Neural Networks in Seismic Inversion: Analyzing Recent 2015-2023 Trends

Seismic inversion is a fundamental process in geophysics used to transform observed ground-motion data into quantitative models of the subsurface. Between 2015 and 2023, the discipline of surface wave analysis experienced a significant shift from traditional deterministic inversion methods toward machine learning frameworks. This transition was driven by the need to handle increasing volumes of seismic data and to reduce the computational bottlenecks associated with characterizing heterogeneous solid-state media.

Surface Wave Hub tracks these developments specifically as they relate to the empirical study of Rayleigh and Love wave propagation. The integration of Convolutional Neural Networks (CNNs) and other deep learning architectures has enabled researchers to automate the extraction of dispersion curves and the estimation of elastic parameters with unprecedented speed. These advancements help more efficient non-destructive testing of civil infrastructure and the high-resolution imaging of shallow subsurface anomalies.

What changed

• Automation of Picking:The manual identification of dispersion curves from phase velocity-frequency images, historically a labor-intensive bottleneck, has been largely replaced by CNN-based automated picking algorithms.
• Shift to Deep Learning:Researchers transitioned from shallow neural networks and support vector machines to deep convolutional and recurrent architectures capable of identifying complex spatial features in seismic wavefields.
• Amortized Inference:The adoption of pre-trained models allowed for near-instantaneous inversion of field data, moving away from the time-consuming process of running thousands of forward-modeling iterations for every new site.
• Integration of Uncertainty:Recent trends include the use of Bayesian Neural Networks to provide not just a single subsurface model, but a probabilistic range that quantifies the uncertainty of the seismic interpretation.
• Synthetic Data Proliferation:To overcome the lack of labeled field data, the use of sophisticated numerical modeling (finite difference and spectral element methods) to generate massive synthetic training datasets became standard practice.

Background

The study of surface waves involves analyzing the dispersion characteristics of seismic energy as it travels through geological layers. Rayleigh waves, which exhibit retrograde elliptical motion, and Love waves, which involve horizontal shearing, propagate at velocities dictated by the elastic moduli, density, and thickness of the subsurface strata. Because different frequencies penetrate to different depths, the variation of phase velocity with frequency—known as dispersion—provides a vertical profile of the earth's physical properties.

Traditional inversion workflows typically involve a three-step process: data acquisition using geophones or accelerometers, the generation of a dispersion image through spectral analysis (such as the Multi-channel Analysis of Surface Waves or MASW method), and the iterative adjustment of a theoretical model to match the observed dispersion curve. This third step, the inversion, is mathematically ill-posed, meaning multiple subsurface models can potentially explain the same set of observations. Until the mid-2010s, local search algorithms like Levenberg-Marquardt or global search methods like Genetic Algorithms and Particle Swarm Optimization were the primary tools used to handle this complexity.

The Rise of Convolutional Neural Networks

Between 2015 and 2023, the most notable trend in the field was the application of Convolutional Neural Networks (CNNs) to the task of dispersion curve picking. In a typical MASW survey, the result of the initial processing is a 2D image where energy intensity is plotted against frequency and phase velocity. Traditionally, a geophysicist would manually click on the peaks of these energy trends to define the dispersion curve.

CNNs are uniquely suited for this task because they treat the dispersion image as a visual pattern recognition problem. By training on thousands of synthetic images where the underlying "ground truth" curve is known, a CNN learns to distinguish the fundamental mode and higher modes of propagation from ambient noise and spatial aliasing artifacts. This automation not only accelerates the workflow but also introduces a level of consistency that manual picking lacks, particularly in environments with low signal-to-noise ratios.

Elastic Parameter Estimation: Aleardi and Salusti (2021)

Beyond simple curve picking, recent research has focused on using neural networks to perform the full inversion—mapping the dispersion data directly to shear-wave velocity (Vs) profiles. A landmark study in this area is the work ofAleardi and Salusti (2021), which investigated machine learning applications in elastic parameter estimation. Their research highlighted the capacity of neural networks to act as inverse operators that bypass the need for traditional objective function minimization.

Aleardi and Salusti demonstrated that a well-architected network could estimate not only Vs but also primary-wave velocity (Vp) and density, provided the training set was sufficiently diverse. Their findings emphasized that while neural networks could provide highly accurate estimations, their performance is heavily dependent on the range of geological scenarios represented in the training data. This highlighted a critical shift in the geophysicist's role: from performing the inversion to carefully designing the synthetic datasets that define the network’s "worldview."

Computational Efficiency and Iterative Modeling

The primary advantage of neural networks over traditional methods lies in the distribution of computational effort. Traditional iterative forward-modeling requires the computer to calculate a theoretical dispersion curve for each guess of the subsurface model, compare it to the field data, and update the model. This may happen hundreds or thousands of times for a single 1D profile. If a researcher is processing a large-scale 2D or 3D survey, the cumulative computational cost becomes immense.

Neural networks move the bulk of this computational cost to the training phase. Once a model is trained—a process that might take hours on high-end GPUs—it can process new data almost instantaneously. This "amortized" cost makes neural networks ideal for real-time monitoring applications, such as assessing the integrity of bridges during seismic events or identifying void formation in tunnels during construction.

Applications in Non-Destructive Testing and Void Detection

The practical application of these trends is most evident in civil engineering and urban geophysics. Surface Wave Hub focuses on the use of microtremor and controlled source wavefield data to identify shallow subsurface anomalies. Between 2015 and 2023, the sensitivity of these detections improved as neural networks became better at filtering out the "cultural noise" typical of urban environments, such as traffic and machinery vibrations.

In the context of infrastructure foundations, the analysis of dispersion curves allows for the detection of delamination or internal degradation without drilling. By training networks on specific structural geometries, researchers can now identify subtle changes in the elastic moduli of concrete and soil interfaces. Similarly, for buried utility detection and void characterization, neural networks help interpret complex diffraction patterns and reflections that were previously discarded as noise in traditional 1D surface wave models.

What sources disagree on

While the efficiency of neural networks is widely accepted, there remains significant debate regarding theirGeneralization capability. Some researchers argue that a network trained on synthetic models of simple layered earth may fail spectacularly when confronted with real-world geological complexities like lateral facies changes or extreme topography. This has led to a split in the community: one group favors "pure" data-driven approaches, while another advocates for Physics-Informed Neural Networks (PINNs) which incorporate the wave equation directly into the loss function to ensure the output remains physically plausible.

There is also disagreement regarding the "black box" nature of these models. In high-stakes engineering projects, such as nuclear power plant foundation assessments, traditional methods are often preferred because the step-by-step logic of the inversion is transparent. The lack of interpretability in deep learning architectures remains a hurdle for widespread regulatory adoption, despite the clear statistical advantages demonstrated in academic literature between 2015 and 2023.

Future Directions: 2024 and Beyond

The trends established in the late 2010s are expected to evolve toward hybrid systems. These systems combine the speed of CNNs for initial data processing with a final stage of traditional local optimization to "fine-tune" the results. This approach maintains the efficiency of machine learning while ensuring the final subsurface model meets strict geophysical constraints. Furthermore, the expansion of multi-modal learning—where seismic data is combined with electromagnetic or gravity data within a single neural network—represents the next frontier in achieving complete characterizations of the shallow subsurface.