Target-oriented elastic full-waveform inversion

Elastic full-waveform inversion (FWI) when successfully applied can provide accurate and high-resolution subsurface parameters. However, its high computational cost prevents the application of this method to large-scale field-data scenarios. To mitigate this limitation, we 1 arXiv:2206.07901v1 [physics.geo-ph] 16 Jun 2022 propose a target-oriented elastic FWI methodology based on a redatuming step that relies upon an extended least-squared migration process. In our approach, the surface-reflection data can be attributed to a given subsurface portion when mapped into the image space. This process allows us to reconstruct reflection data generated by a target area and recorded with a virtual acquisition geometry positioned directly above it. The redatuming step enables the application of an elastic FWI method within the target portion only. The entire workflow drastically diminishes the overall cost of the surface-data inversion and allows the retrieval of accurate elastic parameters of the area of interest. We demonstrate the effectiveness of our approach on a synthetic case based on the well-known Marmousi2 model and on a 3D ocean-bottom-node (OBN) pressure data recorded in the Gulf of Mexico. We first discuss the fundamental aspects of the methodology and apply the proposed workflow to the synthetic test case. We also employ the methodology on the field-data scenario and show its efficacy at correctly retrieving the elastic parameters and rock-physical properties of a gas-bearing sand reservoir positioned in proximity of a salt-dome flank.

 

Since its first definition by Tarantola (1984), FWI has become a fundamental process in velocity-model-building workflows (Virieux and Operto, 2009). The study described by Sirgue et al. (2010) represents one of the earliest successful applications of FWI to 3D field data. In their work, 3D data recorded in the Valhall field in the North Sea are acoustically inverted, and their FWI workflow produces significant image and velocity-model improvements compared to the initial subsurface information. Since then, FWI has continued to be a highly-relevant research topic in the seismic exploration field (Guitton and Alkhalifah, 2013). This growing interested is due to the ability of FWI processes to retrieve high-resolution and accurate subsurface parameters with minimal data processing. The technological advancements in the computer processing speed in recent years is allowing the application of computational intensive inversion and imaging methods (BrandsbergDahl, 2017). In fact, FWI methodologies are not limited to single-parameter and acoustic wave-equation inversion workflows, and multi-parameter estimation strategies applications for seismic exploration have been proposed and discussed by multiple authors (Operto et al., 2013). Specifically, elastic FWI is now widely considered to being able to accurately retrieve the subsurface material properties from seismic data (Sears et al., 2010; Vigh et al., 2014; Pan et al., 2018; Zhang and Alkhalifah, 2020; Chen et al., 2022). However, due to its high computational cost associated with the elastic wavefield modeling, elastic FWI approaches are usually applied to small 3D or only 2D field data. To mitigate the intrinsic cost of elastic FWI and focus the inverse problem to only a limited portion of the subsurface, multiple target-oriented strategies have been proposed. These methods can be separated into two major categories. The first one is represented by 3 approaches in which a redatuming step is performed before an elastic inversion processed is applied to data acquired with a virtual acquisition geometry positioned directly above any target area (Wapenaar, 2014; Ravasi, 2017; Guo and Alkhalifah, 2019; da Costa et al., 2019; Garg and Verschuur, 2020; Li and Alkhalifah, 2022). The second set of methods comprises workflows based on local solver strategies. Within them, the target-area wavefield is computed by changing the boundary conditions of the inversion domain (Malcolm and Willemsen, 2016; Masson and Romanowicz, 2017; Yuan et al., 2017; Kumar et al., 2019; Huang et al., 2020). Both categories have been successfully applied to different geological scenarios, but none of these applications have shown a 3D field application. Our method falls within the first category in which an extended least-squares migrated image is employed to perform the redatuming step before the target-oriented inversion process. Many authors employed this image domain to invert for a subsurface migration velocity based on optimal focusing of the image when the correct velocity is used during migration (Symes and Kern, 1994; Yang and Sava, 2009; Alkhalifah, 2014; Biondi and Almomin, 2014; Barnier et al., 2022a).

 

In other applications, a form of extended-image space based on ray parameter is used to generate angle gathers that preserve the amplitude information of the migrated events (Kuehl and Sacchi, 2002; Wang et al., 2005). The ability to maintain the amplitude behavior of primary reflected events allows for the analysis of the amplitude-versus-angle (AVA) information and its subsequent inversion to retrieve the elastic subsurface parameters (Schleicher et al., 1993; Albertin et al., 2004; Gray and Bleistein, 2009; Biondi et al., 2022). In our method, the extended image generated using the surface data is used to simulate data acquired using a virtual acquisition geometry placed in proximity of a target area. The redatum dataset is then inverted within an elastic FWI process whose modeling domain 4 comprises of only a selected subsurface area. We first describe the theory behind the entire workflow and use synthetic tests to highlights the fundamental aspects of our elastic inversion process. We test the method on synthetic data generated using the Marmousi2 model and estimate the elastic properties of one of the reservoirs present in the subsurface. To demonstrate the efficacy of our method on 3D field data, we apply it to the pressure component of an OBN dataset recorded in the Gulf of Mexico by Shell Exploration and Production company. In this application, we invert the elastic property of a subsurface prospect. The estimated rock-physical parameters agree with field observations showing the possible presence of a gas-bearing reservoir trapped by the salt-dome flank and a highshale-content formation. THEORY Our workflow can be separated into two main steps; namely, the surface-data redatuming and the target-oriented inversion of the virtual-acquisition data. The redatuming is based on the usage of an extended linearized waveform inversion, which is also referred to as extended least-squares reverse time migration (RTM).

 

The generated image is then used to synthesize seismic data recorded by a virtual acquisition geometry placed in the proximity of a target area. The redatumed data are then used within an elastic FWI workflow to retrieve the subsurface elastic parameters. We start this discussion by reviewing the theory behind extended imaging and least-squares migration and then describe the elastic FWI framework we use to estimate the elastic properties of the target portion.