Xi-Net: Transformer Based Seismic Waveform Reconstructor

TL;DR

Xi-Net presents a transformer-based solution for reconstructing seismic waveforms with missing data by fusing time-domain and frequency-domain representations. The architecture uses separate time and frequency encoders and a fused decoder built from 1D Swin-transformer blocks, with frequency data tokenized via a Discrete Time Fourier Transform and represented as two channels. Empirical results show Xi-Net outperforms a CNN baseline on multiple reconstruction metrics and requires substantially less training time, illustrating both higher quality reconstructions and improved efficiency. The work introduces a practical framework for multi-domain time-series reconstruction and suggests avenues for future enhancement, including GAN-based refinements and broader applicability to other signals.

Abstract

Missing/erroneous data is a major problem in today's world. Collected seismic data sometimes contain gaps due to multitude of reasons like interference and sensor malfunction. Gaps in seismic waveforms hamper further signal processing to gain valuable information. Plethora of techniques are used for data reconstruction in other domains like image, video, audio, but translation of those methods to address seismic waveforms demands adapting them to lengthy sequence inputs, which is practically complex. Even if that is accomplished, high computational costs and inefficiency would still persist in these predominantly convolution-based reconstruction models. In this paper, we present a transformer-based deep learning model, Xi-Net, which utilizes multi-faceted time and frequency domain inputs for accurate waveform reconstruction. Xi-Net converts the input waveform to frequency domain, employs separate encoders for time and frequency domains, and one decoder for getting reconstructed output waveform from the fused features. 1D shifted-window transformer blocks form the elementary units of all parts of the model. To the best of our knowledge, this is the first transformer-based deep learning model for seismic waveform reconstruction. We demonstrate this model's prowess by filling 0.5-1s random gaps in 120s waveforms, resembling the original waveform quite closely. The code, models can be found at: https://github.com/Anshuman04/waveformReconstructor.

Figures (3)

• Figure 1: Schematic Illustration of the proposed Xi-Net Model Architecture. The upper branch of the model is the encoder which processes on time domain data. The lower branch is an encoder processing on frequency domain data. The middle branch is the decoder which combinedly processes the multi-channel data to output a reconstructed waveform. An Input waveform goes through upsampling and noise removal before going to the time encoder. The processed waveform also goes through an additional DTFT layer, divider and lateral stacking before going to the frequency encoder. [Here, W and H are the width and the height of the signal respectively. In our case, H=1(time series)]
• Figure 2: Seismic waveform with gap.The upper graph is the original waveform while the lower graph is the waveform with a random gap
• Figure 3: Qualitative Results of Waveform reconstruction using Xi-Net. Three broad categories of results are showcased here. In every figure, the upper graph represents the original waveform, the middle graph shows the random gap, while the bottom graph is the Xi-Net reconstructed waveform. Most of the Xi-Net reconstructed waveforms fall in category (a).