**1. Introduction**

Passive seismic interferometry (PSI) makes use of the noise crosscorrelations (NCC) recorded by receiver pairs to reconstruct the subsurface impulse response. It turns one of the receivers in the pairs into a virtual source whose hypothetical reflection/energy is imaged by the other receiver. In this way, an estimate of the Green's function between the receivers can be obtained [1,2]. The waves in the Green's function usually carry much useful information of the environment between the receivers. This technique provides geophysicists a new perspective to view noise and study the structure of subsurface with no need for an active seismic source [3]. As an environmental-friendly passive imaging technique, PSI significantly enhances the importance of naturally occurring ambient noise and makes it possible to image subsurface structure and monitor temporal subsurface changes conveniently, environmental-friendly, and economically [4–6].

Aki [7] and Claerbout [8] developed the early framework of the technique. The theoretical basis of the technique was completed in the early 2000s [2,9–13]. Later, the application of the theory spreads in multiple research fields including seismology [1,8], helioseismology [14], ultrasonics [9], and underwater acoustics [15]. Nowadays, PSI has become a popular technique in subsurface tomography. Various applications have been done at different scales and for various purposes all over the world [16–20].

One of the key tasks of PSI is the reliable approximation of Green's functions between receiver pairs. It requires that the noise field should be diffuse and equipartitioned [21,22]. Unfortunately, the noise field is usually contaminated by strong, directional sources in the real world, introducing biases into the approximated Green's functions [23–27]. Wu et al. [22] reviewed the techniques which have been proposed to attenuate the interference of strong directional sources, and developed an adapted eigenvalue-based filter to improve the quality of the estimation of the Green's function. The filter is adaptable for different data sets and can reduce the influence of strong, directional sources significantly.

The main objective of the paper is to perform shear-wave tomography on a very short recording of ocean ambient noise with interference and compare the tomographic picture obtained with other tomography results using active sources or much longer ambient noise recordings at the same field. The noise was recorded by a permanent reservoir monitoring receiver array (PRMRA) installed on the seabed of an offshore oil field in Norwegian North Sea. The adapted eigenvalue-based filter is applied as a pre-processing method to suppress the strong, directional interference in the recording and retrieve reliable approximations of Green's functions. Note that the paper focuses on the same dataset with Wu et al. [22] but Wu et al. [22] focuses on the analysis of noise recording at one sensor, while this paper focuses on the whole data array.

The paper is organized as follows: First, we describe the array geometry and perform time and frequency analysis of the measured ambient noise. Then, we summarize the most important ideas of the adapted eigenvalue-based filter and apply the adapted eigenvalue-based filter to the measured ambient noise. Conventional beamforming is applied to the filtered sample covariance matrix (SCM) to evaluate the effectiveness of the adapted eigenvalue-based filter. The NCC is also retrieved based on the filtered SCM at this time. Later, the phase-speed dispersion curves are extracted and a 3D shear-wave tomography is performed. The result is compared with several previously published tomography results using different methods. Finally, we summarize the work and draw some conclusions.

#### **2. Array Geometry and Noise Analysis**
