**1. Introduction**

Ocean bottom seismic survey is a modern platform for exploring the Earth's interior, locating seismometers at the seabed for all-weather, long-term, continuous, real-time observations. Unlike the conventional towed-streamer acquisition, OBS can record 1C pressure and 3C displacement data [1] using four-component (4C) detectors. The observed multicomponent data contain plenty of elastic properties of subsurface media, which can be used to deduct the lithology, fluid content, and pore pressure of rocks [2].

In multicomponent data processing, elastic full-waveform inversion (EFWI) plays an increasingly important role [3]. In the manner of classical FWI [4], EFWI computes parameter gradients by cross-correlating forward- and back-propagated wavefields and updates models to minimize the data misfit function. As governed by the elastic wave equation, EFWI can interpret multiple elastic wave

phenomena, i.e., wave-mode conversion and AVO effects [5], and provide quantitative estimations for subsurface parameter distributions. Although it costs a large number of computing resources in wavefield simulations, its excellent performance still makes it more and more attractive [6–10].

However, the standard elastic wave equation commonly used in the conventional EFWI approaches cannot directly extract pressure components from elastic wavefields. By solving the acoustic and elastic wave equations in different computing areas, a fluid–solid coupled EFWI approach has been proposed [11–13]. It can generate pressure in the water immediately above the seabed and elastic components on the solid seabed. However, it requires to explicitly implement the correct boundary conditions, which is challenging for irregular surfaces [14]. Alternatively, Yu et al. [15] proposed an acoustic-elastic coupled (AEC) equation in elastic imaging of OBS 4C data. It introduces the physical relation between pressure and normal stress into the elastic wave equation. Thus, it can compute the pressure wavefield and avoid applying the boundary conditions. The developed 4C elastic reverse-time migration (ERTM) shows to suppress non-physical artifacts in the back-propagated wavefield and provide better-resolved subsurface images. With consideration of propagating direction and anisotropic property, this equation has been extended with an elastic vector imaging for transverse isotropy media [16,17]. However, these 4C ERTM methods aim to retrieve the subsurface structures but fail to provide quantitative parameter reconstructions.

In this study, we propose a new EFWI method based on a modified AEC equation, which can reconstruct multiple elastic parameters from OBS 4C data. Our method defines a new weighted misfit function; thus, it can adjust the weight of pressure and displacement components, and eliminate the differences in the order of magnitude. As more parameter classes and data components are involved, the blurring effects and parameter couplings [18] in the Hessian operator are prone to be more serious. To better consider the inverse Hessian operator, we reformulate the truncated Gauss–Newton-based (TGN) algorithm [19,20] in the framework of this modified AEC equation. Compared with the preconditioned conjugate gradient (PCG) algorithm, TGN can estimate a more accurate inverse Hessian and provide better parameter update directions. TGN has been widely used in multiparameter inversion for acoustic, elastic, and anisotropic media [21–23] and elastic least-squares RTM [24,25]. Besides, a pseudo-diagonal Hessian [26,27] is used as a precondition operator to remove the influences of limited observation apertures, geometry spreading, and frequency-limited wavelet.

The paper is organized as follows. In Section 2, we first review the general formulas of FWI, and then introduce the theory of the AEC-EFWI method and the implementation of the preconditioned TGN algorithm. In Section 3, we numerically analyze multiparameter sensitivity kernels of pressure and displacement components. In Section 4, we use two numerical examples to validate the effectiveness of the proposed method. Before conclusions, we discuss whether the AEC-EFWI method can invert elastic parameters using only 1C pressure data for OBS and towed-streamer acquisitions.
