Application of seismic boundary-preserving constrained inversion for delineating reservoir body Tieyuan Zhu ∗ and Jerry M. Harris, Department of Geophysics, Stanford University SUMMARY Delineating reservoir units is still a challenge for seis- mic studies. In this paper, we propose to use seis- mic crosswell inversion with a new boundary-preserving constraint for delineating the ambiguous geometry of a reservoir. The advantage of boundary-preserving con- strained inversion is to preserve the geologic bound- ary of target reservoir. Firstly, we use synthetic exam- ples to verify the methodology in comparison with those of conventional smoothly constrained inversion. Then we apply this boundary-preserving inversion method to field data. We found that the boundary preserving con- straints improve image quality by preserving the ex- pected boundaries - top and base of reservoir. INTRODUCTION Cross-well seismic tomography as a high resolution imag- ing method is usually recruited to delineate and charac- terize the reservoir. Traditional tomographic approaches to invert traveltime data employ smoothness and/or flat- ness constraints (Constable et al., 1987). Such methods are able to extract large scale geological structure and tend to produce smoothed models. Therefore sharp con- trasts in the medium such as lithological boundaries are not easily identified and small targets are smeared out. For example, the reservoir boundaries in King moun- tain field in the Permian Basin of west Texas is ambigu- ous, in particular uncertainties about the bottom of reser- voir, which critically influence the location of water well drilling. On the other hand, from previous studies, the lateral extent of reservoir is lost to track when massive carbonate reservoir had detected in another 640 ft well away (Langan et al., 1997). For the further qualitative and quantitative assessment and development of reser- voir, sufficient information about the lateral and vertical extent of reservoir is needed. In this case it is neces- sary to search for a method to improve the knowledge of reservoir boundaries. To overcome this limitation of conventional smoothness regularization, the boundary-preserving regularization has been proposed because they are considered to preserve sharp boundary of target and still smooth small varia- tion due to noise (Charbonnier et al., 1997). Although boundary-preserving functionals were developed in im- age reconstruction to restore sharp edges and high con- trast images (Charbonnier et al., 1997), these schemes have been introduced in geophysical fields (e.g. Portni- aguine and Zhdanov, 1999; Farquharson, 2008; Abubakar et al., 2008). One of attractive boundary-preserving reg- ularization is the minimum gradient support (MGS) pro- posed by Portniaguine and Zhdanov (1999) and then they successfully tested in gravity and magnetic data. Later, Zhdanov et al. (2006) proved its effectiveness in seis- mic cross-well tomography synthetic examples. This approach is barely applied to real datasets. In this paper, we reformulate the traveltime inversion algorithm using the minimum gradient support (MGS) regularization. To solve the inversion problem, we em- ploy a constrained Gauss-Newton minimization scheme. The final algorithm is tested on two synthetic cases. Then, we apply this algorithm on a field seismic dataset. METHODOLOGY The task of a geophysical inversion scheme is to find a approximate model of the subsurface that satisfies the measurements. Because of the incoherent noise of the measurements, the inverse problem usually is an ill-posed and must be regularized by additional constraints to re- duce the non-uniqueness and stabilize the solution. The conventional way of solving this ill-posed inverse prob- lem is the Tikhonov approach (Tikhonov and Arsenin, 1977). Mathematical formulation of the Tikhonov regu- larized method is Φ(m)= φ d (m)+ λ R(m) (1) where the first term φ d is the data residual and the second term R represents regularization. The parameter λ is the positive value regularization constant that moderates the goodness of fit to the measured data. The objective function of linearized cross-well tomogra- phy is φ d (m)= 1 2 ‖W d (Gm - d)‖ 2 2 (2) where G is the forward operator that contains the ray distance through each cell and d is the travel-time vector, m = m(x, z), is the slowness model vector, where x and z denote the center of the 2D discretization cell, and W d is the data weighing matrix. Boundary-preserving regularization DOI http://dx.doi.org/10.1190/segam2013-0695.1 © 2013 SEG SEG Houston 2013 Annual Meeting Page 562 Downloaded 08/19/13 to 128.12.187.34. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/