GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 the recovery of missing low and high frequencies for acoustc impedance inversion (Karsli, 2010; Karsli, 2006). In recent years, deep learning approaches have gained atenton for low-frequency extrapolaton from seismic data. Ovcharenko et al. (2019) and Li & Demanet (2016) have proposed applicaton of deep learning - specifcally convolutonal neural networks - for low-frequency extrapolaton, showing promising results in extrapolatng low frequencies from mult-ofset seismic data. Furthermore, machine-learning-based data recovery has been suggested for simultaneous deblending, trace reconstructon, and low-frequency extrapolaton, indicatng the potental of deep learning in addressing multple challenges in seismic data processing (Nakayama & Blacquière, 2021). Mult-task learning has been proposed for addressing low-frequency extrapolaton and elastc model building from seismic data, showing the potental of integratng classical physics-based methods with deep learning techniques (Ovcharenko et al., 2022). In additon to low-frequency extrapolaton, high-frequency extrapolaton from seismic data has also been a focus of research. Ovcharenko et al. (2020) emphasised the importance of low frequencies in high-frequency land seismic data due to the elastc nature of the Earth's subsurface, highlightng the signifcance of low-frequency extrapolaton in addressing the challenges associated with high- frequency data inversion. Furthermore, a 1-D phase-tracking method has been proposed for extrapolatng low-frequency data based on phases and amplitudes in the observed frequency band, indicatng the signifcance of considering diferent dimensions for efectve extrapolaton (Li & Demanet, 2016). Methods We propose a novel 1-D approach based on LSTM (Long Short-Term Memory) Neural Networks (NN) to address the low- and high-frequency gap (i.e. null space) in refecton seismics. We trained two diferent NNs: one is trained to infer a lower frequency output from a higher frequency signal, from now on called low-frequency model, and another with switched input and output, from now on called high-frequency model, with both the input and output assumed to have maximum phase. The training dataset is generated using a convolutonal approach. The data generaton process involves creatng synthetc noisy seismic traces for training, considering modifcatons to the classical seismic convolutonal model to enhance its generalizaton to beter mimic real seismic data. The NN is trained with a custom loss functon that includes both amplitude and frequency components. The method is easily scalable thanks to the fact that the NN operates without direct consideraton of frequency, tme length and sampling informaton, enabling the generaton of desired frequency output just by adjustng how the input data is sampled. The NN will undergo the training based on a parameter known as Sample Duraton (SD), representng the estmated duraton of the source wavelet. We have the fexibility to resample each input signal provided to the network to align with the sample duraton exploited in NN training. SD serves as the crucial parameter governing frequency content generaton, enabling the network to produce new frequencies in accordance with it. Since it is not always easy to determine SD on feld data, we use the second zero of the auto-correlaton to make it easier to get and more objectvesuch a parameter. Once we have