Exploring the relationship between uncertainty of AVA attributes and rock information

Amplitude versus Angle (AVA) attributes include information about rock properties. Using a dataset from South America, we performed a multiple realization method to get multiple equal-probable AVA intercepts, gradients, and their products. We generated a 3D histogram to evaluate the variability of those AVA attributes. In the same area, we chose a 2-D section by matching it to three wells. Then we calculated the shale volume along these three wells and found the well with low shale volume has high AVA uncertainty, which made us guess the low shale/sand ratio may cause high AVA uncertainty. The further work need to be done is to use more real data to exam our conjecture, namely, whether there exist an empirical relationship between AVA uncertainty and rock information, such as shale volume, impedance or velocity. INTRODUCTION Uncertainty is an inherent problem existing in velocity analysis. It is important for geophysicists to assess the variability of the velocity quantitatively. As an alternative to a common geostatistical method (Isaaks and Srivastava, 1989), Clapp (2000; 2001) introduced multiple realization method for complex operators. Clapp modified the standard geophysical inversion technique by adding random noise into the model styling goal to achieve multiple realizations. By comparing and contrasting the equal-probable realizations, the variability can be evaluated. Since the subsurface image is obtained based on the new velocity model, the uncertainty of velocity model will cause the uncertainty of amplitude information we can acquired from image (Mora and Biondi, 2000). Using the multiple realization method, Clapp (2002) showed how the velocity uncertainty affected the amplitude information. Amplitudes carry important information about rock properties. Amplitude variation with offset (AVO) is a widely used technique in petroleum industry because AVO anomalies often indicates hydrocarbon existence. A good review of AVO analysis is provided by Castagna (1993a). Since AVO is dependent on intrinsic rock parameters such as compressional-wave velocity, shear-wave velocity, density, anisotropy and attenuation, AVO can be used to assess information for rock properties, such as lithology, porosity and pore fluid content. Castagna (1993b) provide a rock physics framework for AVO analysis. 1email: [email protected], [email protected] 259 260 Chen and Clapp SEP–112 The relationship between AVO and rock properties make us guess there may exist empirical relationships between AVO uncertainty and rock information. For example, if we get high variance of AVO attributes (which can be evaluated from multiple realizations) at specific subsurface areas, we can conjecture that there may be some change in rock information in the same area, such as impedance, velocity or shale/sand ratio. In this paper, we explored such relationships. Instead of extracting amplitude variations with offset, we adopted amplitude variation with angle (AVA) analysis because realistic velocities usually break the simple relationship between offset and angle. The dataset we used was from South America. We evaluated the variability of AVA attributes by using a 3-D histogram. A 2-D section was extracted and shale volume along the wells in this section were calculated. We found the well with low shale volume has obvious higher AVA uncertainty than other two wells, which made us conjecture the low shale/sand ratio will cause high AVA uncertainty. The further work need to be done is to use more real data to exam whether our guess is true or there exist other empirical relationships between AVA uncertainty and rock information, such as shale volume, impedance or velocity. METHODOLOGY TO EVALUATE THE UNCERTAINTY OF AVA ATTRIBUTES We will use multiple equal-probable velocity models to get multiple images. From those images, we can extract angle gathers and get intercept A and slope B (Gratwick, 2001). By comparing and contrasting the multiple realizations of these AVA attributes, we can access their variability. Using multiple realization method to get multiple equal-probable velocity models Regularized geophysical inversion problems include two fitting goals: data fitting and model styling. They can be written as: 0 ≈ rd = d−Lm (1) 0 ≈ rm = Am (2) An ideal regularization operator A should be the inverse model covariance. In practice, according to the difficulty to get the explicit model covariance, A is usually approximated as Lapacian, PEF or steering filter. Generally, the regularization operator only describes the two point statistics. The first order statistics, spatial variance, is not included in it. Like in geostatistics, we can add normal noise vector η into model styling goal so that we can get the comparable variance in poorly determined regions as in well determined regions (Claerbout, 1999; Clapp, 2000). The fitting goals including both first and second model statistics can be written as: 0≈ rd = d−Lm (3) σmη ≈ rm = Am (4)