Geostatistically modeling topographicallycontrolled deposition of sub-seismic scale sandstone packages within a mass transport dominated deepwater

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1 Geostatistically modeling topographicallycontrolled deposition of sub-seismic scale sandstone packages within a mass transport dominated deepwater channel belt Lisa Stright 1, Anne Bernhardt 2, and Alexandre Boucher 3 1 Department of Geology and Geophysics, University of Utah 2 Universität Potsdam, Potsdam, Germany 3 Advanced Resources and Risk Technology LLC Abstract Geostatistical modeling methods for deep-water depositional systems, which provide a framework to characterize spatial uncertainty, have generally focused on channel-levee-overbank-lobe models. However, these models do not fit all deepwater depositional settings. For example, irregular surface topography of subaqueous mass-transport-deposits (MTDs) played a primary role in controlling the deposition of sand from turbidity currents in the vicinity of the Puchkirchen field in the Molasse Basin, Upper Austria. The MTD topography created mini-basins in which sand accumulated in irregularlyshaped deposits that are not consistent with a channel-levee-overbank-lobe paradigm. These accumulations are difficult to laterally correlate using well-log data due to their variable and unpredictable shape and size. Prediction is further complicated because the sandstone bodies typical of this setting are difficult to resolve in seismic-reflection data. To overcome these challenges related to the lack of reliable interwell prediction methods, a new geostatistical modeling approach is presented. The modeling process simulates debris flow lobes followed by turbidites that fill in the accommodation on top of and between debris flow lobes. Modeling these large scale debris flow lobes is further justified by the fact they are more reliably classified with the coarse scale seismic attributes than the reservoir facies. As such, leveraging the seismic data to predict the non-reservoir events (debris flow deposits) provides a pathway to predict the locations of significant sandstone accumulations as validated by previously drilled areas. 1

2 1. Introduction Development of geostatistical models for deep-water depositional systems has focused on either sinuous channels that are confined by levees or erosional surfaces (Larue and Hovadik, 2006; Labourdette et al., 2007; Pyrcz et al., 2008; McHargue et al., 2010; Sylvester et al., 2010) or basin-floor or overbank lobes associated with loss of confinement from sinuous channels (Pyrcz et al., 2005; Wellner et al., 2005; Zhang et al., 2009). While broadly applied in many geostatistical modeling studies (e.g., Caers et al., 2003; Liu et al., 2004), these models do not model all deep-water depositional processes. For example, a channel-levee model would not accurately predict sand deposition when it is controlled by the surface topography of subaqueous mass-transport-deposits (MTD) rather than sinuous channel morphologies (e.g., Armitage et al., 2009; Bernhardt et al., in review). As a result, the shape, size and location of sandstone accumulations are difficult to easily describe. In such cases, predicting the location of deposition and resulting topography of debris flow lobes becomes an important part of the modeling process and reservoir and reservoir seal prediction. Moreover, given that sandstone bodies are often below seismic resolution limits or are not clearly separated by seismic attributes due to statistical overlap, modeling the geometries of the non-reservoir components, which are better resolved by seismic attributes due to their larger scale and stronger seismic signature, can provide a pathway to modeling sandstone bodies. The irregular surface topography of MTDs has been documented in highresolution shallow seismic-reflection data (e.g., Hampton et al. 1996; Normark et al. 2004), deeper subsurface seismic-reflection data (e.g., Moscardelli et al. 2008; Garziglia et al. 2008; Hubbard et al. 2009), and outcrop studies (Pickering and Corregidor, 2005; Shultz et al., 2005; Armitage et al., 2009). The irregular nature of these surfaces is important because it often plays a primary role in controlling the deposition of sand from turbidity currents. Based on bed-scale relationships between these two contrasting deep-water depositional processes facies observed in outcrop, Armitage et al. (2009) and Jackson and Johnson (2009) suggested that the topography from MTDs act to deflect turbidity currents, causing a loss of turbulence and a subsequent deposition of sand. Recent work by Bernhardt et al. (in review) has documented sandstone accumulations that are ponded in debris flow mini-basins in the Puchkirchen field of the Molasse Basin in Upper Austria (Fig. 1). These accumulations highlight the potential for stratigraphically trapped sandstone accumulations. This field is one of more than 40 gas fields (close to 700 wells drilled) that have been discovered in the Molasse basin to date, with new gas discoveries annually (de Ruig and Hubbard, 2006). Many of the discoveries have been broad, low-relief combination structural/stratigraphic traps within the channel belt, similar to the Puchkirchen field. The current exploration targets in the channel belt are subtle stratigraphic traps which are MTD-topography-controlled sandstone accumulations in and around the 2

3 A 48 o 15 N German-Austrian Border 3D seismic coverage Linz Legend: Molasse Flysch & Helvetic Northern Limestone Alps Bohemian Massif Lakes Thrust Faults Area of seismic inversion Fig. 1C 48 o 00 Puchkirchen gas field Fig. 1B 47 o 45 N 10 km Salzburg B N 13 o 00 E 13 o o o 30 Fig 2 W8 W7 W6 W1 W2 W3 W4 W5 non-producing wells wells with dipole sonic producing wells (bubble cumulative gas production from A1 & A2) depth contours at 10m intervals km C 10km 21 km W4 W2W3 W1 W6 W7 W8 W5 AI (g/cm 3 m/s) Figure 1: Basemap of the Austrian Molasse Basin and location of study area. (A) The Puchkirchen gas field location (after Hubbard et al, 2009). (B) Well and cross section locations. Gas production bubbles show cumulative production from both the A1 and A2 reservoir zones (see Figure 2). (C) Acoustic impedance from the seismic inversion shown on the Puchkirchen sandstone base reflector (picked by Bernhardt et al,. in review) stratigraphic surface. The Puchkirchen gas field (outlined) was drilled on a structural high. Each sphere represents the amount of cumulative gas production, from red (high) to blue (low). 3

4 Puchkirchen field. Prediction of such accumulations is complicated because the minimum resolvable theoretical thickness from the seismic-reflection data is approximately 30 m. This limited resolution makes it difficult to 1) determine the topography of upper surfaces of MTDs, and 2) resolve sandstone accumulations, which are 1-20 m thick. Furthermore, the MTD topography produces mini-basins for sandstone accumulations that are unpredictable in shape and size. Lateral correlation of reservoir units using well-log data is difficult and a correlation is commonly established by comparing pressure data between wells (de Ruig and Hubbard, 2006). The presence, quality and distribution of the sealing facies are also critical to stratigraphic trap definition, but are not the focus of this work. To overcome challenges related to the lack of reliable lateral prediction methods, a new geostatistical modeling approach is proposed. In this paper, we present a methodology to stochastically model sandstone accumulations whose irregular shape is defined by the underlying topography of the upper surface of one or multiple MTD(s). We then apply the modeling approach to a section (20 km x ~4 km x 60 m) of the Puchkirchen deep-water channel belt in the Molasse Basin. A thorough data analysis is first performed in order to quantify how reliably the soft data (seismic inversion attributes) are able to inform the presence or absence of each of the defined facies. Stanford Geostatistical Modeling Software (SGeMS; Remy et al., 2009) with a generic object plug-in (Tetris; Boucher et al., 2010) were combined with Python scripts ( Punch and Enbody, 2010) to model these nonreservoir debris flow lobes that comprise the MTDs and MTD-dependent sandstone bodies. Bernhardt et al. (in review) provided the description of the size and shape of the debris flow lobes, the sedimentological relationship between the lobes and sandstone bodies, and a distribution of sizes of sandstone bodies. The placement of the depositional bodies during modeling was constrained to 1) preceding topography, and 2) seismic attributes. The goal was to see if it is possible to predict sub-seismic sandstone accumulations based on seismic attributes that are used to predict MTD topography alone. 2. Study Area 2.1. Geologic Setting and Previous Work The Tertiary Molasse Basin is a classical asymmetric foreland basin, which contains a thick succession of deep-water sediments (de Ruig and Hubbard, 2006). De Ruig and Hubbard (2006) used RMS amplitude maps from regional 3D seismicreflection data, wireline log and core data to develop a geological model for the deepwater deposits of the Upper Austrian Molasse basin fill. Their work highlighted a west- to east trending basin confining an axial deep-water channel belt (3-6 km wide by >100 km long) that runs subparallel to the Alpine thrust front (Fig. 1a). They 4

5 described and interpreted depositional elements within the basin; channel belt, overbank wedge, overbank lobe, and tributary-channel and slope-fan deposits. Hubbard et al. (2009) analyzed cores and wireline logs from hundreds of wells, and correlated them with the 3D seismic-reflection data set throughout the Molasse Basin. Based on their observations within the channel belt, they interpreted the bed-scale processes associated with turbidity currents and developed a model to explain facies distribution. Their model depicts an organized inner channel, levee and overbank deposition confined by the larger channel belt margins. Bernhardt et al., (in review) refined the model presented by Hubbard et al. within the vicinity of the Puchkirchen field. The model was based on bed-scale interpretation of more than 300 m of sediment core, logged on a centimeter scale combined with interpretation of seismically-derived facies proportion models from Stright et al. (2009). The results of Bernhardt et al. (in review) show that in the vicinity of the Puchkirchen field, sedimentation is largely dominated by debris flow mudstone and conglomerate and, to a lesser extent, turbiditic sandstone. They observed a vertical relief of debris flow mudstone topography that is consistent with the maximum thickness of turbiditic sandstone accumulations. Based on these observations, they interpreted the control of sandstone deposition as a MTDtopography-dominated (Fig. 2). The refined model describes mass transport processes depositing large debris flow build-ups in the form of levees and lobes, which partially or fully fill the width of the channel belt. Succeeding turbidity currents deposit significant amounts of sand preferentially behind these build-ups, within debris flow mini-basins, and in local topographic lows on top of debris flow deposits. With this understanding of the sedimentology, it is possible to start to generate accurate geostatistical models Available Data A wealth of core, well log and seismic data from the Puchkirchen Field lends itself well to an extensive geostatistical study to address the difficult task of predicting sub-seismic, stratigraphically trapped reservoir sandstone (Fig. 1b). More than fifty wells have been drilled in and around the Puchkirchen Field, all of which have been logged with a standard suite of wireline logs; spontaneous potential (SP) or gamma ray (GR), sonic (DT) and resistivity. Greater than 330 m of core have been sampled in thirteen wells through reservoir and non-reservoir intervals. 3D seismicreflection data cover the Puchkirchen field and a significant portion of the Molasse Basin (Fig. 1a). It has been pre-stack time migrated, filtered to Hz and automatic gain control scaled with a 1500 ms window. The dominant frequency is 28 Hz and the average velocity is 2800 m/s which results in a maximum theoretical resolution of 33 m. A simultaneous inversion (Russell et al., 2006) completed by HOT Engineering (2007), generated P-impedance (Ip), S-impedance (Is) and density volumes in a near-field exploration project (Fig. 1c). There is an adequate match between the Ip volume and Ip logs calculated in two wells with dipole sonic (location 5

6 of wells shown in Fig. 1b and match shown in Fig. 2). The Is also shows an adequate match (not shown in Fig. 2), however, the resulting volume is significantly noisier than the Ip volume. Five lithology-based facies were defined for this study; 1) conglomerate (clastsupported and matrix-supported), 2) disturbed mudstone (debris flow deposits, not to be confused with shale deposited during depositional quiescence), 3) soft, organicrich shale (deposited during depositional quiescence), 4) thinly-interbedded sandstone and mudstone, and 5) massive sandstone (Fig. 2 and Fig. 3). The latter two facies (4 and 5) are turbiditic sandstone reservoir facies, whereas the first two (1 and 2) are the debris flow facies that comprise MTDs which control the depositional location and morphology of the reservoir facies. It is uncertain whether the soft, organic-rich shale (3) is a biogenic source of gas, however, what it clear is that its acoustic properties are similar to the gas sandstone. To ensure that a consistent set of facies logs were available for the prediction, cored intervals were used to predict facies in non-cored intervals as a function of wireline logs using a neural network (e.g., Fig. 4). 3. Data Analysis Measurement error, noise and limited bandwidth yield an inexact relationship between facies and seismic attributes (Widess, 1973; Takahashi, 2000). The difficulty of reservoir prediction directly from seismic-reflection data for the Puchkirchen formation is illustrated in Figures 2 and 3. In Figure 2, the seismic amplitude character across the top of the known gas sandstone is continuous and bright and the P-impedance signature is continuous and low, indicating gas sand (Fig. 2). However, when the log data are analyzed, the reservoir sandstone thins from west to east (Fig. 2). The log data also show known producing thin-bedded gas sandstone below the major gas producing zone, which do not have a strong amplitude character, or an impedance contrast. A cross-plot of Vp/Vs versus Ip from well log samples (15 cm sample rate) reveals that the high impedance facies are primarily composed of conglomerate and can be differentiated by Ip alone (Fig. 3). Mudstone is a low impedance facies, and is difficult to differentiate from reservoir sandstone, interbedded sandstone and mudstone, and soft, organic rich shale solely with acoustic impedance. This is due to a weak acoustic contrast with these facies and its sub-seismic scale thickness. The addition of Vp/Vs shows a strong delineation of facies over simply using Ip alone. The Vp/Vs ratio reveals a more distinct sandstone signature, pointing to using both acoustic and elastic inversion attributes for predicting facies. These relationships, while informative, are at the well log scale and do not account for the scale differences between the well logs and seismic attributes. Therefore, a thorough analysis of the seismic attributes and well log data was performed to elucidate what facies can or cannot be reliably informed from the available seismic attributes (Ip, Is, and the ratio of the two, Vp/Vs) at the seismic 6

7 P-Imp Seismic P-Imp Wells 5 13 Amplitude Facies VShale Total Porosity Puchkirchen Facies Interbedded SS/MS Sandstone Perforated SS Conglomerate Soft Shale Mudstone Gas Production Bubble A1 20 m A2 720 m 820 m 1700 m 815 m W1 W2 W3 W4 W m W m W m W8 Figure 2: Well section (flattened on the top of the A1 reservoir sand) showing the distal thinning of sandstone (yellow and gray facies) onto debris flow mudstone (red and green; Stright et al., 2009). The upper sandstone accumulation is the Puchkirchen A1 reservoir while the lower sandstone accumulation is the A2 reservoir. Seismic amplitudes and P-impedance from the inversion and from the wells are also plotted, along with total porosity and VShale. The A1 is a thicker, more productive accumulation of sandstone, while the A2 is a thinner, lower quality reservoir. The A1 sandstone accumulation is sandwiched between thick debris flow deposits of either disturbed mudstone or matrix-supported conglomerate (Berhnardt et al., in review). A Interbedded SS/MS Well log Vp/Vs Mudstone Conglomerate Sandstone 4 Soft Shale (blue, not shown) Well log P-Impedance (g/cm 3 km/s) Figure 3: Plot of Vp/Vs ratio vs. P-impedance showing the separation of facies categories in logs. The facies category definitions were based on detailed core observations of bedscale sedimentology. A rock physics template is overlain as a reference. Same facies color scale as Figure 2 (Stright et al., 2009). 7

8 W3 MD (m) 1160 A Input Predict GR 1177m B 1171m 1165m 1159m Matrixsupported conglomerate m 1172m 1166m 1160m cored interval shown in B 1179m 1173m 1167m 1161m m Thick-bedded sandstone Thin-interbedded sandstone/mudstone Disturbed mudstone Matrix-supported conglomerate Ripples 1181m Soft sediment deofrmation Dish structures Plane lamination Microfaulted sandbeds 1182m Folded sandbeds Consolidated mud clasts Unconsolidated mud clasts Disturbed mudstone 1174m 1175m 1176m 1168m 1169m 1170m 1162m 1163m 1164m mud f m c cgl mudf m c cgl mudf m c cgl mud f m c cgl Figure 4: Neural network (NN) facies log prediction. (A) Well logs showing the cored interval, rock types ( Input ) from core description, results from NN, and gamma-ray log (GR; for reference). To arrive at the NN prediction, multiple logs (GR, V p, Vs, Ip, Is, Vp/Vs, ρ) and the Input rock types are provided to the NN. The prediction results show more detail than was provided in the Input rock type description from core revealing that the log data has refined the prediction in a way that is consistent with the core description (B). (Appendix A; Stright, 2011) 8

9 scale. Two approaches were used to extract information from the seismic for predicting facies: 1) probabilities based on Baye s classification (Fig. 5), and 2) subseismic scale proportions based on a multi-attribute, multi-scale (MA-MS) calibration (Fig. 6; Stright et al., 2009). These data serve as constraining data for the modeling either in a direct and quantitative manner to place depositional bodies in the model, and in qualitative interpretative manner to provide an avenue to describe and parameterize the geometries to use in the modeling (e.g. Fig. 7A and 7B) Probabilities from Baye s Classification To capture the inexact relationship between seismic attributes (soft data) and facies logs (hard data), the seismic attributes are cast into a simple probabilistic framework. This is performed with a simple Bayesian classification using Baye s theory (for an in-depth discussion regarding Bayesian classification of rock types using seismic attributes, see Avseth et al., 2005): where A = facies class,. A [sandstone, interbedded sandstone and mudstone, disturbed mudstone, muddy matrix conglomerate] D = inverted seismic-reflectivity attribute, D [Ip, Is, Vp/Vs], and are captured at the well locations in the form of a calibration between the wells and collocated seismic attributes. This calibration was then used in an inverse manner to predict for each voxel in the seismic volume from the seismic attributes. We did not expect, given the variation in acoustic properties of the different facies (Fig. 3), that seismic predicts each facies accurately and equally. To test this hypothesis and to validate how well each attribute informs each facies, probabilities generated with the Bayesian classification were extracted at each well location and compared to existing facies in those wells. This was done by comparing the probability of misclassification (probability of predicting from when is not present, ) with the probability of correct classification (probability of predicting from when is present, ). As a visual tool, a modified box and whisker plot was used (cf. McGill et al., 1978) to analyze the quality of the seismic attribute prediction power (Fig. 5). 9

10 A B C P( Facies Ip) P( Facies Is) P( Facies Vp/Vs) P 10 P 25 P 50 P 75 P 90 Sandstone Interbedded SS/MS Disturbed mudstone Debris flow conglomerate D P( Facies Ip, Is, Vp/Vs) Figure 5: Box plots showing the probability distributions of predicting each facies with seismic attributes from a simultaneous inversion, P( Facies Ip ), P( Facies Is ), and P( Facies Vp/Vs ). The first three plots (A, B, and C) show the individual contributions of each attribute in predicting each facies. The top box for each facies is the probability of misclassifying a seismic voxel as conglomerate (cross-hatch fill) and the bottom box is the probability of correctly predicting conglomerate (solid fill). D) Box plots of the probability of predicting each facies with the combination of seismic attributes form a simultaneous inversion, P( Facies Ip, Is, Vp/Vs) using the Nu model to combine the individual probabilities. Combining the attributes generated a significantly stronger correlation of disturbed mudstone and debris flow conglomerate, while increasing the predictability of sandstone. Interbedded sandstone and mudstone is poorly predicted due to the fine-scale nature of the beds and its overall lower proportion. 10

11 The reliability of each seismic attribute to predict a given facies (i.e., is the probability of correct classification greater than the probability of misclassification) was quantified using the difference in the expected values of the two distributions (i.e., B0; Zhu and Journel, 1993; Goovaerts, 1997). 0 Δμ When the probability of correct classification is close to 1.0 and the probability of misclassification is close to 0.0, the seismic attribute provides perfect information in predicting a given facies. For this case, the expected values are far apart and the differences are close to 1.0 (Δµ ~= 1.0). When the probability of correct classification is approximately the same as the probability of misclassification, the difference in means is close to 0.0 (Δµ ~= 0.0). In this case, the seismic attribute contains no information to predict a given facies. Finally, the worst-case scenario occurs when the probability of misclassification is greater than the probability of correct classification (Δµ < 0.0), and the seismic attribute will consistently be misclassified as the wrong facies. The realistic case generally exists somewhere between perfect information and no information. Furthermore, a large difference in the median values provides information on the skewed distributions particularly if the difference between the expected values is small. We performed this analysis of the probabilities for facies and seismic attributes independently (i.e., the elementary conditional probabilities,, and ; Figs. 5A, 5B, and 5C). For single attributes, Ip and Is are better predictors of disturbed mudstone and debris flow conglomerate (the debris flow facies that comprise the MTDs) than Vp/Vs. This is in support of the cross-plot results (Fig. 3). None of the individual attributes reliably predict the turbiditic sandstone and interbedded sandstone and mudstone, showing how this differentiation is lost when upscaling the relationships in Figure 3 to the seismic scale. We then combined each of the individual conditional probabilities into a joint conditional probability (,, ; Figs. 5D). This combination was performed accounting for data redundancy (or data interaction) between each soft data (,, and in its contribution to informing the primary variable. This approach asks the question, is the information provided by (e.g., I s ) to predict the presence of (e.g., sandstone) redundant, new, or contrary to the information already provided by (e.g., I p )? Each of these cases would require a different combination of the individual conditional probabilities into a final combined conditional probability that reflects the combined information of all data inputs. For example, if the information provided by and is redundant, the final combined probability should be lower than if and are independent. The combination method, referred to as the Nu model (Polyakova and Journel, 2007), casts each of the individual elementary probabilities into a set of ratios (Journel, 2002; Krishnan, 2008): 11

12 1, 1 1,,,,. which are then combined with the following expression:,, 1,and, 0 One critical component and potential complication to using this method is in inferring the Nu parameters, ν_i. Polyakova and Journel (2007) proposed an interpretation for the weights as: ν_i= 1: is the case of data non-interaction ν_i> 1: amplifying/diminishing sensitivity ν_i< 1: reversal of sensitivity However, the strength of this method is that a Nu parameter need not be specified for each ratio. Instead, a global interaction parameter, ν_0, can be specified. The specification is somewhat forgiving in that a ν_0 = 1 does not necessitate that all ν_i = 1. This is because there are multiple combinations of ν_i that could produce a global interaction parameter, ν_0 = 1. Therefore, for the case presented herein, the global interaction parameter was assumed to be on. The classification of facies based on the joint combined conditional probability from multiple seismic attributes provides a more reliable classification overall than considering each conditional probability individually (Fig. 5D). Combining the attributes provides a strong predictability of disturbed mudstone and debris flow conglomerate, while increasing the predictability of sandstone. Interbedded sandstone and mudstone is still poorly predicted due to the fine-scale nature of the beds and its overall lower proportion. Furthermore, disturbed mudstone and conglomerate are better identified with the coarse scale seismic attributes than sandstone and interbedded sandstone and mudstone. However, with our understanding of the sedimentological relationship between these non-reservoir rocks deposited from debris flow events (MTDs) and reservoir sandstones, we can rely on the seismic attributes to predict non-reservoir deposits to aid in predicting reservoir deposits Proportions from a multi-attribute, multi-scale calibration Although probabilities derived from seismic have been shown to inform seismic scale debris flow facies, we would like a finer scale predictor for turbiditic sandstone 12

13 and interbedded sandstone and mudstone. Proportion models from a multi-attribute, multi-scale (MA-MS; Fig. 6; Stright et al., 2009) well-to-seismic calibration can be leveraged to provide some finer-scale information from the inverted seismic attributes. Using the MA-MS method, the proportion of a lithofacies was defined as the percentage of each defined lithofacies within a single seismic voxel (25 by 25 m bin size and 4 m vertical sample rate). These proportions were obtained through a calibration of points at each well location, and supplemented with additional calibration points from a Markov chain based on statistics extracted from wells logs. The resulting lithofacies proportion volumes are data-driven observations of seismic and subseismic scale features that directly relate lithofacies proportions to seismic attributes and are used to rank resulting models after geostatistical simulation. Subseismic is defined herein as a scale smaller than the theoretical seismic resolution (i.e., < 33 m) Sizes and shapes of debris flow lobes Bernhardt et al. (in review) used the proportion volumes to extract lithofacies geobodies to validate the hypothesized depositional geometries within the channel belt. The debris flow lobe shape was inferred from Bernhardt et al. (in review) based their interpretation of the facies proportion geobodies and thickness maps generated from the geobodies (Fig. 7B). Furthermore, a smoothed distribution of volumetric sizes of these bodies was compiled (Fig. 7B). These provide a first order approximation of shapes and sizes of the debris flow lobes. 4. Geostatistical Modeling 4.1. Background The goal of the geostatistical modeling process is to build geocellular models that will reliably predict reservoir intervals and properties for well planning and/or fluid flow performance prediction. A typical modeling workflow will attempt to convert a geologist s conceptual image of the reservoir to a numerical representation that honors both hard (well and core) and soft (seismic and production) data collected from the reservoir. However, historically available tools such as covariance-based (2- point), Gaussian-based, geostatistical methods (cf. Goovaerts, 1997) limit the modeler s ability to include realistic interpretive geologic information into reservoir models, while Boolean object-based methods (cf. Stoyan et al., 1987) cannot match the diverse and often abundant data sampled from the reservoir interval. Furthermore, object-based methods are hindered by their inability to parameterize complex depositional bodies and relationship between the bodies. Surface-based modeling (Pyrcz et al., 2005; Wellner et al., 2006), rules-based algorithms (McHargue et al., 2010; Sylvester et al., 2010), and process-based algorithms (e.g., Griffiths et al., 2001) provide promise in capturing body geometries that are tied back to the sedimentological processes that generated them without the need for complex 13

14 B Seismic Vp/Vs Sand Por = 35% 30 Sw = 1 Interbedded SS/MS Sandstone Conglomerate Soft Shale Mudstone Sand Por =10% 1.6 Sw = Seismic P-Impedance (g/cm 3 km/s) Figure 6: MA-MS calibration where each pie chart shows the fine-scale facies proportions within a seismic sample (Stright et al., 2009). The rock physics template overlain is again overlain to add as a reference to Figure 3. 14

15 numerical solutions. However, to date, these algorithms have only been developed for channel-levee-overbank and channel-lobe models. Furthermore, at this point, it is difficult to constrain these methods to well data and seismic attributes. Advances in training image-based modeling algorithms (Strebelle, 2002; Zhang, 2006; Arpat, 2007) have made it possible to reproduce the geometry of complex sedimentary bodies while conditioning to the diverse suite of soft (seismic) and hard (well log and core) data typically encountered in petroleum reservoirs. Training image-based modeling techniques provide the avenue to include qualitative interpretative information into reservoir models through training images, thus allowing the geologist more control to include important descriptive information. Although the training image is the basis of a shift in model building workflows, from covariance-based statistical methods toward quantitative integration of descriptive geological interpretations with field data, it is not always the appropriate tool to choose for model building. In the case of deposits around the Puchkirchen field, sandstone sedimentary bodies are irregularly shaped and cannot be placed into a training image paradigm. A hierarchical approach, not unlike that of Maharaja (2004), is adapted to capture the irregularly-shaped multi-scale architecture of the Puchkirchen channel deposits Stanford Geostatistical Modeling Software (SGeMS) and Tetris Plug-in The foundation for the modeling process presented is a plug-in to the Stanford Geostatistical Modeling Software (SGeMS) called Tetris. SGeMS is an open-source computer package for solving problems involving spatially related variables (Remy et al, 2009; The Tetris plug-in adds flexibility by defining complex shapes for training image generation (Boucher et al., 2009). The Tetris design overcomes a major hurdle of rigidly pre-defined geological objects, and provides a framework to define complex objects from pre-coded shapes, such as ellipsoid, cuboid, kernels, or user defined shapes. These basic shapes are then combined with operations (difference, union and intersection) to create new complex shapes. For added flexibility, any shape can be translated, rotated and sheared. This addresses the issue of parameterization of complex bodies and the spatial relationships between them. Although Tetris was originally developed as a tool to generate training images, it becomes a powerful generic rules-/object-based simulation tool when it is combined with Python scripting Workflow (SGeMS, Tetris and Python) A topographically-driven rules-/object-based modeling workflow is proposed utilizing SGeMS, Tetris and Python. First, debris flow lobe shape, comprised of disturbed mudstone and conglomerate, is created with Tetris using the intersections between multiple spheres and ellipsoids of varying sizes. This shape is one possible 15

16 shape for a debris flow lobe and will serve as an initial test shape for simulations. The shape of the turbidity current is defined by the uneven underlying topography of one or multiple debris flow lobes and is comprised of sandstone and interbedded sandstone and mudstone facies. Facies probabilities obtained from a calibration between facies defined in the wells and multiple seismic attributes (Fig. 7A), are the driving force for placement of the seismic-scale debris flow lobes. These local probabilities to control each successive placement of debris flow lobes. Python scripting is used to direct Tetris controls whether a debris flow lobe or a turbidite is chosen to be simulated (Fig. 7C). The choice is made by checking how close either debris flow deposits or turbidites are to their total target proportions. This distance is converted to a probability: ; 0,1 ; 0,1 1 A debris flow lobe or turbidite step is stochastically chosen based on this distance from the target proportions using a simple draw from a uniform distribution. This constraint ensures that the target proportions will be met (Fig. 7B and 7C). The size of the debris flow lobe or turbidite is selected stochastically from the histogram in Figure 7B. The shapes are then dropped into the model space (or grid). The positioning of the shape is controlled by 1) the lowest point in the grid for both debris flow lobes and turbidites, and 2) the highest probability from the predefined probability volume, P(DF Ip,Is,Vp/Vs) (for debris flow lobes only). Each subsequent debris flow lobe or sandstone layer is draped on top of the previous topography. This process of simulating debris flow lobes and turbidites is repeated until the simulation grid is filled. The modeling workflow produces multiple alternative numerical models or realizations of sediment accumulation within the channel belt. Each of the model match/mismatch was assessed using an accept/reject criteria that keeps the models that best fit the data and rejects the ones that do not (Fig. 7D). Although direct data conditioning of well data was not employed, this approach generates the same result as direct data conditioning and allows us to directly test the fit of our sedimentological model with the data. Furthermore, we can assess how well the seismic attributes performed on their own predicting the large scale non-reservoir facies such that the predominantly sub-seismic scale reservoir facies would be predicted. 16

17 Data Analysis A Inverted Pre-stack Seismic Volume (P-Impedance, S-Impedance, Vp/Vs) Well logs and core interpretation B 82% 18% Global Proportions B A Bayesian Classification: Seismic-scale Probabilities MA-MS Calibration: Sub-seismic scale Proportions Sedimentological Model Processes and Deposits Depositional Bodies Shapes & Sizes Flow direction A B *Outer bend of channel belt Flow direction A A B * B Object Simulation C Neural Network Facies Logs Count km 3 n = km 3 n = 12 Turbidity current deposit Debris flow deposit x10 8 m 3 Derived from proportions models and Bernhardt et al. (in review) n Post-processing D Accept/reject models based on match with: 1. Facies well log data 2. Proportion volume derived from MA-MS calibration realizations Figure 7: Data flow and process workflow for the debris-flow mini-basin data analysis and simulation. A) Input data and results for the data analysis. B) Global facies proportions of debris flow lobes and turbidites from core data, diagrammatic sketch of a debris flow lobe (section A-A depicts the tail to snout morphology of an idealistic lobe and scenario of where sand deposition will occur behind the debris flow lobe and section B-B shows the preferential build-up of the lobe toward the outer bend of the channel belt) and distribution of the sizes (volumes) of debris flow lobes and turbidity currents measured from geobodies in Bernhardt et al. (in review). C) Workflow for simulation of sandstone accumulations in a topographically-controlled depositional system. D) Data conditioning as a post-processing step where each of the realizations are ranked by and accept/ reject criteria based on best match with facies in well logs and proportion volumes from MA-MS calibration. 17

18 Step 0 Step 2 W1 W2 W3 W4 W5 W6 W7 60 m 1000 m 1000 m North 2 Debris Flow Lobes 6 Debris Flow Lobes 1 Turbidite Figure 8: A model from a single realization. Debris flow lobes (red) initially enter the model and subsequent turbidite (yellow) and debris flow lobe (red) simulation generate irregularly-shaped sandstone accumulations that thin onto the debris flow build-ups in the mini-basins generated by the topography of the MTD upper surfaces. This view is flattened on the base horizon and vertically exaggerated 20x s. Step 9 10 Debris Flow Lobes 3 Turbidites Step16 19 Debris Flow Lobes 17 Turbidites Step 37 Step Debris Flow Lobes 26 Turbidites Turbidite Debris Flow 18

19 5. Results A model from a single realization of this workflow is presented in Figure 8 and Figure 9A showing the simulation of debris flows and turbidites with each step of the simulation. The topography is built by multiple debris flow lobes and subsequent turbidite simulation generates irregularly-shaped sandstone accumulations that thin onto the debris flow build-ups in the mini-basins generated by the topography of the MTD upper surfaces. The top ranking model in terms of matching well data is shown in Figure 9A for the well cross-section from Figure 2. By using the seismic to predict the coarse scale events (debris flow deposits; Fig. 9B) and modeling the fine scale events as a function of the coarse scale events, we were able to predict the locations of significant sandstone accumulations as validated by these previously drilled areas. Furthermore, a root mean square error between the model and well data was calculated. The top 10% best matching models, based on a minimum RMS error, were used to generate an Etype model (Fig. 9C; average of all models where turbidite is indicator coded as 1.0 and debris flow is indicator coded as 0.0). Furthermore, an Etype of the same cross-section shows that all 100 realizations show a high probability of predicting a turbidite deposit at the crest of the structure (at W4 and W5; Fig. 10A). When the models are ranked by the best matches to turbidite proportions derived from the MA-MS calibration (Fig. 10B) and the Etype calculated again for the top 10% best matching models (Fig. 10B), a high proportion of the models predict the same turbidite deposit at the crest of the structure, while also predicting some of the less distinct thin turbidites of the A2 reservoir zone. The proportion models produce a higher prediction of the A2 reservoir zone at the expense of predicting a smaller accumulation from the A1 reservoir zone. 6. Discussion 6.1. Is this conceptual model consistent with the data? This work was designed to assess the ability of seismic attributes and knowledge of sedimentology to predict poorly resolved turbidite sandstone accumulations in a MTD-topography-controlled deep-water channel belt. Moreover, this approach allows us to further test the hypothesis that sandstone body volume and morphology are dictated by the topography generated by one or many debris flow lobes. The model predictions are validated with ample well data. Although each model generated does not necessarily match the well log data, models accepted based on a low mismatch with the well data produce a reservoir accumulation that is the size and shape of what is expected. If the models have a very low acceptance rate, it is a signal that the sedimentological model is not correct and it is then essential to return to the conceptual model and modify it to allow for a better fit to the data. However, that said, well data are a critical input for preparing the data input for modeling; i.e., 19

20 A W1 W2 W3 W4 Model Turbidite Debris Flow W5 Well data Sandstone Interbedded SS/MS Disturbed mudstone Debris flow conglomerate W6 W7 W B Probability of Debris Flow C Top 10 Realizations ranked by low RMS error between model and well data Turbidite EType (Turdibite = 1.0, Debris Flow = 0.0) Figure 9: A) Cross Section of a single realization of the model showing the strong prediction of the turbiditic sandstone accumulation in the debris flow mini-basin. B) The probability of debris flow (PDF Ip, Is, Vp/Vs) was used as a control for where to place each debris flow lobes in the simulation, C) EType of the top 10 realizations matching the well log data (lowest RMS error with well logs facies). The Etype is the average of a number of realizations where values in model are turbidite = 1.0 and debris flow =

21 A EType of All 100 Realizations W1 W2 W3 W4 0 W W6 W7 W8 Turbidite EType (Turbidite = 1.0, Debris Flow = 0.0) B Proportion of Turbidite C EType of Top 10 Realizations ranked match to turbidite proportion volume Turbidite EType (Turbidite = 1.0, Debris Flow = 0.0) Figure 10: A) Etype of all 100 realizations, B) Turbidite proportion volume from MA- MS calibration, and C) Etype of top 10 realizations with best match to proportion models. The Etype is the average of a number of realizations where values in model are turbidite = 1.0 and debris flow =

22 an accurate seismic inversion, depth conversion, and MA-MS calibration. Furthermore, elucidating the sedimentology without well log and core data would be risky. So, that begs the question, is this model consistent with the data? Prior to the work by Bernhardt et al. (in review) and this work, it was difficult to explain the anomalous thickness and extent of this reservoir sandstone. The model presented herein, validates that the data fits a debris-flow mini-basin paradigm (Fig. 9). However, the A2 Puchkirchen interval is a different case. The facies deposits in this zone are different than that of A1 as it is comprised of thinner bedded and lower quality sandstone interbedded with debris flow mudstone, of a lesser thickness than zone A1. The A2 zone, therefore, has a slightly different sedimentology and rock properties than the A1. There are two ways to approach building a model that fits this zone; 1) use the same depositional model and modify a component of it to attempt to fit the data, or 2) generate a new model altogether. In the first approach, we could attempt to see if the same model fits the data by separating the model out into two zones (A1 and A2) and then modifying the size and shape of the debris flow lobes independently in each zone. For example, we could hypothesize that the debris flow lobes are thinner and longer in the A2 zone, as the NN-derived well data seem to suggest (Figs. 9 and 10). In the second approach, we declare that the thin bedded turbidite and debris flow facies are a result of a depositional process that we have not included in the model. Bernhardt (in review) had proposed two processes that we are directly capturing in this model. First, the thin-bedded turbidites are interpreted as the deposits from the tail of a turbidity current bypassing the upstream debris-flow mini-basin and being deposited over the nose of the topographic high of the debris-flow lobe. Second, the thin debris flow facies could be part of a lag or levee facies to the debris flow lobes. Because the A1 zone was the focus of the work in Bernhardt et al. (in review), further work needs to be performed on the sedimentology of the A2 zone to build a more accurate model of this zone Broader applicability of the modeling approach: Beyond Puchkirchen This modeling approach shows the importance of understanding the data and sedimentology of the system that is being modeled and not applying a generic modeling algorithm. First, we demonstrated that it is important to know which facies the seismic data are informing and at what scale, and to attempt to quantify the relationship for a more targeted and robust modeling workflow. Furthermore, to build a predictive model that is consistent with the geology of the system, the sedimentology of the reservoir facies, and more importantly as we have demonstrated, the non-reservoir facies must be investigated thoroughly. We have only presented models ranked by a match with the data. The next 22

23 logical step would be to place this modeling approach into an optimization workflow (e.g., Stright, 2006). However, it is important to first understand the sedimentology well enough to know what are the uncertainties and parameters to change during the optimization. Again, just simply generating multiple training images based on existing models (i.e., channels-levee-overbank models of with channels of difference sizes, orientations and sinuosities) would be insufficient to describe and model sandstone deposits for this specific case. Moreover, observations of modern seafloor (e.g., Hampton et al. 1996; Normark et al. 2004) and ancient outcropping (Pickering and Corregidor, 2005; Shultz et al., 2005; Armitage et al., 2009) deep-water systems demonstrate that situations analogous to the Puchkirchen deposystem likely form a widespread class of irregularly shaped sand body accumulation in debris-flow minibasins. 7. Conclusions This paper presented a new approach for modeling deep-water turbidite deposits that do not fit the channel-levee-overbank-lobe paradigm. The methodology stochastically models turbidite accumulations whose irregular shape is defined by the underlying topography of the upper surface of one or multiple MTD(s). The modeling process simulates debris flow lobes followed by turbidites that fill in debris flow lobe mini-basins. The modeling approach is constrained such that each successive depositional body is controlled by the 1) preceding topography, and 2) a combination of facies probabilities derived from seismic attributes. The model was applied to the Puchkirchen deep-water channel belt in Upper Austria and successfully modeled the reservoir accumulation in the upper reservoir zone. The model does not explicitly capture the thinner bedded lower reservoir zone. Nevertheless, the modeling framework in place is flexible and can be modified to capture different debris flow lobe shapes or a debris flow lag facies and a turbidite overspill facies. Furthermore, because this modeling approach is general in nature, it could be more widely applied to areas where sandstone reservoirs are suspected to be the result of debris-flow mini-basins. The strength of this approach over a standard covariance-based indicator method (e.g., sequential indicator simulation) is that it accounts for the sedimentology in this debris-flow dominated system as well as conditions the models to soft data (directly) and hard data (indirectly). This approach is a significant improvement over simply generating multiple training images based on existing models (i.e., channels-levee-overbank models of with channels of difference sizes, orientations and sinuosities), which we have shown would be insufficient to describe and model the reservoir deposits for this case. 8. Acknowledgements We would like to thank Rohöl-Aufsuchungs A.G. (RAG) for financial and logistical support of our research, as well as for permission to publish their data in 23

24 this study. In particular, we wish to thank Richard Derksen for his ongoing support of this research. This work has benefited greatly from discussion on petroleum geology and sedimentology with Stephan Graham, Donald Lowe and Stephen Hubbard, rock physics and seismic data interpretation with Tapan Mukerji and Gary Mavko, and geostatistical modeling with Andre Journel. We also acknowledge generous software donations from Schlumberger (Petrel) and the inversion models produced by HOT Engineering in 2009 using Hampson-Russel. Finally, valuable feedback and support has been provided by the Stanford Project on Deepwater Depositional Systems (SPODDS), an industrial affiliates program whose members include Aera Energy, Anadarko Petroleum Corporation, BHP Billiton, Chevron, ConocoPhillips, Hess Corporation, Marathon Oil Company, Nexen Energy, Occidental Petroleum, Petrobras, Reliance Industries Ltd., Rohöl-Aufsuchungs A.G. (RAG), Schlumberger and Shell. References Armitage, D.A., Romans, B.W., Covault, J.A., and Graham, S.A., 2009, The influence of mass transport deposit topography on the evolution of turbidite architecture: The Sierra Contreras, Tres Pasos Formation (Cretaceous), southern Chile: Journal of Sedimentary Research. Arpat, G.B., and Caers, J., 2007, Conditional Simulation with Patterns, Mathematical Geology, v. 39, no. 2, p Avseth, P., Mukerji, T., and Mavko, G., 2005, Quantitative seismic interpretation: applying rock physics tools to reduce interpretation risk, Cambridge University Press, 359 p. Bernhardt, A., Stright, L., and D. R. Lowe, in preparation, Debris Flow vs. Turbidity Current Interactions in a Large Submarine Axial Channel Belt Puchkirchen Formation, Austrian Molasse Basin. Boucher, A., 2009, A flexible and expandable design to generate training images for sedimentary environment, in Proceedings Sediment Body Geometry and Heterogeneity: Analogue Studies for Modelling the Subsurface, The Geological Society, Burlington House, Piccadilly, London. Caers, J., Strebelle, S., and Payrazyan, K., 2003, Interpreter's Corner Stochastic integration of seismic data and geologic scenarios: A West Africa submarine channel saga, The Leading Edge, v. 22, no. 3, p De Ruig, M.J., and Hubbard, S.M., 2006, Seismic facies and reservoir characteristics of a deep-marine channel belt in the Molasse foreland basin, Puchkirchen Formation, Austria, AAPG Bulletin, v. 90, no. 5, p Garziglia, S., Migeon, S., Ducassou, E., Loncke, L., and Mascle, J., 2008, Masstransport deposits on the Rosetta province (NW Nile deep-sea turbidite system, 24