Geophysicists have leveraged advanced deep learning techniques in various innovative research efforts to address the limitations inherent in conventional full waveform inversion. Typically, two primary approaches exist: the supervised learning approach, which utilizes an extensive seismic dataset to train a network, and the network parameterization approach, which employs the network’s weights as parameters for inversions. For the supervised learning approach, extensive computational issues, such as GPU memory limitations resulting from the use of time-domain wavefields as input data, have restricted inversions to small-scale synthetic velocity models. Within the network parameterization approach, robust inversion capabilities have been demonstrated for field-scale synthetic velocity models; however, exploration of optimal initial weight configurations for network parameterization remains scarce. This article presents a novel deep learning-based seismic inversion in the Laplace domain, integrating supervised learning with network parameterization. This innovative strategy, known as transfer learning-based network parameterization, has been successfully applied to traveltime tomography. Nevertheless, Laplace-domain inversion provides a significant advantage in constructing more accurate velocity models compared to those derived from deep learning-based traveltime tomography, while maintaining computational efficiency. For supervised learning, we generated a substantial volume of field-scale synthetic velocity models along with their corresponding Laplace-domain wavefields. After supervised learning, we conducted seismic inversion using network parameterization based on transfer learning. This approach mitigated the need for extensive computational resources for supervised learning and significantly enhanced the inversion performance of network parameterization. The numerical examples demonstrate that the innovative deep learning-based seismic inversion in the Laplace domain provided superior inversion results compared to network parameterization with the initial weights of an untrained network and conventional Laplace domain full waveform inversion.

Researchers have sought to overcome the limitations of traditional seismic inversion methods, such as full-waveform inversion (FWI), by applying deep learning techniques. Two primary approaches have emerged: the supervised learning approach, which uses an extensive dataset of seismic information to train a network, and the network parameterization approach, which treats the network’s weights as parameters for inversion. Within the supervised learning approach, the use of time-domain wavefields as input has led to graphics processing unit (GPU) memory limitations, confining inversions to small-scale synthetic velocity models. For the network parameterization approach, field-scale synthetic velocity models have demonstrated strong inversion capabilities, yet the optimal initial weight set of the network has remained unexplored. This article introduces an innovative deep learning traveltime tomography method that applies network parameterization via transfer learning. Our findings indicate that weights refined through supervised learning capture essential features of the velocity models, thereby enhancing subsequent inversion using network parameterization. The study leverages a transfer learning strategy to enhance the robustness of network parameterization inversions. For supervised learning, we generate field-scale synthetic velocity models and their corresponding first-arrival travel times for seismic waves as inputs, bypassing the full time-domain wavefields. Subsequently, the method applies transfer learning to network parameterization. This approach reduces the computational demand of supervised learning and establishes an effective starting point for network parameterization. The numerical examples reveal that this novel deep learning traveltime tomography method outperforms both network parameterization with random weight initialization and conventional traveltime tomography in producing superior inversion results.

Seismic inversion techniques based on supervised deep learning have shown promising results with synthetic data targeting small areas. These techniques use seismograms as input data and subsurface velocity models as output data. However, their application to field-scale data for high-resolution final models demands huge computational resources and is currently impractical. To overcome this limitation, we propose a new approach called deep-learning traveltime tomography that predicts large-scale velocity models using only first-arrival traveltimes of seismic waves as input data. This approach reduces data size and speeds up network training. To train the network, we generate field-scale synthetic velocity models and corresponding first-arrival traveltimes, and then use them for supervised learning. We adopt a marine towed-streamer acquisition geometry to simulate field acquisition situations. Since a lightly trained network has limited generalization ability and the output has low resolution, we use the predicted results as initial models for subsequent conventional first-arrival traveltime tomography. This strategy mitigates the need for huge computational resources and the problem of dependency on the correct initial model of conventional traveltime tomography. Numerical examples demonstrate that the outputs of the lightly trained deep-learning network can enhance inversion results of conventional traveltime tomography for both synthetic and field data.

Objective functions are critical for successful seismic fullwaveform inversions (FWIs). Deconvolution-based objective functions yielded promising results in time- and frequency-domain inversions. In this study, we developed two deconvolution-based objective functions for Laplace-domain inversions. These objective functions are based on convolutional filters that transform one of the observed or modeled data into another. The objective functions are derived by forcing the convolutional filter to be a zero-lag delta function by updating the model parameters. We could obtain a relatively simple objective function in the Laplace domain since the convolution in the time domain is equivalent to the multiplication function in the Laplace domain and the Laplace transform of the delta function is unity. We compared the new deconvolution-based objective functions and the conventional logarithmic objective function using synthetic and Gulf of Mexico field data and obtained similar inversion results. We showed that the logarithmic objective function conventionally used in Laplace-domain FWIs can be understood in the framework of deconvolution-based objective functions, which explains the similar inversion results.

The Laplace-domain waveform inversion is a full-waveform inversion method that recovers large-scale subsurface models. The inversion updates subsurface model parameters to minimize the differences between the modeled and the observed wavefields in the Laplace domain. The inversion results can be used as an accurate initial model for subsequent high-resolution waveform inversions. Pure Laplace-domain wavefields can be obtained by transforming the time-domain signals using the Laplace transform of real variables. The real Laplace transform is mathematically identical to the Fourier transform using the imaginary angular frequency; however, the Laplace transform using only real variables is computationally more efficient than that using complex variables. The Laplace-transformed wavefields are real-valued signals, and thus, it is natural to use real values in the Laplace-domain waveform inversions. However, the real logarithm function in the logarithmic objective function cannot handle negative values. Inversions using complex logarithms can solve this problem, but they demand more memory and computations than those required for inversions using real variables only. We suggest a simple method to overcome the negative-value problem for the real logarithm in the objective function. By taking the absolute values of the negative signals in the logarithmic objective function, we can obtain inversion results from inversions using real variables only that are equivalent to those from inversions using complex variables. We demonstrate the proposed method using the Society of Exploration Geophysicists (SEG)/European Associations of Geoscientists & Engineers (EAGE) salt model and a field data set. The inversions using real variables only took less than 22% of the time of the inversion using complex variables in the numerical examples.