Pre-stack Elastic Inversion Research Articles

Oil and gas prediction basing on seismic inversion of elastic properties in Chaoshan depression, south China sea

The marine Mesozoic is widely distributed in the northeastern waters of the South China Sea and is an important field for oil-gas exploration in the South China Sea. The Chaoshan Depression is the largest residual depression in this sea. At a previous well, LF35-1-1, no oil and gas have been discovered with then pre-drilling prediction techniques. Post-drill analysis shows that the physical properties of the Mesozoic reservoir are not favorable there. So, in accurate prediction of the oil-gas reservoirs is necessary. Since the drilling at the LF35-1-1, extensive surveys and studies have been carried out which shows a number of favorable trapping structures. In the middle low bulge of the Chaoshan Depression, the DS-A structures found with potential reservoirs, complete trap structures, and dual source hydrocarbon supply on both sides, making it the most favorable zone for oil-gas accumulation. We apply the state of art prediction techniques for it using pre-stack seismic raw gather. The sensitivity analysis results of reservoir physical properties indicate that the difference in P- wave velocity between sand and mudstone is 500 m/s, the difference in density is 0.02 g/cm3, and the Poisson’s ratio ranges between 0.11 and 0.33. The Mesozoic sandstone reservoirs in the Chaoshan Depression have characteristics of high velocity and low Poisson’s ratio, and the P-wave velocity, density, and Poisson’s ratio are the main sensitive parameters for predicting reservoir and its oil-gas bearing properties. The density inversion, P-wave impedance inversion, and S-wave impedance inversion jointly characterize the “wedge-shaped” sand body in the DS-A structural area, with a maximum thickness of over 400 m and an area of ∼130 km2. The overlap of the sand body contour map and Poisson’s ratio inversion results indicates that the “wedge-shaped” sand body is an oil-gas bearing sand body. It can be concluded that pre-stack elastic parameter inversion is an effective method for reservoir prediction in deep-sea no-well exploration areas. It has the characteristics of high signal-to-noise ratio, strong stability and reliability, and high accuracy, which is conducive to reduce the non-uniqueness and uncertainty of seismic inversion. The inversion results predict that the DS-A structure is an oil-gas bearing structure.

Study on Anisotropic Petrophysical Modeling of Shale: A Case Study of Shale Oil in Qingshankou Formation in Sanzhao Sag, Songliao Basin, China

Seismic petrophysics is an important link between seismic elastic properties and reservoir physical properties. Based on the petrological and microstructure characteristics of shale in the Qingshankou formation of Sanzhao sag in the north of Songliao Basin, this paper presents an anisotropy petrophysical model with complex pore structure suitable for organic shale constructed with the use of the Voigt-Reuss-Hill average model, an anisotropy self-consistent approximation+differential effective medium model, and the layering of clay and kerogen is simulated by using the Voigt-Reuss-Hill average and bond transform to achieve the simulation of shale anisotropy. Based on the proposed model, the effects of the organic volume fraction, porosity, and pore aspect ratio on rock elastic properties are discussed. The result shows that with the increase of matrix porosity, all elastic parameters show a decreasing trend; with the increase of the organic volume fraction, except shear modulus, other elastic parameters show an increasing trend. Through comparative analysis, the elastic parameters (Lamé impedance and Shear impedance) sensitive to the organic volume fraction and porosity are optimized; the seismic petrophysical cross-plot template with core calibration is constructed. The application shows that the predicted S-wave velocity based on the proposed model is in good agreement with the S-wave velocity derived from dipole source logging. Combined with the high-precision prestack elastic parameter inversion, the “sweet spot” characteristics can be well described, and the research could contribute to a better “sweet spot” description and provide a better support for shale exploration in Sanzhao sag.

Seismic diagenetic facies prediction of tight sandstone in the offshore sparse well area: An example from the Xihu Depression of the East China Sea Basin

The purpose of this study is to forecast the spatial distribution of diagenetic facies (DF) of tight sandstone in the offshore sparse wells area. Analytical test data, rock physics experiment data and prestack seismic data were used to study the spatial distribution of seismic diagenetic facies (SEISDF) of tight sandstone of the second (H4b) submember of the fourth (H4) member of the Huagang (E3h) Formation in the N gas-field, Xihu Depression, East China Sea Basin. Based on diagenesis and diagenetic minerals, core-based DF of the H4b sandstone were divided into chlorite-coated facies (CHF), calcite-cemented facies (CAF), dissolution facies (DIF), tightly compacted facies (TIF), and quartz-cemented facies (QUF). Various seismic elastic parameters were obtained by prestack elastic parameter inversion method, and sensitive seismic elastic parameters were selected according to the seismic identification principle of DF. In order to predict the spatial distribution of DF, four DF and sensitive seismic elastic parameters were integrated to establish a SEISDF prediction model based on supervised learning, and obtain a diagenetic facies comprehensive index (DFCI) that can distinguish four DF. Then, the 90° phase conversion technique of seismic lithology was used to realize the consistency of the DFCI between isochronous stratigraphic interfaces with core-based DF. The stratal slicing technique of seismic geomorphology was used to make stratal slices of the DFCI between isochronous stratigraphic interfaces. Representative stratal slices were singled out, and the spatial distribution of the SEISDF was interpreted. This study shows that the H4b1 sublayer primarily develops the TIF, while the H4b2 and H4b3 sublayers chiefly develop the QUF, CHF, and DIF. Compared with the H4b2 and H4b3 sublayers, the areas of the QUF and DIF in the H4b4, H4b5, and H4b6 sublayers slightly increase. The QUF are mainly distributed in the subaqueous distributary channel and a small number of sheet sand and channel bar depositional facies in the form of continuous sheets. The CHF are primarily developed in lenticular shape in the channel bar and a small amount of sheet sand and subaqueous distributary channel depositional facies. The most favorable DIF are chiefly developed in the subaqueous distributary channel, channel bar, and sheet sand depositional facies near the fault, which are distributed in strips. This study proposes a very valuable method for the SEISDF prediction of tight sandstone, which can provide a reference for the study of DF of similar strata in other sedimentary basins.

Construction and application of an adapted rock physics template (ARPT) for characterizing a deep and strongly cemented gas sand in the Nam Con Son Basin, Vietnam

The Hai Thach field is one of the biggest gas and condensate producing fields in Vietnam. Located in the Nam Con Son Basin, offshore southern Vietnam, the field consists of multiple, stacked reservoir units, for which petrophysical characterization is challenging and a site-adapted rock physics template (ARPT) was proposed to solve this task. As reported in many publications, rock physics templates (RPTs) have been successfully applied for the characterization of shallow unconsolidated and weakly cemented reservoirs with cementation of less than 5% like in the North Sea or some other sites. However, the construction of RPT is very site-dependent. In this study, an approach of rock physical modelling, named the adapted stiff sand model (ASSM), was proposed to construct a site-adapted RPT of Vp/Vs versus acoustic impedance (AIP) for characterizing the upper part of Middle Miocene Sand in the Nam Con Son Basin, which is a 3.5-km deep and strongly cemented gas sand with 10% up quartz-overgrowth and clayey cementation. A key point in this approach was the use of a modified Biot-Gassmann's equation and in situ well log data to calculate the dry moduli of reservoir rock frame. As a result, the elastic and petrophysical parameters of this upper MMS sand, named as MMF30, are well evaluated, i.e., AIp from 9000 to 11,000 m/s*g/cc, Vp/Vs from 1.65 to 1.8, porosity from 12 to 16%, and gas saturation from 50% up, which match well with the core data and were used further in a prestack elastic inversion of a seismic inline that could map well the multiple stacked gas zones of the study reservoir. The rock physical modelling approach in this study could help characterize successfully deep and highly-cemented clayey gas sands in the Nam Con Son Basin.

Estimating rock physical parameters using anisotropic 3D seismic data to characterize unconventional Vaca Muerta oil shale deposits in the Neuquèn Basin, western Argentina

Summary Acquisition and processing of wide azimuth large offset and high fold (WA/LO/HF) 3D seismic data in the Aguada Federal concession is presented. Preserved amplitude/azimuthal workflows (e.g. anisotropy analysis, pre-stack elastic inversion, reservoir characterization) facilitate the quantitative interpretation. Layering, fracture distribution and stress cause measurable velocity anisotropy. Well ties and residual normal move-out help to determine the anisotropy parameters (η, e and δ). Non-hyperbolic 4th-order move-out improves flattening of gather reflections. Sinusoidal residual move-out on common-offset, common-azimuth gathers is diagnostic for HTI anisotropy. Azimuthal Residual Move-out (ARMO) on gathers improves the seismic quality. Anisotropic 3D tomographic raytracing and velocity model building increase the depth imaging efficiency. The new processing better focuses the seismic reflections and boosts higher frequencies. The migration repositions the energy in depth and the mismatch of geologic markers at the well locations is reduced. Higher fidelity datasets are better suited for seismic inversion, reservoir characterization and fracture prediction. The anisotropic workflow serves to estimate Vp, Vs, density, total organic contents, Young’s modulus E and pore pressure. Delineation of Vaca Muerta sweet spots is thus made possible. Seismic anisotropy analysis allows optimization of the well landing point, selection of well spacing and a preferred trajectory orientation.

Study of the Sensitive Properties of Marine Gas Hydrate Based on the Prestack Elastic Inversion

Using a bottom simulating reflector (BSR) on a seismic profile to identify marine gas hydrate is a traditional seismic exploration method. However, owing to the abundance differences between the gas hydrate and free gas in different regions, the BSR may be unremarkable on the seismic profile and invisible in certain cases. With the improvement of exploration precision, difficulty arises in meeting the requirements of distinguishing the abundance differences in the gas hydrate based on BSR. Hence, we studied other sensitive attributes to ascertain the existence of gas hydrate and its abundance variations, eventually improving the success rate of drilling and productivity. In this paper, we analyzed the contradiction between the seismic profile data and drilling sampling data from the Blake Ridge. We extracted different attributes and performed multi-parameter constraint analysis based on the prestack elastic wave impedance inversion. Then, we compared the analysis results with the drilling sampling data. Eventually, we determined five sensitive attributes that can better indicate the existence of gas hydrate and its abundance variations. This method overcomes the limitations of recognizing the gas hydrate methods based on BSR or single inversion attribute. Moreover, the conclusions can notably improve the identification accuracy of marine gas hydrate and provide excellent reference significance for the recognition of marine gas hydrate. Notably, the different geological features of reservoirs feature different sensitivities to the prestacking attributes when using the prestack elastic inversion in different areas.

Integrated facies modeling in unconventional reservoirs using a frequentist approach: Example from a South Texas field

Modeling of rock types or facies in unconventional reservoirs presents numerous challenges that are not encountered in conventional reservoirs. Because the exploitation of unconventional reservoirs frequently relies on the use of large numbers of long, data-poor horizontal wells, routine tasks in conventional reservoirs, such as petrophysical analyses and rock-physics diagnostics, become problematic in unconventional reservoirs due to insufficient data. Similarly, the inability to generate synthetic seismograms in the horizontal section of the wells makes seismic well ties and time-depth conversions more difficult. Our approach for facies modeling in unconventional reservoirs attempts to overcome these challenges by using the abundant log information available along the vertical pilot well to extract discrete facies indicators (facies flags) from logging-while-drilling information along the horizontals. After performing a time-depth conversion constrained by geosteering information, we estimate facies probabilities using facies flags and prestack elastic inversion results also extracted along the horizontals. As opposed to the Bayesian formalism commonly used for facies probabilities estimation, our frequentist approach estimates probabilities directly from proportions derived from crossplots of inverted elastic properties without using the Bayes formula. No prior information is required. The margin of error in the probabilities is also estimated by applying a well-known formula used to estimate the margin of error in opinion polls. Finally, we use seismic probability results to select only points with high probability and high reliability, which are treated as hard constraints for stochastic facies modeling. The selection of the seismic constraints is also weighted by the vertical facies trend expected for the area of interest. Our final facies model closely follows horizontal and vertical well facies data, vertical proportion curves, and selected seismic constraints. The application of the methodology is illustrated in a carbonate-rich, unconventional reservoir in South Texas.

Prestack simultaneous inversion to predict lithology and pore fluid in the Realgrunnen Subgroup of the Goliat Field, southwestern Barents Sea

An integrated multidisciplinary workflow has been implemented for quantitative lithology and fluid predictions from prestack angle gathers and well-log data within the Realgrunnen Subgroup in the Goliat Field, southwestern Barents Sea. We have first performed a qualitative amplitude-variation-with-angle (AVA) attribute analysis to assess the spatial distribution of lithology and fluid anomalies from the seismic data. A simultaneous prestack elastic inversion was then carried out for quantitative estimates of the P-impedance and [Formula: see text] ratio. Probability density functions, a priori lithology, and fluid class proportions extracted from well-log training data are further applied to the inverted P-impedance and [Formula: see text] seismic volumes. The AVA qualitative analysis indicates a class IV response for the top of the reservoir, whereas anomalies from the AVA attribute maps agree largely with the clean sand probabilities predicted from the Bayesian facies classification. The largest misclassification in the lithology classification occurs between shaly sands and shales. A mixed lithology and fluid classification indicates a smaller degree of overlap and allows for the discrimination of hydrocarbon sands. Integration of a qualitative AVA analysis and a quantitative Bayesian probability approach helps in constraining the depositional facies variability within the Realgrunnen Subgroup. Finally, a possible influence of tectonic activity during the deposition of the Realgrunnen reservoir is inferred based on the facies distribution maps.

Seismic forward and inverse simulation in a tight reservoir model of loess plateau region

Abstract To find out the seismic wave field propagation principles in loess plateau near surface of the Ordos Basin and the seismic response characteristics of tight oil reservoirs, this study established a geological-geophysical model under the real conditions of ground surface of loess plateau, and launched full elastic seismic wave equation forward modeling and pre-stack elastic seismic inversion study. Comparison of modeling and real seismic data shows that, the loose and wavy loess plateau surface is the main reason for causing the problems of seismic static correction and interference wave. Tomographic static correction method with the constraint of traces near shot point can effectively solve the problem of seismic static correction in the loess plateau and enhance seismic imaging accuracy, S-wave impedance obtained from pre-stack seismic inversion can identify sandstone effectively, and Poisson's ratio can identify oil-bearing reservoirs. The seismic forward and inverse simulation and rock physical analysis provide a solid theoretical and experimental basis for the seismic prediction of tight oil reservoir, and have worked well in the oil exploration and development in the loess plateau of the Ordos Basin.

Qestimation using modifiedStransform based on pre-stack gathers and its applications on carbonate reservoir

Pre-stack seismic data is acknowledged to be more favorable in estimating Q values since it carries much more valuable information in traveltime and amplitude than post-stack data. However, the spectrum of reflectors can be strongly altered by nearby reflector or side lobes of the wavelet, which thereby degrades the accuracy of Q estimation based on the pre-stack spectral ratio method. To solve this problem, we propose a method based on the modified S-transform (MST) for estimating Q values from pre-stack gathers, in which Q values can be obtained with regression analysis based on the relationship between spectral ratio slope and the square of offset. Through tests on a numerical model, we first prove advantages of this pre-stack spectral ratio method compared to the traditional post-stack method. Besides, it is also shown that application of MST would lead to a much more focused intercept, which is the kernel for the pre-stack method. Therefore, the accuracy of Q estimation using MST is further improved when compared with that of conventional S-transform (ST). Based on this Q estimation method, we apply relevant processing methods (e.g. inverse Q filtering and dynamic Q migration) in practice, in order to improve imaging resolution and gathering quality with better amplitude and phase relationships. Applications on a carbonate reservoir witness remarkable enhancements of the imaging result, in which features of faults and deep strata are more clearly revealed. Moreover, pre-stack common-reflection-point (CRP) gathers obtained by dynamic Q migration well compensate the amplitude loss and correct the phase. Its ultimate pre-stack elastic inversion result better characterizes the geologic rules of complex carbonate reservoir predominated by secondary-storage-space.

Variable-depth streamer acquisition: Broadband data for imaging and inversion

Conventional marine acquisition uses a streamer towed at a constant depth. The resulting receiver ghost notch gives the maximum recoverable frequency. To push this limit, the streamer must be towed at a quite shallow depth, but this compromises the low frequencies. Variable-depth streamer (VDS) acquisition is an acquisition technique aimed at achieving the best possible signal-to-noise ratio at low frequencies by towing the streamer very deeply, but by using a depth profile varying with offset in order not to limit the high-frequency bandwidth by notches as in conventional constant-depth streamer acquisition. The idea is to use notch diversity, each receiver having a different notch, so that the final result, combining different receivers, will have no notches. The key step to process VDS acquisitions is the receiver deghosting. We found that the optimal receiver deghosting, instead of being a preprocessing step, should be done postimaging, by using a dual-input, migration and mirror migration, and a new joint deconvolution algorithm that produces a 3D real amplitude deghosted output. This method can be applied poststack, the inputs being the migration and mirror migration images and the output being the deghosted image. Using a multichannel joint deconvolution, the inputs are the migrated and mirror migrated image gathers and the outputs are the prestack deghosted image gathers. This method preserves the amplitude-versus-offset behavior, as the deghosted output can be seen on synthetic examples to be equal to a reference computed by migrating the data modeled without any reflecting water surface. A real data set was used to illustrate this method, and another one was used to check the possibility of performing prestack elastic inversion on the deghosted gathers.

Variable-depth streamer acquisition: broadband data for imaging, post and pre-stack inversion

Variable-depth streamer acquisition is a broadband streamer acquisition technique where the depth profile of the streamer is optimized in order to ensure receiver ghost diversity, which in turn allows the deconvolution of the residual ghost at the imaging stage, pre-stack or post-stack. This technique allows the streamers to be towed at an average depth of several tens of meters, which combined with the use of solid streamers, ensures the raw data has an exceptionally good signal-to-noise ratio, especially at low frequencies. This variable-depth streamer acquisition and processing has been field-tested on a variety of locations, achieving bandwidth up to 6 octaves (2.5Hz -160 Hz). This broad bandwidth translates into improved results for the acoustic impedance inversion. The lack of low frequencies in conventional seismic data means that a low frequency model must be incorporated in the inversion process, obtained by interpolating low-passed filtered impedance logs between well locations. With variable-depth streamer data, high-resolution NMO-derived seismic velocities are used to define the low frequency model in a range 0-5Hz, while the reflectivity provides information from 2.5Hz. Variable-depth streamer data thus have the potential to fill the usual gap between the high frequencies of the seismic velocities and the low frequencies of the reflectivity, the 2.5-5 Hz octave being the overlapping zone. Pre-stack elastic inversion has also been performed, providing both impedance and Vp/Vs sections, proving the feasibility of pre-stack deghosting of variable-depth streamer data.

Introduction to this special section: Carbonate research in China

Carbonate reservoirs in western China have tremendous potential and are the key area for oil and gas exploration in that country. Compared to conventional carbonate reservoirs, discovering and characterizing this kind of reservoir is much more difficult and presents significant challenges. Solutions to the major geophysical problems began with a detailed analysis of exploration issues for such complex carbonate reservoirs and, subsequently, a set of techniques for complex carbonate reservoir prediction was established. These include highly accurate seismic acquisition, prestack amplitude-preserved processing including prestack depth migration, new rock physics models, prestack elastic inversion, seismic multiattribute optimization and integrated prediction, fracture detection using prestack data with limited azimuthal distribution, and fluid identification based on prestack inversion. Additionally, to solve some special problems, diffraction wavefield separation and imaging algorithms were developed for better imaging of caves. Q-migration and nonstationary deconvolution algorithms were also developed for resolution enhancement. Application of these techniques to field data has proven effective, and drilling results show good agreement with our research. Nevertheless, the field is still in its infancy.

Gas sand distribution prediction by prestack elastic inversion based on rock physics modeling and analysis

Seismic inversion is one of the most widely used technologies for reservoir prediction. Many good results have been obtained but sometimes it fails to differentiate the lithologies and identify the fluids. However, seismic prestack elastic inversion based on rock physics modeling and analysis introduced in this paper is a significant method that can help seismic inversion and interpretation reach a new quantitative (or semi-quantitative) level from traditional qualitative interpretation. By doing rock physics modeling and forward perturbation analysis, we can quantitatively analyze the essential relationships between rock properties and seismic responses and try to find the sensitive elastic properties to the lithology, porosity, fluid type, and reservoir saturation. Finally, standard rock physics templates (RPT) can be built for specific reservoirs to guide seismic inversion interpretation results for reservoir characterization and fluids identification purpose. The gas sand distribution results of the case study in this paper proves that this method has unparalleled advantages over traditional post-stack methods, by which we can perform reservoir characterization and seismic data interpretation more quantitatively and efficiently.

The application of elastic impedance inversion in reservoir prediction at the Jinan area of Tarim Oilfield

The Triassic reservoir in the Jinan area of Tarim Oilfield consists largely of interbedded sand and shale. Because of the large overlap between sandstone and shale impedance, it is difficult to distinguish sandstone from shale by acoustic impedance alone. Compared to acoustic impedance, elastic impedance contains more lithologic and physical information of the reservoir. Based on meticulous well-tie calibration, elastic impedance data volumes for 10°, 20°, and 30° emergence angles are obtained using pre-stack elastic impedance inversion. A non-linear statistical relationship between elastic impedance and shale content is set up by a PNN neural network. The non-linear mapping relationship is used to predict the reservoir shale content from elastic impedance, which will depict and predict the reservoir oil-bearing sands.

Application of joint elastic impedance inversion in the GD Oilfield

For the complicated reservoir description of the GD oilfield, P-wave and S-wave elastic impedance inversion was carried out using pre-stack seismic data to accurately identify the lithology of the reservoir. The joint inversion was performed using three or more partial stacks to overcome the singularity of post-stack seismic inversion that can not satisfy the requirements of complex reservoir description and to avoid the instability of the inversion result caused by low signal-noise ratio in the pre-stack gather. The basic theory of prestack elastic impedance inversion is briefly described in this paper and, using real data of the GD oilfield, the key steps of angle gather wavelet extraction, horizon calibration, S-wave velocity prediction, and elastic parameter extraction were analyzed and studied. The comprehensive interpretation of multiple elastic parameters determined from log analysis is a key to improving the effect of prestack seismic inversion.

Combined seismic inversion and gravity modeling of a shallow anomaly in the southern Barents Sea

A combination of prestack elastic inversion with gravity modeling has been applied to a shallow seismic anomaly in the southern Barents Sea. The anomaly is crosscutting dipping layers of late Paleocene age. Earlier seismic interpretations indicate a possible origin in gas‐hydrated sediments trapping underlying free gas. Our interpretation includes seismic inversion of a seismic model which consists of a stack of isotropic, homogeneous, and anelastic layers. The unknown parameters are the P‐ and S‐wave velocities, density, and thickness for each layer. As densities are poorly determined by this method, we included gravity modeling, which improved the density estimates. The resulting parameters have been integrated by rock physics calculations and the knowledge of typical attributes of gas hydrate occurrences. The top of the seismic anomaly is interpreted as a reflection from the base of a gas‐hydrated sediment trapping underlying free gas. The base of the anomaly is the gas‐water contact, which deviates from a flat spot due to capillary pressure differences related to lithology and the generation process of gas hydrate. The estimated density has been interpreted together with well results and indicates a significant amount of gas filling the pore volume.

An integrated target‐oriented prestack elastic waveform inversion: Sensitivity, calibration, and application

An integrated target‐oriented prestack elastic waveform inversion procedure is implemented to estimate lithology, fluid type, and pay thickness of a layered target zone from surface seismic PP reflection data. The integrated inversion procedure consists of three parts: data processing and preparation, iterative seismic inversion, and rock property integration. In the data processing and preparation, the seismic field gathers are processed and transformed into plane‐wave seismograms, and the well‐logs are prepared for establishing a well tie. The well tie is established using synthetics from a layered model obtained from blocking sonic, shear sonic, and density logs. The layered model is later used as the a priori starting model for the iterative seismic inversion. Based on the a priori starting model and using the processed plane‐wave seismograms as input, P‐wave velocity ( [Formula: see text]), S‐wave velocity ([Formula: see text]), density ρ, and thickness (h) of each layer in the layered target zone are estimated at each CDP location in the iterative seismic inversion. Through the rock property integration, the inverted seismic parameters are related to the reservoir properties: the lithology/fluid contents, and the net pay thickness. Synthetic examples of gas‐related bright spot models are used to illustrate the functionality of the procedure. The sensitivity and the vertical resolution of the inversion procedure are investigated. Under favorable conditions, the inversion procedure is able to estimate the net pay thickness down to a tenth of a wavelength. In noisy situations, the inversion tends to break down where the thickness of target is approximately equal to the tuning thickness. The procedure was successfully applied to a gas‐related shallow bright spot prospect offshore Gulf of Mexico. The lithology (sand shale distribution), [Formula: see text] ratio, and the net pay thickness of gas‐sand were derived for the prospect. The estimated net pay thickness of gas‐sand was within acceptable error range when compared with the actual net pay thickness measured from well logs.