# A Scalable and Consistent Method for Multi-Component Gravity-Gradient Data Processing
## 1 Introduction  
The advancement of airborne gradiometry allows the use of gravity-gradient data to facilitate the interpretation of gravity sources in mining and hydrocarbon explorations (e.g., [1, 2, 3, 4, 5, 6, 7, 8]). The equivalent-layer and Fast Fourier Transform (FFT) techniques are feasible approaches for de-noising and/or transforming between conventional gravity and gravity-gradient components. For example, refs. [9, 10] developed techniques to calculate the full gravity-gradient tensor from pre-existing vertical components of the gravitational attraction (\(g_{z}\)-component) by using FFT and a fast equivalent-layer technique, respectively. Ref. [11] used a data-adaptive 1D wavelet filtering technique to de-noise gravity-gradient data. Ref. [12] also computed the tensor components from the \(g_{z}\)-component; however, using the cosine transform technique shows it is less affected by noise than the FFT approach. Ref. [13] presented the first method to assess and highlight the internal consistency of airborne gravity-gradient components by representing all measured data through a common potential function that accounts for both lateral and vertical variations. Ref. [14] introduceda de-noising method for full-tensor gravity-gradiometer data using translation-invariant wavelets with mixed and adaptive Bayesian thresholding to effectively suppress noise while preserving high-frequency details and minimizing artifacts. Ref. [15] presented a joint inversion algorithm for gravity and magnetic data based on a sequential strategy and cross-gradient structural coupling, deriving a novel formula for minimizing the structural similarity term by combining an alternating strategy with the randomized singular value decomposition algorithm to improve computational performance. Ref. [16] proposed a real-time joint filtering method for gravity and gravity-gradient data that uses the derivative relationship between the two to construct the system and measurement equations of a Kalman filter. An improved Kalman filter is then applied, enabling simultaneous noise reduction in both datasets while ensuring that the filtered outputs satisfy the Laplace equation constraint. By using variational mode decomposition and the Hilbert transform to extract time-frequency features of airborne gravity-gradient data, ref. [17] applied a time-frequency feature threshold to suppress noise while preserving high-frequency features of the data. The equivalent layer is a well-known method based on the potential theory. Following this theory, a set of potential-field data produced by a 3D source can be reproduced by a 2D infinite layer. In practice, ref. [18] showed that this layer can be represented by a finite and discrete physical-property distribution (e.g., point masses). The classical approach consists of estimating the physical-property distribution by solving a linear system subject to fitting the observed data. Nevertheless, the processing of a large potential-field dataset by using the classical equivalent-layer method may lead to costly computational schemes. As a result, some authors search for ways to increase the computational efficiency of the equivalent-layer technique, (e.g., [5; 19; 20; 21; 22; 23]). From the above-mentioned authors, there are just a few works for processing measured gravity-gradient measurements. Ref. [24] were the first to use the equivalent-layer technique for processing gravity-gradient data. Ref. [27] compared the equivalent-layer technique and FFT for processing airborne full-tensor gravity-gradient data. Ref. [5] used the equivalent-layer technique for de-noising gravity-gradient data and estimating the errors associated with the de-noised data. Ref. [29] combined the Gauss-FFT with [PERSON]'s iteration to propose a fast equivalent layer technique for processing two-component of the gravity-gradient data simultaneously. Recently, refs.