have a estimation of the uncertainty in the AVO response; in other words, how reliable is the lithology discrimination from AVO analysis given the presence of a complex overburden zone? In this paper, we do forward modeling, simulating an earth model with an overburden that includes complex velocity anomalies. We generate several migration-velocity realizations by introducing coherent percentage velocity errors in the overburden zone of the original velocity model. We migrate the synthetic data using each velocity realization, and measure the variability in the resulting gradient and intercept AVO attributes that results from the velocity error. ELASTIC MODELING To investigate the effect of velocity anomalies in AVO attributes, we generated two synthetic datasets using a finite-difference elastic modeling program. Below is a description of the earth models simulated and the resulting synthetic data. Models The two 2-D synthetic datasets were computed assuming an earth model that includes A 1.8 km thick overburden. A 0.2 km cap rock layer (shale). A 0.2 km target zone with three different lithologies for comparison (cemented brine sands, cemented oil sands, and tuff). Figure 1 shows the P-wave velocity for both models. In model 1, the overburden contains two flat layers with constant elastic properties on each layer, whereas model 2 includes a zone of complex velocity anomalies in the overburden. The rock properties for the model were taken from real well logs of a North Sea field. Typical values for different lithologies at this field are listed in Table 1. Lithology Vp (km/s) Vs (km/s) (g/cm3) Shale 2.4 0.95 2.25 Cemented brine sands 3.1 1.55 2.15 Uncemented brine sands 2.6 1.3 2.1 Cemented oil sands 2.9 1.6 2.05 Uncemented oil sands 2.35 1.33 2 Volcanic ash (tuff) 2.75 1.23 2.2 Limestone 4 2 2.4 Table 1. Typical rock properties for different lithologies at the North Sea. SEP–103 AVO sensitivity 207 Figure 1: P-wave velocity models used to generate the synthetic data. Model 1 (top): overburden with flat layers, model 2 (bottom): overburden with velocity anomalies. cmora1-model [CR] 208 Mora & Biondi SEP–103 Average values for overburden properties in the field are Vp 2.2 km/s, Vs 0.75 km/s, 2.15 (g/cm3). In model 1, overburden properties above the flat interface were taken to be the average values indicated above; overburden properties below the interface were the average values with a 10% increase. For model 2, we introduced lateral velocity anomalies by including a smoothed sinusoidal interface between the two layers. Synthetic seismograms The synthetic data was generated using an explosive source and a Ricker2 wavelet with a fundamental frequency of 22.5 Hz. The source/receiver offsets ranged from 16 m (minimum offset) to 3.6 km (maximum offset). Figure 2 shows a shot gather at in-line location=5 km for each model; note that the events in model 2 are not perfect hyperboles due to the lateral velocity variations. Figure 2: Shot gather at in-line location=5 km. Left: model 1, Right: model 2 cmora1-shot [CR] Preprocessing Divergence correction, coherent noise suppression, and CMP sorting were applied to the data before 2-D prestack depth migration. In order to compensate for spherical divergence, we scaled the data in the time axis using a function trace(t)= trace(t)*t. Coherent noise suppression was also applied to eliminate the P-wave and S-wave first arrivals. To eliminate the P-wave first arrival, we applied a linear outer mute to the data. The S-wave arrival was suppressed by applying a 2-D dip filter. Finally, the data was windowed to extract the CMPs with maximum SEP–103 AVO sensitivity 209 offset coverage and sorted by CMP location. Figure 3 shows the zero-offset section of the resulting data. Figure 3: Zero-offset section of the resulting synthetic data. Left: model 1, Right: model 2 cmora1-zero-off [CR] PRESTACK MIGRATION From the original velocity model, we generated several velocity model realizations by applying a percentile perturbation at the overburden zone. Using each velocity realization, we applied a 2-D prestack wave-equation migration (Prucha et al., 1999) to the synthetic data. The resulting image is a function of the offset ray parameter phx , which is related to the aperture angle , the dip along the in-line direction, and the velocity function V (z,m), as follows: phx 2sin cos V (z,m) (1) Figure 4 shows the result of applying prestack wave-equation migration to the synthetic data, using the original velocity models (0% perturbation) . AVO INVERSION The physical relation between the variation of reflection/transmission coefficients with incident angle (and offset) and rock parameters has been widely investigated. This relation is established in the Zoeppritz equations, which relate reflection and transmission coefficients for plane waves and elastic properties of the medium. Because of the nonlinearity of the Zoeppritz equations, several approximations have been generated, such as those presented by 210 Mora & Biondi SEP–103 Figure 4: Result of applying prestack wave-equation migration to the synthetic data using the original velocity model. Left: model 1, right: model 2. cmora1-mig [CR] SEP–103 AVO sensitivity 211 Aki and Richards (1997) and Shuey (1985). The simplified versions of Zoeppritz equations allow the computation of AVO inversion to estimate elastic parameters from the observed reflection amplitude variation with angle. Equation (2) from Castagna and Smith (1994) is a version of Shuey’s approximation for the P-wave reflection coefficient as a function of angle of incidence, which is linear in sin . This equation characterizes the reflection coefficient, at normal incidence, and at intermediate angles (0 30 degrees), R( ) A B sin (2)