Target-oriented wavefield tomography using demigrated Born data

introduction

Velocity estimation is always a challenging task in exploration seismology. In the past decade, ray-based tomography has been widely used in practice to derive velocity models. Although ray-based methods are efficient, the infinite-frequency approximation and the caustics inherent in ray theory prevent them from accurately modeling complicated wave phenomena (Hoffmann, 2001). As seismic exploration is moving towards structurally complex areas, ray-based methods become less reliable. On the other hand, wave-equation-based tomography (Mora, 1989; Shen, 2004; Pratt, 1999; Woodward, 1992; Tarantola, 1984; Sava, 2004) uses wavefields as carriers of information. It more accurately describes the bandlimited wave phenomena, and therefore more suitable for complex geologies.

Wavefield tomography can be implemented in either data domain or image domain. In this paper, however, we mainly focus on the image-domain wavefield tomography, which is also widely known as wave-equation migration velocity analysis (Shen, 2004; Sava, 2004). It derives an optimum velocity model by driving an objective function defined in the image domain to its minimum. Despite its advantages in modeling bandlimited wavefields, practical application of image-domain wavefield tomography is still rare and small in scale due to its huge computational cost (Biondi and Sava, 1999; Shen et al., 2005; Albertin et al., 2006). The high cost arises because of the use of more expensive wavefield modeling engines. The other reason is that it lacks flexibility and the recorded full data set is usually used for velocity estimation.

Several methods have been proposed to make wavefield tomography more cost effective. The main idea is to reduce the size of the data used for velocity estimation. One method is to assemble the originally recorded point-source gathers into a smaller number of areal-source gathers. Among others, the plane-wave source gather (Shen and Symes, 2008; Tang et al., 2008; Whitmore, 1995; Zhang et al., 2005) is the most popular one because the plane-wave phase-encoding function is effective in attenuating the crosstalk artifacts (Tang, 2008; Liu et al., 2006). The other method is to model a new data set in a target-oriented fashion using the concept of prestack-exploding-reflector modeling with a bottom-up strategy (Guerra et al., 2009; Biondi, 2007,2006). However, the modeling generates crosstalk when multiple image events are modeled simultaneously. Stochastic encoding methods, such as random-phase encoding, seem to be the only encoding methods available to attenuate the crosstalk produced when imaging the image-domain encoded gathers (Guerra and Biondi, 2008b,a).

In this paper, we present a new strategy to reduce the size of the data set used for image-domain wavefield tomography. The proposed strategy combines advantages of both prestack-exploding-reflector modeling and data-domain encoding: Not only can it model a new data set in a target-oriented fashion, but it also can use plane-wave sources to effectively attenuate the crosstalk. We start with an initial image and gathers obtained using a starting velocity model. The initial image and gathers are further normalized using the diagonal of the imaging Hessian, efficiently computed using the phase-encoding method (Tang, 2009), to optimally compensate for the uneven subsurface illumination and remove the effects of the original acquisition geometry. Instead of using prestack-exploding-reflector modeling, we then use Born modeling or demigration (Stolt and Benson, 1986) to simulate the new data set. The modeling procedure is based on the single-scattering approximation to the full wave equation. The resulting Born modeled data is obtained by convolving the source wavefield, computed using any type of source function (e.g. plane-wave sources), with the initial image and gathers and then propagating the convolved wavefields to receiver locations, which can be located anywhere in the model. The target-oriented data set is obtained by only modeling image points within a target zone or several key reflectors that carry important velocity information. This target-oriented velocity analysis strategy is useful, because it allows us to use the most powerful velocity estimation tool to focus on improving velocities in the most challenging areas, e.g., subsalt regions, provided that velocities at other locations are sufficiently accurate, e.g., regions above the salt, where the velocities are usually very accurately determined even by ray-based tomography thanks to the relatively simple geologies.

In the next section, we briefly review the theory of Born modeling. In the subsequent sections, we apply the proposed target-oriented velocity-estimation method to invert the local velocity anomalies in a modified Sigsbee2A model.

Target-oriented wavefield tomography using demigrated Born data