The natural combination of full and image-based waveform inversion

Abstract

A B S T R A C TIntegrating migration velocity analysis and full waveform inversion can help reduce the high non-linearity of the classic full waveform inversion objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the migration velocity analysis working when we need it, and we mitigate its influence when the velocity model produces accurate reflections (possibly first for the low frequencies). This is achieved using a novel objective function that includes both objectives. Applications to a layered model and the Marmousi model demonstrate the main features of the approach. I N T R O D U C T I O NIntroducing migration velocity analysis (MVA) to full waveform inversion (FWI) has been a common affair lately (Xu et al. 2012;Ma et al. 2012;Almomin and Biondi 2012;Fleury and Perrone 2012;Wang et al. 2013). The general objective here is to somehow use MVA to extract velocity information from imaged reflections capable of adhering to the FWI requirements for an initial velocity model. Such requirements include velocity models that are capable of producing reasonably accurate reflections within a half-cycle (controlled by the frequency) of the observed data. Reflections that fit the data are a result of a high-resolution velocity model, which is the main objective of FWI. Missing in this formula for MVA+FWI is often the role that diving waves play early in the velocity model building process in steering the background model.However, MVA has always been lurking in the background as one of our options for building a generally smooth velocity model capable of focusing an image (AlYahya 1989;Symes and Kern 1992;Plessix, De Roeck, and Chavent 1995;Clement, Chavent, and Gómez 2001). That velocity model * can serve sometimes as an initial velocity for FWI, particularly if the frequencies in the data are low enough. However, inserting MVA within the FWI kernel (or in other words marrying the two together) have given us mixed results, and in some cases, a divorce was necessary. The marriages included an objective function that incorporates both objectives (the FWI one and the MVA one) data fitting, and image focusing with a user-defined weighting between the two (i.e., Fleury and Perrone 2012). Moreover, it includes the possibility of a migration/demigration process where we generate the reflections from the demigration instead of requiring highresolution velocity models to produce reflections (i.e., Xu et al. 2012). In this process, we move the residual measure operation of the classic MVA to the data space, and we refer to the approach as reflection waveform inversion (RWI). Alternat...

Efficient full waveform inversion using the excitation representation of the source wavefield

“…Alternatively, Biondi & Almomin (2014) successfully inverts the full bandwidth of the data. Recently, the merger of migration velocity analysis with FWI (Symes 2008;Almomin & Biondi 2012;Allemand & Lambaré 2015;Wu & Alkhalifah 2015b;Alkhalifah & Wu 2016) has gained popularity in the context of improving the prospect of converging to a global minimum. Moreover, the isolation of desired wavenumbers in the gradient using conditioning and filtering (Albertin et al 2013;Tang et al 2013;Alkhalifah 2015;Kazei et al 2016) helps such convergence prospect.…”

Waveform inversion for acoustic VTI media in frequency domain

“…As a result, RWI inverts mainly for the background model, like in MVA, without the need for extended images or angle gathers. Alkhalifah and Wu (2016); Wu and Alkhalifah (2015b) suggested a new objective function, which can use the information of both the diving and reflected waves to update the background in the case of isotropic media. They also proposed a scattering angle filter (Wu and Alkhalifah, 2015a) to clean up the gradient and admit only smooth update in the early iterations.…”

A nonlinear approach of elastic reflection waveform inversion

“…Acoustic wavefield inversion of P-waves has been the focus of research and inversion implementations over the past few years (Tarantola, 1986;Xu et al, 2012;Alkhalifah and Wu, 2015). With the rise of full waveform inversion (FWI) and its possible use in delineating the reservoir, the elastic description of the Earth is drawing a lot of attention.…”

“…In the absence of a good initial guess of the background model, the optimization problem using gradient methods is not capable of providing low wavenumber updates. Thus, gradient based inversion methods tend to converge to local minima (Tarantola, 1986;Alkhalifah and Wu, 2015). Xu et al (2012), based on the work of Plessix et al (1995), suggested using the recorded reflections to predict the P-wave reflectivity using a migration/demigration process, referred to as RWI.…”