Target-oriented wavefield tomography: A field data example

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 (or maximum). 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 whole 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. But this strategy lacks flexibility, and full-domain wavefield propagation is still required at each velocity inversion iteration. Therefore, the cost reduction can not be substantial.

Guerra et al. (2009); Biondi (2007,2006); Guerra and Biondi (2010) approach this problem in a completely different way. They synthesize a new data set based on the initial image using the concept of prestack-exploding-reflector modeling. The new data set is then used specifically for velocity analysis. The advantage of this strategy is that it can model a new data set in a target-oriented fashion, therefore the wavefield propagation can be restricted to regions with velocity inaccuracies, substantially reducing the computational cost. However, the modeling generates crosstalk when multiple image events are modeled simultaneously. This limits the number of reflectors to be modeled. Manual picking and stochastic encoding methods, such as random-phase encoding, are required to minimize the impact of the crosstalk (Guerra et al., 2009).

Another way to synthesize a target-oriented data set is through Born wavefield modeling, or demigration (Tang and Biondi, 2010). This technique has been used by Wang et al. (2005), who generate a post-stack data set and use it for efficient subsalt velocity scan. In our method (Tang and Biondi, 2010), however, we generate a prestack Born data set and use it for wavefield-based tomography. As shown by Tang and Biondi (2010), our modeling strategy is very flexible. Except for windowing out the target image from the initial image, no picking is necessary, but picking can also be introduced if it is desired. Human intervention can also be incorporated by carefully conditioning the initial image to be modeled.

Born wavefield modeling is based on the single-scattering approximation to the full wave equation. The modeled data is obtained by convolving the incident source wavefield, computed using any type of source function (e.g. plane-wave sources), with the initial image 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 strategy to a field data set acquired from the Gulf of Mexico.

Target-oriented wavefield tomography: A field data example