Simultaneous joint inversion of refracted and surface waves Simone Re *, Claudio Strobbia, Michele De Stefano and Massimo Virgilio - WesternGeco Summary In this paper, we review the near-surface challenges and present a new technique to address issues of shallow velocity model building. The method is based on simultaneous joint inversion of surface waves and firstbreak picks. We show its application to a 2D line acquired in Egypt. Introduction The shallow subsurface often exhibits large and rapid vertical and horizontal variations due to structural and stratigraphic reasons. The low compaction and cementation of shallow formations can generate extreme velocity changes, especially in arid areas without a shallow water table. From a geological and geophysical point of view, the near surface can be extremely complex, with multiple velocity inversion and sharp lateral velocity variations. It is well known that the impact of near-surface perturbations on seismic reflection data must be removed to obtain the correct geometrical image of deeper horizons and representative reservoir attributes. Additionally, the near surface is an important, but challenging, portion of velocity model building in depth imaging. The near-surface characterization is, therefore, an important part of seismic data processing, in particular for land data. Conventional approaches involve the use of refracted waves, or diving waves, for P-wave velocity model estimation. The use of Rayleigh waves can be an alternative when data are acquired properly. Refraction tomography (RT) and surface-wave inversion (SWI) are based on different physical principles, make use of different components of the wavefield, and have different limitations and strengths. Refraction tomography often provides deeper models and estimates directly the compressional wave velocity. But, with land data, refraction techniques can be challenging in areas with a complex near surface. The data quality can be critical; for instance, picking the near offset can be difficult. Often, only a limited offset range can be picked reliably. Moreover, velocity inversions and hidden layers can produce ambiguities, and they might not be resolved uniquely. Surface waves have a very high resolution in the shallow near surface and are very robust versus model complexity and data quality. However, even if the low-frequency penetration reaches hundreds of meters, the vertical resolution decreases with depth and the resolution at the final investigation target may be insufficient in some areas. Finally, conversion from shear to compressional velocities requires calibration with P-wave events. When RT and SWI are used, integration and reconciliation of the two models can be done in different ways. A robust framework for this task is simultaneous joint inversion (SJI). The two measurements are input into a single inverse problem, where a unique model with multiple properties is estimated, minimizing the data prediction error and a link between the two domains. The synergies between the two techniques can be exploited. Different portions of the model are resolved by the interacting contributions of the measurements. Surface waves and refractions in land data Land seismic acquisition usually involves deployment of sources and receivers at the surface. Such a configuration implies the generation and propagation of different wave types, including several events propagating in the near surface, primarily refracted waves and surface waves. Rayleigh waves, the so-called ground roll, constitute the largest component of the source radiation. Refracted P- waves are far less energetic, but often can be easily identified in gathers as first arrivals. Historically, surface waves were usually regarded only as coherent noise, and in conventional land acquisition, receiver arrays attempted to attenuate Rayleigh waves in the field. On the other hand, point-receiver acquisition with low-frequency sources and receivers provides a correct sampling of the Rayleigh wave modes and enables implementation of methods based on the analysis and inversion of surface waves for near-surface characterization. Raw point-receiver data are processed to extract the propagation properties, usually the dispersion curve, which is finally inverted to get a velocity profile. A comprehensive workflow for surface-wave analysis based on continuous and adaptive surface-wave processing, has been developed for land 3D data (Strobbia et al., 2009). This surface-wave processing workflow extracts the local Rayleigh wave properties, in particular the modal dispersion curves. For each given location within a survey, the Rayleigh wave properties are estimated considering a frequency-dependent receiver aperture to honor the frequency-dependent near-field effects, intrinsic attenuation, and variable lateral resolution. The result for an individual receiver line can be plotted as 2D dispersion pseudosection (Figure 1). Each column of the pseudosection represents the local dispersion curve for the considered mode. Multiple receiver and source lines are processed to get a dispersion volume with 3D geometries. The surface-wave propagation properties are then inverted to a shear-wave velocity (V s ) model, matching modeled properties to the measured ones. The vertical and lateral 1914
resolution is high and the method can solve velocity inversions and complex near-surface structures, but the investigation depth is generally limited to 100 to 200 m. Figure 1: Modal dispersion pseudosection for a receiver line. Refraction-based techniques, on the other hand, make use of the part of the body wave energy that is (continuously) refracted in the near surface and is observed in records as first arrivals. Refraction tomography tries to determine the subsurface velocity by means of fastest raypaths associated with first-break arrivals. First arrival traveltimes are picked and then inverted to a compressional wave velocity (V P ) model. Given a source-receiver pair and an interval velocity model, it is possible to compute first-arrival time by integrating the slowness along the trajectory of the refracted (i.e., fastest) raypath: t s( x, y, z) dr (1), = r where t is the total traveltime, r is the ray trajectory, and s is the slowness. V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 V 9 V 10 V 11 V 12 Figure 2: Example of a refracted ray for a given source-receiver pair and the formulation of RT problem for a simple 2D case. The subsurface is divided into cells: V P is constant inside the cell and the size of the cells defines the spatial resolution of tomography. Making the subsurface discrete leads to the discretization of equation 1 that can be expressed as: N t i = s j j= 1 l (2), where t i is the traveltime for the i-th source-receiver pair, s j is the slowness of the j-th cell of the model, and l is the length of the i-th raypath inside the j-th cell. Equation 2 is written for the 2D case shown in Figure 2, but the extension to the 3D case is straightforward. Collecting equations like equation 2 for each sourcereceiver pair allows building a linear system as: ij ij t = Ls (3), with t being the vector containing all traveltimes, L the matrix of all raypaths in each model cell, and s the slowness vector. Therefore, given a guess velocity (slowness) model, linear system 3 provides traveltimes for all source-receivers pairs (forward modeling). The difference between traveltimes computed using expression 3 and traveltimes coming from first-break picking can be used to invert the linear system and then to update the initial guess velocity model (inversion process). The tomography must then iterate to try to converge on the best estimate of the true model by minimizing the differences between the observed data (refracted pick times) and those computed by ray tracing for the current guess of the model. In areas characterized by shallow dipping reflectors and/or high lateral velocity contrasts, the process of Dix inversion, being based on a flat-layered earth model, cannot give an accurate description of the subsurface. In the same context, refraction tomography is a powerful tool for improving both time and depth processing. On the time-processing side, the interval velocity coming from tomography can be used for accurate static correction computation, while on the depth-processing side, the same velocity model is usually the first step in the model-building workflow by means of the depth migration process and CMP residuals analysis. However, due to issues related to inversion stability, the resolution of a velocity model achieved by refraction tomography is lower than that needed for depth imaging techniques. In addition, some geological configurations, such as cases with velocity inversions, cannot be resolved without independent information. These limitations can be overcome by solving refraction and surface-wave problems simultaneously. RT and SWI present several synergies. They have different depths of investigation, different intrinsic limitations, and different distribution of sensitivity and resolution with depth, but the two measured physical properties (V P and V S ) have a strong correlation. The joint use of the two techniques has, therefore, several advantages. The high lateral resolution and robustness of surface waves allow resolving shallow complex structures such as velocity inversions. Surface-wave data can fill the information gap due to missing offset ranges in the picked traveltimes, for instance, the noisy near offset. On the other hand, the joint inversion of the two measurements allows robust V S to V P conversion, and refraction data provide deeper velocity models. The final model can be used to compute near-surface corrections (for instance, statics) for depth imaging and other data processing applications. Additionally, it provides useful information for near-surface geological modeling in which the V P /V S ratio can play an important role. 1915
The simultaneous joint inversion method The term, joint inversion, is commonly used in the oil and gas industry to indicate a wide range of technologies and workflows that aim to integrate different measurements for geophysical exploration. Dell Aversana (2001) integrated seismic and electromagnetic data for structural imaging, Li and Oldenburg (1996b) used borehole and surface magnetic data to invert for susceptibility, and De Stefano and Colombo (2007) inverted linked data within a single cost function. This approach is called simultaneous joint inversion, given that the workflow integrates the measurements in the inversion phase and it is not simply an alternating sequence of single measurement inversions. SJI uses the same regularization and preconditioning that the single domains use for standard inversions. This is one of the key benefits provided by SJI; each domain is regularized (and/or preconditioned) as in single-domain inversions. Most importantly, SJI solves simultaneously for different scales, so that we can handle separately the denser V S unknowns to define precisely the very shallow portions of the models and the coarser V P unknowns to invert down to the main refractors of the model (Figure 4). Within this approach, SJI maintains the single-domain operators and workflows, reaching the benefits of a common inversion as described in the following section. Figure 4: Left: Grid used for refraction tomography. Right: Grid used for surface-wave inversion: short wavelengths (blue) have less penetration than long wavelengths (green). Different measurements invert data on different grids. Example Figure 3: Left: Single-domain approach to invert for V S and V P. Right: The SJI workflow to invert simultaneously for the two different measurements. For the first time, we propose SJI as a technology to invert simultaneously any combination of refracted, reflection, and surface-wave seismic data. In particular, in this paper we focus on real data applications in West Gharib (Egypt) using refracted and surface waves only, and we use a single objective function that is defined and minimized (De Stefano and Colombo, 2007), in contrast to an approach in which multiple objective functions are inverted in separate domains. As shown in Figure 3, SJI acts at the inversion phase where a kernel of the objective function is built from three different elements: 1. Residuals from different domains (misfits in the dispersion curves for V S and delays for first arrivals for V P ). 2. Single-domain constraints (second-order regularizations for lateral and vertical consistency). 3. Inter-domain constraints (empirical law linking V S and V P and some geometrical constraint forcing the models to have the same anomalies). To show the benefits of the presented method, we discuss the results of a 2D line, about 10-km long, extracted from a point-receiver 3D survey. The site is a gravel plain between the Gulf of Suez and the Red Sea Mountains in Egypt. Figure 5: Shear-wave velocity section from surface-wave inversion. Point-receiver data were acquired with 7.5-m receiver spacing and a vibroseis source. For the whole line, data show the presence of strong Rayleigh waves dominated by a fundamental mode, with large lateral velocity variations. Both the surface-wave and refracted-wave properties are estimated on point-receiver data. The extracted dispersion pseudosection and the first breaks are first inverted with a single-domain approach, independently. The result of surface-wave single-domain inversion is plotted in Figure 5. The velocity model does not indicate 1916
the presence of major velocity inversion in the near surface. There are, however, sharp lateral velocity variations. It is important to notice that the low-velocity zones identified by the V S inversion are extremely relevant from a geological point of view. They correspond to fault zones, they are observed throughout the whole survey area, and they are consistent with the structural setting of the region (Laake et al., 2010). They are spatially consistent and evident in the raw dispersion volume before inversion. In Figure 6, a wavelength slice is presented, with the location of the 2D line. The final results show good agreement with the shallow stack section, plotted in Figure 8. Figure 8: Shallow stack section of the considered 2D line. Conclusions Figure 6: Principle of surface-wave characterization and dispersion section. The simultaneous joint inversion of the two measurements is run using a link defined on the basis of the two singledomain inversions. The result of the simultaneous joint inversion is shown in Figure 7. Figure 7: Final V P section from SJI of refracted first arrivals and Rayleigh wave dispersion. This final V P section is obtained using the information from both measurements. The deeper part is controlled only by the refracted wave data, while in the shallow portion, the SW data provides high resolution. The final traveltime misfit of the SJI inversion is not larger than the one of the single domain refraction tomography. It is important to remark that, in this case, surface-wave data have confirmed the absence of critical features, such as velocity inversions. The presented method allows construction of a near-surface model, merging in a rational manner, the contribution of refracted waves and surface waves, usually treated as noise and simply removed from seismic records. Surface and refracted waves have different resolution, penetration, and therefore, depth of investigation; they have also different intrinsic limitations. Merging refracted and surface waves properly means taking benefits from both of them, and thus, deriving a better definition of the shallow subsurface parameters. Surface-wave methods are robust and offer high vertical and lateral resolution in the shallow near surface without suffering from the intrinsic limitations of refraction methods (hidden layer, velocity inversions, and others). At the same time, the investigation depth may not be sufficient for some applications, and the refraction techniques provide deeper models, giving directly the P-wave information that can be used in the data processing workflow for statics and velocity modeling, for example, without the need of conversion from V S to V P. The combination of the two techniques has, therefore, several synergies that can be exploited using simultaneous joint inversion. The joint inversion will also contribute to improve the shear-wave model reliability with Poisson s ratio anomalies. In these cases, the a priori assumption of the Poisson ratio may lead to model errors (Foti and Strobbia, 2002), and the use of the refraction data avoids this pitfall. Acknowledgments The authors acknowledge TransGlobe Energy and Dara Petroleum Company for the authorization to show the data. The authors also acknowledge WesternGeco for the authorization to publish this work. 1917
EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2010 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES De Stefano, M., and D. Colombo, 2007, Pre-Stack Depth Imaging via Simultaneous Joint Inversion of Seismic, Gravity, and Magnetotelluric Data: Presented at the 69th EAGE Conference and Exhibition, EAGE. Dell Aversana, P., 2001, Integration of Seismic, MT, and Gravity Data in a Thrust Belt Interpretation: First Break, 19, no. 6, 335 341, doi:10.1046/j.1365-2397.2001.00158.x. Gallardo, L. A., and M. A. Meju, 2004, Joint two-dimensional DC resistivity and Seismic travel time Inversion with Cross-Gradients constraints: Journal of Geophysical Research, 109, 1 11. doi:10.1029/2003jb002716 Hu, W., A. Abubakar, and T. M. Habashy, 2009, Joint Electromagnetic and Seismic Inversion Using Structural Constraints: Geophysics, 74, no. 6, R99 R109, doi:10.1190/1.3246586. Li, Y., and D. W. Oldenburg, 1996 Joint Inversion of Surface and Three Component Borehole Magnetic Data: 66th Annual International Meeting, SEG, 1142 1145. Strobbia, C., A. Laake, P. L. Vermeer, and A. Glushchenko, 2009, Surface waves: use them, then lose them: EAGE. Foti S., C. Strobbia, 2002, Some Notes on Model Parameters for Surface Wave Data Inversion, Proceeds of SAGEEP Laake A., M. Sheneshen, C. Strobbia, L. Velasco, A. Cutts, 2010, Surface-subsurface Integration Reveals Faults in Gulf of Suez Oilfields: EAGE Virgilio, M., D. Colombo, and A. Dyke, 2008, Seismic Imaging Strategies for Thrust-Belt Exploration: Extended Offsets, Seismic/Gravity/EM Simultaneous Joint-Inversion and Anisotropic GBM Pre- Stack Depth Migration: CSPG CSEG CWLS Joint Convention. 1918