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 com- ponent 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 op- timal 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 densi- ties. 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 inter- bedded 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 yono et al., 2014; Colombo et al., 2013, 2010, 2008; Opfer, In common depth point (CDP) survey, statics preparation 2003). To solve the inverse problem, initial data such as the is carried out by the times of first arrivals on reflection seismo- observed gravity field and its local components obtained by grams. A near-surface velocity model can be derived from au- particular means are used. However, significant errors in the tomated methods (Zhu et al., 2014; Raef, 2009; Cox, 1999). The statics corrections arise due to limitations of these methods, main disadvantage of the majority of these methods is that they namely, formal selection of the local component of the gravity do not guarantee high precision results in many regions since field, the use of the near-surface model in a form of a plane they try to solve the inverse problem with simplified models of layer, and the absence of regression equation between velocity subsurface structure. Therefore, it is necessary to work out bet- and density in the near-surface formation in particular explora- ter methods to calculate near-surface velocity, heterogeneity tion areas. and statics correction in seismic prospecting. In areas where three-dimensional seismic works have been 1 SOLUTION ALGORITHM done, there are generally sufficient 2D seismic profiles and oil We suggest the following algorithm to interpret gravity da- wells are drilled deeper there, in which up-hole velocity surveys ta to calculate the near surface rock density with further statics (UVS) and areal gravity explorations on different scales have computation. been previously conducted. Due to a close correlation between (1) Determine the average near-surface rock density (inter- seismic wave propagation and rock density (Gardner et al., bedded layer), with respect to which anomalous densities for 1974), the near-surface heterogeneity influences both seismic further calculations will be determined. For this purpose, conven- and gravity fields. It allows using gravity data to interpret seis- tional methods using gravity data and terrain relief altitudes can mic data, particularly, to determine first-estimate statics before be applied. Previous experience of such works shows that simple 3D seismic works. Nettleton’s method is the most effective (Nettleton, 1940). The existing methods of applying gravity data for statics (2) Allocate the gravity field component determined by the calculation mainly reduce themselves to the solution of the near surface effects. All data available and possible methods to linear inverse problem, i.e., calculation of near-surface rock divide the field including geological reduction, frequency filter- densities with their further interval velocity-conversion (Seti- ing and correlation transformation should be used. (3) Calculate the near-surface rock density by solving the *Corresponding author: [email protected] linear inverse gravity problem using the field component ob- © China University of Geosciences and Springer-Verlag Berlin tained at the previous stage. For the first approximation, the Heidelberg 2015 average near surface rock density is used. Decision problem forward and inverse gravity in 2D or 3D option to layer limited Manuscript received January 5, 2015. above terrain, bottom-datum. Approximation of layer is made of Manuscript accepted April 7, 2015. 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 σij. The solution of inverse linear problem is carried out on the Earth’s surface points {xi, yj} by the formula nn1inmod ij ij()gg ij ij where n-number of iteration, Δgin and Δgmod-initial and model fields accordingly, α-parameter of regularization. This parame- ter 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 approxi- mation 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 coeffi- cient of correlation between the values of elastic wave veloci- ties 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 Figure 1. Solution of the forward problem of gravity. (a) Pat- formation with the obtained densities and specify the local field terns of initial and model gravity fields; (b) near-surface density component. The iterative process of selecting a local component curve; (c) geo-density model. 1. Source; 2. model field at con- ends with the maximum coefficient of correlation between the stant near-surface density; 3. model field at variable near- values of velocities and densities reached, and the coincidence surface; 4. retrieved near-surface densities; 5. average rock within the given error of the observed and calculated gravity densities (g/cm3); 6. density interfaces. fields. (6) Elastic wave velocity-conversion of values of the rock model errors and regional background represent in the first density using established correlation and statics evaluation. place the influence of unconsidered near-surface heterogeneities. The interpretation process can be repeated after the first To solve the linear inverse problem, differences between the stage of determination of statics corrections, i.e., by using the priory and determined anomalies are converted into variable established correlation we obtain a set of the near-surface rock rock densities. The iterative process of density retrieval ends densities, solve the forward problem, and obtain the local com- with the coincidence of the observed and calculated curves g ponent of gravity field. At the end of the interactive iterative within the desired precision or error of gravity observations. As process, we get values of the near-surface seismic wave veloci- Fig. 1b shows the systematic mismatch between the observed ties, used for statics evaluation, and values of gravity anomalies, and model fields g is completely removed due to the increase calculated with a variable density of the interbedded layer. Thus, of the near-surface density from 2.40 to 2.60 g/cm3 by the end the solution of the problem reduces to the building of a detailed of the profile. seismic-gravity model of the near surface. Thus, in the result of the first stage of the model development we get a set of near-surface rock densities on the 2 DEVELOPMENT OF A SEISMIC-GRAVITY MODEL profile, satisfying the gravity data. OF THE NEAR SURFACE For this area, a set of velocities of seismic wave propaga- The building of the model is complicated due to general tion in the near surface can be calculated by using seismic data. lack of information on the near-surface rock density. Therefore, In this case, the iterative process of the interpretation of wave the first stage of the building of the model is to determine and fields recorded during seismic survey is carried out. Based on specify the correlation between the near-surface velocity and the successive solution of the inverse and forward seismic prob- rock density for a particular exploration area. For this purpose lems, an optimal near-surface model retrieves, correlating with- on the basis of drilling data, seismic information, well-log data in the accuracy limits of observations with the observed seismic and effective densities obtained from gravity data (Nettleton, data (Fig. 2). At the same time, practice proves that it is appro- 1940) a detailed geologic-geophysical (geo-density) model of priate to use as a priori seismic data time fields of the first the whole investigated section is established (Fig. 1c). The waves, recorded in the initial part of CDP seismograms (Mityu- gravity response of the section is excluded from the gravity nina et al., 2003).