Near-Surface Correction on Seismic and Gravity Data

Journal of Earth Science, Vol. 26, No. 6, p. 851 857, December 2015 ISSN 1674-487X Printed in China DOI: 10.1007/s12583-015-0546-7 Near-Surface Correction on Seismic and Gravity Data S. Bychkov*, I. Y. Mityunina Perm State University, Mining Institute of Ural Branch of Russian Academy of Sciences, Perm 614001, Russia ABSTRACT: It is important and urgent to work out better statics correction methods to facilitate seismic prospecting. This paper presents a new method of statics correction calculation based on development of a seismic-gravity model of the near surface. Gravity interpretation includes determination of the local component caused by the near surface effects and calculation of the near-surface rock density by solving the linear inverse gravity problem. To obtain the near-surface velocities, priori seismic data such as time fields of the first waves recorded in the initial part of common depth point (CDP) seismograms are used. An optimal near-surface model is retrieved on the basis of the successive solution of the inverse and forward seismic problems, correlating with the observed seismic data. Matching of seismic and gravity model of the near surface yields the maximum coefficient of correlation between the values of velocities and densities. At the end of the interactive iterative process we get values of the near-surface seismic wave velocities, used for statics evaluation, and values of gravity anomalies, calculated with a variable density of the interbedded layer. The applications of the proposed method at geophysical exploration of oil and gas confirm the possibility of calculation of statics correction using the gravimetric data by constructing a coherent seismic-gravity model of the near surface. KEY WORDS: gravity, near-surface velocity, seismic-gravity model, statics correction. 0 INTRODUCTION In common depth point (CDP) survey, statics preparation is carried out by the times of first arrivals on reflection seismograms. A near-surface velocity model can be derived from automated methods (Zhu et al., 2014; Raef, 2009; Cox, 1999). The main disadvantage of the majority of these methods is that they do not guarantee high precision results in many regions since they try to solve the inverse problem with simplified models of subsurface structure. Therefore, it is necessary to work out better methods to calculate near-surface velocity, heterogeneity and statics correction in seismic prospecting. In areas where three-dimensional seismic works have been done, there are generally sufficient 2D seismic profiles and oil wells are drilled deeper there, in which up-hole velocity surveys (UVS) and areal gravity explorations on different scales have been previously conducted. Due to a close correlation between seismic wave propagation and rock density (Gardner et al., 1974), the near-surface heterogeneity influences both seismic and gravity fields. It allows using gravity data to interpret seismic data, particularly, to determine first-estimate statics before 3D seismic works. The existing methods of applying gravity data for statics calculation mainly reduce themselves to the solution of the linear inverse problem, i.e., calculation of near-surface rock densities with their further interval velocity-conversion (Seti- *Corresponding author: bsg@mi-perm.ru China University of Geosciences and Springer-Verlag Berlin Heidelberg 2015 Manuscript received January 5, 2015. Manuscript accepted April 7, 2015. yono et al., 2014; Colombo et al., 2013, 2010, 2008; Opfer, 2003). To solve the inverse problem, initial data such as the observed gravity field and its local components obtained by particular means are used. However, significant errors in the statics corrections arise due to limitations of these methods, namely, formal selection of the local component of the gravity field, the use of the near-surface model in a form of a plane layer, and the absence of regression equation between velocity and density in the near-surface formation in particular exploration areas. 1 SOLUTION ALGORITHM We suggest the following algorithm to interpret gravity data to calculate the near surface rock density with further statics computation. (1) Determine the average near-surface rock density (interbedded layer), with respect to which anomalous densities for further calculations will be determined. For this purpose, conventional methods using gravity data and terrain relief altitudes can be applied. Previous experience of such works shows that simple Nettleton s method is the most effective (Nettleton, 1940). (2) Allocate the gravity field component determined by the near surface effects. All data available and possible methods to divide the field including geological reduction, frequency filtering and correlation transformation should be used. (3) Calculate the near-surface rock density by solving the linear inverse gravity problem using the field component obtained at the previous stage. For the first approximation, the average near surface rock density is used. Decision problem forward and inverse gravity in 2D or 3D option to layer limited above terrain, bottom-datum. Approximation of layer is made of rectangular set boxes, each of which is specified with the Bychkov, S., Mityunina, I. Y., 2015. Near-Surface Correction on Seismic and Gravity Data. Journal of Earth Science, 26(6): 851 857. doi:10.1007/s12583-015-0546-7. http://en.earth-science.net

852 S. Bychkov and I. Mityunina density of σ ij. The solution of inverse linear problem is carried out on the Earth s surface points {x i, y j } by the formula ( g g ) n 1 n in mod ij ij ij ij where n-number of iteration, Δg in and Δg mod -initial and model fields accordingly, α-parameter of regularization. This parameter α is selected experimentally. It is smaller than that of the slower convergence of the iteration process, but with higher accuracy. At high values of the parameter, consistent approximation may disagree. End of iteration process criterion is a coincidence within the specified accuracy of initial and model fields or achieving a certain number of iterations. (4) Determine correlations between a priori velocities of elastic waves and the obtained densities. Obviously, the coefficient of correlation between the values of elastic wave velocities and densities can serve as a criterion of reliability of the interpretation as the whole method is based on the strength of this correlation. (5) Solve the forward gravity problem for the near surface formation with the obtained densities and specify the local field component. The iterative process of selecting a local component ends with the maximum coefficient of correlation between the values of velocities and densities reached, and the coincidence within the given error of the observed and calculated gravity fields. (6) Elastic wave velocity-conversion of values of the rock density using established correlation and statics evaluation. The interpretation process can be repeated after the first stage of determination of statics corrections, i.e., by using the established correlation we obtain a set of the near-surface rock densities, solve the forward problem, and obtain the local component of gravity field. At the end of the interactive iterative process, we get values of the near-surface seismic wave velocities, used for statics evaluation, and values of gravity anomalies, calculated with a variable density of the interbedded layer. Thus, the solution of the problem reduces to the building of a detailed seismic-gravity model of the near surface. 2 DEVELOPMENT OF A SEISMIC-GRAVITY MODEL OF THE NEAR SURFACE The building of the model is complicated due to general lack of information on the near-surface rock density. Therefore, the first stage of the building of the model is to determine and specify the correlation between the near-surface velocity and rock density for a particular exploration area. For this purpose on the basis of drilling data, seismic information, well-log data and effective densities obtained from gravity data (Nettleton, 1940) a detailed geologic-geophysical (geo-density) model of the whole investigated section is established (Fig. 1c). The gravity response of the section is excluded from the gravity anomaly in the course of the solution of the forward problem. Since the original model was built with a constant density of rocks, calculated gravity anomaly does not coincide with the observed. For example, in Fig. 1a variance curves have systematic characteristics of -2 mgal at the beginning of the profile to +2 mgal in the end. It is believed that the residual anomaly together with the Figure 1. Solution of the forward problem of gravity. (a) Patterns of initial and model gravity fields; (b) near-surface density curve; (c) geo-density model. 1. Source; 2. model field at constant near-surface density; 3. model field at variable nearsurface; 4. retrieved near-surface densities; 5. average rock densities (g/cm 3 ); 6. density interfaces. model errors and regional background represent in the first place the influence of unconsidered near-surface heterogeneities. To solve the linear inverse problem, differences between the priory and determined anomalies are converted into variable rock densities. The iterative process of density retrieval ends with the coincidence of the observed and calculated curves g within the desired precision or error of gravity observations. As Fig. 1b shows the systematic mismatch between the observed and model fields g is completely removed due to the increase of the near-surface density from 2.40 to 2.60 g/cm 3 by the end of the profile. Thus, in the result of the first stage of the model development we get a set of near-surface rock densities on the profile, satisfying the gravity data. For this area, a set of velocities of seismic wave propagation in the near surface can be calculated by using seismic data. In this case, the iterative process of the interpretation of wave fields recorded during seismic survey is carried out. Based on the successive solution of the inverse and forward seismic problems, an optimal near-surface model retrieves, correlating within the accuracy limits of observations with the observed seismic data (Fig. 2). At the same time, practice proves that it is appropriate to use as a priori seismic data time fields of the first waves, recorded in the initial part of CDP seismograms (Mityunina et al., 2003). This allows the use of the correlations between time fields of the first waves and fields of the vertical time, for making the wavefield continuation into subsurface velocity profiles more efficiently. Plotting the correlation dependence between the values of the obtained velocities and densities and calculating coefficients of pair correlation and the regression equation (Fig. 3a) we get a new set of densities and use them to solve the forward gravity

Near-Surface Correction on Seismic and Gravity Data 853 Figure 4. Block diagram of the algorithm for the best-fit gravity-seismic model establishment. Figure 2. Time fields of the first waves. (a) The observed; (b) model after the first stage of iteration. Figure 3. Correlation between rock velocity and density for the original (a) and retrieved (b) near-surface models. problem. In this case, the iterative process ends with the maximum coefficient of correlation reached (Fig. 3b) and the coincidence within a specified error of the observed and determined gravity fields. The next stage of the model building is conversion of density values by the determined correlation dependence to seismic wave velocities and making them more precise by solving the forward seismic problem. The obtained velocity values are checked once again by solving the forward gravity problem, i.e. the completely iterative process is repeated (Fig. 4), at the same time, the behavior of the regional gravity trend is made more precise, and the model of deep parts of the section is corrected. The procedure of converting rock density to velocity and vice versa with the correction of their values continues until the bestfit seismic gravity model, satisfying both methods, is established. In the result of the interactive iterative process, we get val- Figure 5. CDP stacks obtained with different statics technique. (a) Statics correction plots; (b) terrain relief; (c) time section with standard statics technique; (d) stack with static corrections corresponding to gravity anomalies. 1. Standard statics technique plot; 2. statics plot calculated corresponding to gravity anomalies; 3. wells with vertical-velocity survey. ues of the gravity anomaly, determined with variable density of the interbedded layer and values of the velocity of seismic waves in the near surface, which is used for statics calculation. As Fig. 5a shows values of uphole-based statics and calculated

854 S. Bychkov and I. Mityunina from the gravimetric data differed by almost 10 ms. Comparison of CDP sections obtained with different statics technique revealed (Figs. 5c, 5d) that use of the statics corrections calculated from the gravimetric data significantly improved the continuity of practically all reflecting horizons. This is most clearly noticeable in the middle part of the profile (x=2.3 3.0 km), where by gravity data it is possible to find low-velocity nearsurface anomalies, which do not correlate with the elevations of surface topography (Fig. 5b). What is more, the obtained correlation between the rock velocity and density can be used to develop a first approximation near-surface model for areas with similar geological structures. 3 A PRIORI STATICS CALCULATION IN AREAL SURVEYS We consider an example of the interpretation of geophysical information in one of the areas situated in the Solikamsk depression of the Cis-Ural foredeep within the spread of Verkhnekamskoe potassium accumulation at the depth of 200 400 m. The formation of salt interferes with seismic imaging and causes high-amplitude gravity anomaly significantly exceeding the effect of target geological features. Under the salt formation at the depth of 1.9 2.1 km there is an oil deposit dating to Late Devonian reefs. In the area of detailed study of the geological structure of the oil deposit 3D seismic (OJSC Permneftegeofizika ) and gravimetry scaled 1 : 10 000 (Mining Institute of UB of RAS) were set. Gravity observations were made by using Autograv CG-5 gravimeters on 3D seismic profiles over a network 250 300 m in increments of 50 m. The rootmean-square error of determining Bouguer anomalies was 0.028 mgal. The main task of the gravity measurements was to study density structure of the region and first of all the localization of density heterogeneities in suprasalt and salt formations. This area is particularly convenient to test the method of the building of the best-fit gravity-seismic model of the near surface for statics calculation due to the previous 2D seismic survey and a sufficient number of the wells in which uphole velocity survey (UVS) was made. Besides, on the margins of the investigated area there are two-and-a-half-inch conditional gravity anomaly maps used to calculate edge effects at field continuation. The interbedded layer density, nearest to the true density of the rocks composing the relief, was determined by Nettleton s method. For each profile, a series of Bouguer anomaly curves was plotted, calculated at different densities of the interbedded layer. From the series, one curve was selected, which least correlated with the relief. Fig. 6a shows position of two lines (7 and 101) for which Bouguer gravity profiles are displayed (Fig. 6b). Nettleton s method found that the average rock density of the interbedded layer for the whole area was about 2.40 g/cm 3. This density was used for Bouguer anomaly calculation and further solution of the forward and inverse problems. As it has been mentioned, the main density contrast in this area is the top of salt with density differences 0.2 0.3 g/cm 3. The morphology of salt surface was investigated by salt exploration holes and was then enhanced by gravity data, which renders it reasonable to exclude the influence of this formation from the observed gravity field, i.e., to use geological reduction. As Fig. 7, presenting reduction results, shows a change in absolute elevation of the top of salt of more than 100 m in this area (Fig. 7b) and causes gravitational effect over 3 mgal, whose exclusion results in a significant change of the gravity field morphology (Fig.7c). The next problem is to obtain the local field component Figure 6. Determination of the interbedded layer density by Nettleton s method of (a) terrain relief, (b) graphics of gravity anomalies for different densities of the interbedded layer (curve parameter-density, g/cm 3 ). Figure 7. Gravity reduction of gravitational field. (a) Original gravity anomaly map; (b) top of salt map (points represent holes); (c) residual gravity map.

Near-Surface Correction on Seismic and Gravity Data 855 determined by the near-surface influence. As is mentioned above, this problem is ambiguous and can be solved to some extent by a way of vector scanning developed at the Mining Institute of UB of RAS (Bychkov at al., 2003). The computebased system VECTOR, realizing the procedure of vector scanning, allows dividing gravity field into components, characterizing particular intervals of the geological cross-section and getting a three-dimensional image of the interior density. It is based on stable calculation of horizontal derivatives, their processing, and transformation with further integration of the results. All transformations are carried out within horizontal gradients space. Smoothing data using running window in consideration of vector direction gives an opportunity for determination local and regional components of gravity field. Subsequent integration of the component allows obtaining reconstruction field. Gravity response of deep sources reduction achieved by vector scanning is caused by different characteristics of attenuation of gravity field and its horizontal gradient within large distance from the source. Transformation parameter is a factor k, which determines the relative size of the running window. As the size of the running window increases averaging vectors of horizontal gradient over a larger area, decreasing the frequency content of the local component of the field and to some extent, we can assume that increases the depth of the scanning field. To estimate the near-surface gravity influence from a set of field transforms, calculated in the VECTOR system with different sizes of k, that local component is selected, which best correlates with the fixed values of near-surface velocities calculated on the UVS data. The results of dividing gravity field into components are shown in Fig. 8. The source (reduced) field (Fig. 8b) is divided into local components, calculated with different parameters of the VECTOR k transformation (Fig. 8c). The obtained local anomalies were compared with the near-surface velocity map (Fig. 8a). Relationship between the original field of gravity anomalies and the velocity of elastic waves in the upper part of the section is practically absent (the correlation coefficient R is 0.204) (Fig. 8d). For the local component of the field calculated in the VECTOR at k=0.15, the correlation coefficient is 0.802 (Fig. 8e), indicating that it may be used to calculate the velocity of elastic waves. The linear inverse problem was solved by retrieving density of the layer, limited from above by the terrain relief and from below-datum plane. Layer approximation was carried out by a set of rectangular parallelepipeds. Figure 9 presents retrieved near-surface rock densities. The densities were retrieved at points on the land surface (Fig. 9b). The mean square error of retrieval made 0.028 mgal. The result of the calculations a map of the near-surface density values is shown in Fig. 9c. Figure 8. Dividing gravity field. (a) Velocity map of elastic waves in the near-surface (points represent UVS wells); (b) the observed gravity field; (c) field transforms calculated in the vector system at different values of k; (d) correlations between velocities and observed gravity anomalies; (e) correlations between velocities and the field transform at k=0.15.

856 S. Bychkov and I. Mityunina Figure 9. Results of the near-surface rock density retrieval. (a) Map of gravity local anomalies; (b) terrain relief; (c) retrieved nearsurface rock densities. Figure 10. Maps of statics corrections calculated by different methods. (a) by refracted waves (Millennium complex programs); (b) by gravity data (points on map represent UVS wells). Using the obtained regression equation a velocity map of the near surface was constructed for the whole exploration area and was further converted with the calculation of the nearsurface thickness into a map of statics corrections (Fig. 10b). Comparison of the obtained data with the corrections, calculated during the processing of first arrivals of the whole of 3D seismic records in a complex of the Millennium (Green Mountain Geophysics, USA) programs at OJSC Permneftegeofizika (Fig. 10a) shows their good convergence. It proves reliability of the results and the possibility of predicting the near-surface velocity heterogeneities on gravity data before 3D seismic works. In case of absence of UVS wells in the area for a priori data on elastic wave velocities, results of the previous 2D seismic data interpretation can be used. The near-surface seismic wave velocities, converted to rock densities, can be further used for gravity data interpretation. Thus, if to solve the forward problem for the layer, bounded from above by terrain relief and from below-datum plane, with the calculated densities, we will get the interbedded layer variable density correction in the Bouguer anomaly analogical to terrain correction. This will allow removing anomaly interference, which is of no interest in studying oil prospective fields at great depth. 4 CONCLUSIONS For important seismic CDP problem of determining a priori statics, we propose a method based on the construction of a coherent seismic-gravity model. processing Our method mainly differs from the existing methods using gravity data in the seismic data by the following three features. (1) Division of the gravity field on the components and the release of the one that best agrees with a priori values of elastic wave velocities. (2) Gravity inversion of the selected components with the calculation of the density of near-surface rocks. (3) Determination of the regression coefficients between the

Near-Surface Correction on Seismic and Gravity Data 857 values of calculated densities and seismic velocities from which converts the density near-surface section into the velocity one. To implement the method, we have developed an interactive iterative process, the output of which has velocities of seismic waves in the near surface. That is used for the calculation of statics corrections, and the values of gravity anomalies, computed with variable density of the interbedded layer. The method can be used in 2D, and 3D seismic surveys. REFERENCES CITED Bychkov, S., Novoselitskiy, V., Prostoloupov, G., et al., 2003. The Computer-Based System VECTOR as a Tool for Detection and Localization of Both Gravity and Magnetic Field Sources and Its Applications at Geological Interpretation. Abstracts of Contribution of the EGS-AGU-EUG Joint Assembly, Nice. 5: EAE03-A-01497 Colombo, D., Cogan, M., Hallinan, S., et al., 2008. Near- Surface P-Velocity Modeling by Integrated Seismic, EM, and Gravity Data: Examples from the Middle East. First Break, 10: 91 102 Colombo, D., Mantovani, М., Sfolciaghi, M., et al., 2010. Near Surface Solutions in South Rub Al-Khali, Saudi Arabia Applying Seismic-Gravity Joint Inversion and Redatuming. First Break, 2: 77 84 Colombo, D., Rovetta, D., Curiel, E. S., et al., 2013. 3D Seismic-Gravity Simultaneous Joint Inversion for Near Surface Velocity Estimation. Expanded Abstracts of 75th EAGE Conference & Exhibition incorporating SPE EUROPEC, London. 1 5 Cox, M. J. G., 1999. Static Corrections for Seismic Reflection Surveys. SEG, Tulsa Mityunina, I. Y., Spassky, B. A., Laptev, A. P., 2003. First Waves in Seismic Reflection Seismograms and Near- Surface Studies. Geophysics, 5: 5 12 (in Russian with English Abstract) Nettleton, L. L., 1940. Geophysical Prospecting for Oil. McGraw-hill Book Company, New York, London. 452 Opfer, R., 2003. Imaging Seismic Data with High Resolution Gravity Data. VIII Symposia Bolivariano-Exploration Petrolera en las Cuencas Subandinas, Colombia. 438 442 Raef, A., 2009. Land 3D-Seismic Data: Preprocessing Quality Control Utilizing Survey Design Specifications, Noise Properties, Normal Moveout, First Breaks, and Offset. Journal of Earth Science, 20(3): 640 648. doi:10.1007/s12583-009-0053-9 Setiyono, K., Gallo, S., Boulanger, C., et al., 2014. Near Surface Velocity Model of the Dukhan Field from Microgravity and Resistivity to Enhance PSDM Seismic Imaging. Expanded Abstracts of 76th EAGE Conference & Exhibition, Amsterdam. 1 5 Zhu, X. S., Gao, R., Li, Q. S., et al., 2014. Static Corrections Methods in the Processing of Deep Reflection Seismic Data. Journal of Earth Science, 25(2): 299 308. doi: 10.1007/s12583-014-0422-x