arXiv subjects

Pawan Bharadwaj

Publications and source records attributed to Pawan Bharadwaj.

10 recordsLinked to original sources

arXiv2026

Virtual receiver functions via conditional diffusion transformers for robust crustal imaging

Receiver functions (RFs) are widely used to image crustal and upper-mantle structure, and their variation with backazimuth and epicentral distance contains key information about layering and azimuthal anisotropy. In practice, however, RFs are contaminated by nuisance effects from unknown earthquake source signatures and seismic noise, which obstruct reliable crustal imaging. Sparse RF coverage across backazimuths and epicentral distances also leads to biased anisotropy estimates. We address these challenges using conditional diffusion models, conditioned on backazimuth, epicentral distance, and station coordinates, to produce high-quality virtual radial and transverse RFs. RFs from earthquakes with similar backazimuths and epicentral distances share consistent crustal responses but differ in nuisance effects, allowing the model to suppress the latter. Our framework generates virtual RFs within gaps in backazimuth and epicentral distance coverage, enhancing the interpretation of crustal anisotropy and layering. On synthetic RFs with realistic non-Gaussian noise, virtual RFs correlate more strongly with the true RFs than traditional linear or phase-weighted stacking. Applied to the Cascadia Subduction Zone, virtual radial RFs sharply image scattered S-waves from the dipping slab, with enhanced phase clarity and backazimuthal coverage relative to previous work. In southern California, anisotropy parameters inferred from virtual RFs are spatially coherent and consistent with regional fault geometry. Our approach leverages all available RFs, regardless of quality, to increase spatial coverage and support robust, automated RF analysis.

physics.geo-ph↗

arXiv2026

Coherent Source Subsampling: A Data-Driven Strategy for Restoring Causal-Acausal Symmetry in Ambient Seismic Wavefield Correlations

Ambient noise tomography relies on the assumption that the seismic wavefield is equipartitioned. In practice, ambient noise sources are spatially and temporally heterogeneous, producing biased estimates of the Green's function between stations. We introduce a data-driven method, Coherent Source Subsampling (CSS), which selects and averages only cross-correlation time windows associated with excitation of sources in the stationary zone. By restricting the ensemble average to these windows, CSS mitigates the effects of nonuniform source distribution and restores causal-acausal symmetry in the retrieved interstation response. Applications to regional ambient-noise datasets show that CSS stabilizes surface-wave dispersion measurements even when source statistics violate the assumptions of standard seismic interferometry. For the central California dataset, CSS-derived group-velocity tomograms consistently image a high-velocity block between the Rinconada and San Andreas faults across multiple periods. In comparison, the full-ensemble (linear) average does not capture this block, which is well established. Our approach is particularly useful for short-duration passive surveys.

physics.geo-ph↗

arXiv2025

Cold-Diffusion Driven Downward Continuation of Gravity Data

Gravity data can be better interpreted after enhancing high-frequency information via downward continuation. Downward continuation is an ill-posed deconvolution problem. It has been tackled using regularization techniques, which are sensitive to the choice of regularization parameters. More recently, convolutional neural networks such as the U-Net have been trained using synthetic data to potentially learn prior information and perform deconvolution without the need to adjust the regularization parameters. Our experiments reveal that the U-Net is highly sensitive to correlated noise, which is ubiquitously present in geophysical field data. In this paper, we develop a framework based on the $\textbf{cold-diffusion model}$ using the exponential kernel associated with downward continuation. The exponential form of the kernel allows us to train the U-Net to tackle multiple concurrent deconvolution problems with varying levels of blur. This allows our framework to be more robust and quantitatively outperform traditional U-Net-based approaches. The performances also closely matches that of $\textbf{oracle}$ Tikhonov reconstruction technique, which has access to the ground truth.

physics.geo-ph↗

arXiv2025

Enhanced receiver function imaging of crustal structures using symmetric autoencoders

The receiver-function (RF) technique aims to recover receiver-side crustal and mantle structures by deconvolving either the radial or transverse component with the vertical component seismogram. Analysis of the variations of RFs along the backazimuth and slowness is the key in determining the geometry and anisotropic properties of the crustal structures. However, the deconvolution introduces pseudorandom nuisance effects, due to unknown earthquake source signatures and seismic noise, which obstruct the precise extraction of backazimuth and slowness dependent crustal effects. Our goal is to obtain RFs with minimal nuisance effects, while preserving the crustal effects. In this study, we introduced a new method for reducing nuisance effects in RFs. This method generates virtual RFs through a deep generative model, namely symmetric variational autoencoders (SymVAE). Our autoencoder efficiently learns to disentangle coherent crustal effects and nuisance effects within its latent space, given a set of RFs derived from a cluster of nearby earthquakes. This disentanglement enables generation of virtual RFs which exhibits minimal nuisance effects while preserving the coherent crustal effects. We tested SymVAE using synthetic RFs with ambient seismic noise. We also tested using dense seismic networks in two distinct geological settings: the Cascadia subduction zone and southern California. We compared our method with linear and phase-weighted averaging. In both synthetic and real RFs, the generated virtual RFs demonstrate enhanced information related to crustal structures. We have also quantitatively assessed the performance. One major advantage of our method over traditional methods is its ability to utilize all available earthquake data, regardless of signal quality, resulting in improved backazimuth and slowness coverage.

physics.geo-ph↗

arXiv2025

Learning earthquake sources using symmetric autoencoders

This study examines almost thirty deep-focus earthquakes, magnitudes starting from Mw 6.0 and higher, with the aim of accurately determining the source-time function (STF) of P arrival and its azimuthal dependence. We use the variational symmetric autoencoder (SymVAE), a neural network architecture designed to automatically isolate earthquake information from far-field seismic waves. Our findings demonstrate that the STFs produced by the network uncover weak secondary episodes in numerous earthquakes, providing evidence that the majority deep-focus earthquakes release bursts of seismic moment. This groundbreaking study is the first to generate high resolution STFs without requiring traditional path-effect deconvolution, a process that usually introduces substantial uncertainties and hinders achieving high temporal resolution. Our unsupervised learning method for obtaining STFs does not require labeled seismograms and is based on the principle of scale separation, which allows the accumulation of earthquake information from nearby receivers. This principle states that the variations in far-field band-limited seismic measurements resulting from finite faulting occur across two spatial scales: a slower scale associated with the source processes and a faster scale corresponding to path effects. This research compares the STFs obtained from SymVAE with those gathered by stacking envelopes and traditional deconvolution. We evaluated the quality of SymVAE output and performed a synthetic experiment to recover the source in the presence of path scattering.

physics.geo-ph↗

arXiv2025

Coherent Spectral Feature Extraction Using Symmetric Autoencoders

Hyperspectral data acquired through remote sensing are invaluable for environmental and resource studies. While rich in spectral information, various complexities such as environmental conditions, material properties, and sensor characteristics can cause significant variability even among pixels belonging to the same material class. This variability poses nuisance for accurate land-cover classification and analysis. Focusing on the spectral domain, we utilize an autoencoder architecture called the symmetric autoencoder (SymAE), which leverages permutation invariant representation and stochastic regularization in tandem to disentangle class-invariant 'coherent' features from variability-causing 'nuisance' features on a pixel-by-pixel basis. This disentanglement is achieved through a purely data-driven process, without the need for hand-crafted modeling, noise distribution priors, or reference 'clean signals'. Additionally, SymAE can generate virtual spectra through manipulations in latent space. Using AVIRIS instrument data, we demonstrate these virtual spectra, offering insights on the disentanglement. Extensive experiments across six benchmark hyperspectral datasets show that coherent features extracted by SymAE can be used to achieve state-of-the-art pixel-based classification. Furthermore, we leverage these coherent features to enhance the performance of some leading spectral-spatial HSI classification methods. Our approach especially shows improvement in scenarios where training and test sets are disjoint, a common challenge in real-world applications where existing methods often struggle to maintain relatively high performance.

physics.geo-ph↗

arXiv2024

On extracting coherent seismic wavefield using variational symmetric autoencoders

We discuss the variational formulation of the Symmetric Autoencoder (SymAE) and its role in achieving disentanglement within the latent space to extract coherent information from a collection of seismic waveforms. Disentanglement involves separating the latent space into components for coherent information shared by all waveforms and components for waveform-specific nuisance information. SymAE employs a generative model that independently generates waveforms based on coherent and nuisance components, and an inference model that estimates these components from observed wavefield. By assuming the independence of waveforms conditioned on coherent information, the model effectively accumulates this information across multiple waveforms. After training, a metric based on Kullback-Leibler divergence is used to evaluate the informativeness of individual waveforms, enabling latent-space optimization and the generation of synthetic seismograms with enhanced signal-to-noise ratios. To demonstrate the efficacy of our proposed method, we applied it to a data set of teleseismic displacement waveforms of the P wave from deep-focus earthquakes. By training the SymAE model on high-magnitude events, we successfully identified seismograms that contained robust source information. Furthermore, we generated high-resolution virtual seismograms enriched with relevant coherent source information and less influenced by scattering noise, allowing a deeper understanding of the characteristics of the earthquake source. Importantly, our method extracts coherent source information without relying on deconvolution, which is often used in traditional source imaging. This enables the analysis of complex earthquakes with multiple rupture episodes, a capability that is not easily achievable with conventional approaches.

physics.geo-ph↗

arXiv2022

Redatuming physical systems using symmetric autoencoders

This paper considers physical systems described by hidden states and indirectly observed through repeated measurements corrupted by unmodeled nuisance parameters. A network-based representation learns to disentangle the coherent information (relative to the state) from the incoherent nuisance information (relative to the sensing). Instead of physical models, the representation uses symmetry and stochastic regularization to inform an autoencoder architecture called SymAE. It enables redatuming, i.e., creating virtual data instances where the nuisances are uniformized across measurements.

physics.comp-ph↗

arXiv2018

Focused blind deconvolution

We introduce a novel multichannel blind deconvolution (BD) method that extracts sparse and front-loaded impulse responses from the channel outputs, i.e., their convolutions with a single arbitrary source. A crucial feature of this formulation is that it doesn't encode support restrictions on the unknowns, unlike most prior work on BD. The indeterminacy inherent to BD, which is difficult to resolve with a traditional L1 penalty on the impulse responses, is resolved in our method because it seeks a first approximation where the impulse responses are: "maximally white" -- encoded as the energy focusing near zero lag of the impulse-response auto-correlations; and "maximally front-loaded" -- encoded as the energy focusing near zero time of the impulse responses. Hence we call the method focused blind deconvolution (FBD). The focusing constraints are relaxed as the iterations progress. Note that FBD requires the duration of the channel outputs to be longer than that of the unknown impulse responses. A multichannel blind deconvolution problem that is appropriately formulated by sparse and front-loaded impulse responses arises in seismic inversion, where the impulse responses are the Green's function evaluations at different receiver locations, and the operation of a drill bit inputs the noisy and correlated source signature into the subsurface. We demonstrate the benefits of FBD using seismic-while-drilling numerical experiments, where the noisy data recorded at the receivers are hard to interpret, but FBD can provide the processing essential to separate the drill-bit (source) signature from the interpretable Green's function.

eess.SP↗

arXiv2018

A parameterization analysis for acoustic full-waveform inversion of sub-wavelength anomalies

In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used, different choices of parameterization can be interpreted as different preconditioners that change the condition number of the Hessian. If the non-linear inverse problem is well-posed, then the inversion should converge to a band-limited version of the true solution irrespective of the parameterization choice, provided we start sufficiently close to the global minimum. However, the choice of parameterization will affect the rate of convergence to the exact solution and the best choice of parameterization is the one with the fastest rate. In this paper, we search for the best choice for acoustic multi-parameter full-waveform inversion, where 1. anomalies with a size less than a quarter of the dominant wavelength have to be estimated without the risk of converging to a local minimum; 2. the scattered wavefield is recorded at all the scattering angles; 3. a steepest-descent minimization scheme is used. Our examples suggest that the best choice of parameterization depends on the contrast of the subsurface scatterer that the inversion tries to estimate. Based on the results, we observe that there is no best parameterization choice for full-waveform inversion. We also observe that a parameterization using the acoustic impedance and mass density has the worst convergence rate. Finally, we also show that the parameterization analysis during a hierarchical inversion, where the data have limited scattering angles, only helps to select a subspace for mono-parameter inversion. For multi-parameter hierarchical inversion, the search for the best parameterization in terms of the convergence speed might be obfuscated by non-uniqueness problems.

physics.geo-ph↗