Seismic impedance inversion is a vital way of geological interpretation and reservoir investigation from a geophysical perspective. However, it is inevitably an ill-posed problem due to the noise or the band-limited characteristic of seismic data. Artificial neural network have been used to solve nonlinear inverse problems in recent years. This research obtained an acoustic impedance profile by feeding seismic profile and background impedance into a well-trained self-attention U-Net. The U-Net got convergence by appropriate iteration, and the output predicted the impedance profiles in the test. To value the quality of predicted profiles from different perspectives, e.g., correlation, regression, and similarity, we used four kinds of indexes. At the same time, our results were predicted by conventional methods (e.g., deconvolution with recursive inversion, and TV regularization) and a 1D neural network was calculated in contrast. Self-attention U-Net showed to be robust to noise and does not require prior knowledge. Furthermore, spatial continuity is also better than deconvolution, regularization, and 1D deep learning methods in contrast. The U-Net in this paper is a type of full convolutional neural network, so there are no limits to the shape of the input. Based on this, a large impedance profile can be predicted by U-Net, which is trained by a patchy training dataset. In addition, this paper applied the proposed method to the field data obtained by the Ceduna survey without any label. The predictions prove that this well-trained network could be generalized from synthetic data to field data.

Marchenko equation-based imaging methods have been proved as an effective way to remove the internal multiples. Conventional Marchenko imaging needs the reflection response at the surface and an estimate of the direct arrival times from the virtual source point to the acquisition surface. It contains the procedure of redatuming and imaging. The redatuming process is valid only for layered media with a moderately curved interface. We rederive the single reflection retrieval by a focusing source method based on the scattering theory and avoid the use of redatuming plane and the upgoing/downgoing decomposition. This scheme reproduces a new data free from internal multiples for complex structures, such as salt dome. Our theory/method expands the application range of Marchenko imaging and internal multiple elimination. With an artifact-free image obtained by this procedure, an illumination compensation can be further applied to obtain a high-fidelity image, especially in the subsalt area. Numerical examples using the 2-D SEG/EAGE salt model are shown to validate this method.

Deep neural networks can automatically fetch specific features from seismic data, which can be used in the process of multiple elimination. An extended single-sided autofocusing guided by inverse-scattering theory is introduced to remove internal multiples in a data-driven manner, which can be used as labels in deep neural networks. In this research, we have developed a novel workflow to explore the potential of neural networks in identifying the internal multiples with the guidance of inverse-scattering theory. In particular, we use the U-net with a self-attention block during the training process, which could extract features from seismic data effectively. The neural network is fed with training data pairs, consisting of the shot records with internal multiples, and the primary-only datasets as labels, which are generated by an extended single-sided autofocusing method. The testing pairs show that internal multiple elimination via the neural network takes the advantage of the extended single-sided autofocusing method and is cheaper when the neural network is well-trained. The numerical results demonstrate promising performances of the self-attention U-net method in terms of the noise resistance, internal multiples elimination, and the reverse time migration (RTM) images, in comparison with the extended single-sided autofocusing method.

Irregular salt bodies complicate the seismic wavefield propagation and cause multipathing, leading to intricate internal multiples that cannot be easily suppressed during data processing. To investigate the performance of internal multiple removal in salt bodies, we compare two types of Marchenko-based internal multiple removal strategies. One focuses on internal multiple prediction (IMP) based on Marchenko redatuming and seismic interferometry. With the retrieved upgoing and downgoing Green’s functions, internal multiples can be reconstructed using convolutional interferometry. The second method emphasizes primary reflection retrieval (PRR) by capturing primary reflections without adaptive subtraction. It is derived from a modified method based on the Gel’fand-Levitan-Marchenko equation. Testing with the Pluto salt model, we find that for the IMP the critical point is obtaining the purely scattering components of the upgoing and downgoing Green’s functions from the complicated wavefield. Our complex salt model indicates that the predicted internal multiples’ adaptive subtraction also introduces an extra challenge for attenuation quality. We develop a layer-by-layer adaptive subtraction scheme for the IMP to obtain primary reflections. The constant-time truncation operator in the time domain makes the PRR independent of additional model information, which can exclude internal multiples from the primary reflections. However, selecting an appropriate smoothing window for truncation requires further investigation. We evaluate the weaknesses of these methods and enhance each method individually. Our numerical results indicate that these improved schemes can correctly handle internal multiples in salt structure scenarios. In the addition, we study the robustness of the IMP when an erroneous background velocity model is used to estimate the direct arrival and the effects of sampling on the virtual receiver/source lines in IMP.

Applying deep neural networks (DNNs) to broadband seismic wave impedance inversion is challenging, especially in generalizing from synthetic to field data, which limits the exploitation of their nonlinear mapping capabilities. While many research studies are about advanced and enhanced architectures of DNNs, this article explores how variations in input data affect DNNs and consequently enhance their generalizability and inversion performance. This study introduces a novel data pre-processing strategy based on histogram equalization and an iterative testing strategy. By employing a U-Net architecture within a fully convolutional neural network (FCN) exclusively trained on synthetic and monochrome data, including post-stack profile, and 1D linear background impedance profiles, we successfully achieve broadband impedance inversion for both new synthetic data and marine seismic data by integrating imaging profiles with background impedance profiles. Notably, the proposed method is applied to reverse time migration (RTM) data from the Ceduna sub-basin, located in offshore southern Australia, significantly expanding the wavenumber bandwidth of the available data. This demonstrates its generalizability and improved inversion performance. Our findings offer new insights into the challenges of seismic data fusion and promote the utilization of deep neural networks for practical seismic inversion and outcomes improvement.