GlobalTomo

A global dataset for physics-ML seismic wavefield modeling and FWI

1 Institute for Artificial Intelligence, Peking University 2 School of Earth and Space Sciences, Peking University
3 School of Engineering and Applied Science, Harvard University 4 NVIDIA 5 Rutherford Appleton Laboratory

overview

Abstract

Global seismic tomography, leveraging seismic waves from natural earthquakes, provides essential insights into Earth's internal dynamics. Advanced Full-waveform Inversion techniques, whose aim is to meticulously interpret every detail in seismograms, confront formidable computational demands in forward modeling and adjoint simulations on a global scale. Recent advancements in Machine Learning offer a transformative potential for accelerating the computational efficiency of FWI and extending its applicability to larger scales. This work presents the first 3D global synthetic dataset tailored for seismic wavefield modeling and full-waveform tomography, referred to as the GlobalTomo dataset. This dataset is uniquely comprehensive, incorporating explicit wave physics and robust geophysical parameterization at realistic global scales, generated through state-of-the-art forward simulations optimized for 3D global wavefield calculations. We illustrate that FWI is particularly suitable for modern neural network training, overcoming the limitations of traditional methods with trial and error. We address the challenges through extensive analysis and the establishment of ML baselines and outline future research directions. This work represents an initial attempt of a cross-disciplinary effort to apply modern ML techniques to FWI, potentially revolutionizing the resolution of the 3D partial differential wave equation and impacting a broad spectrum of scientific communities.

Demo

Data

We present three data tiers invloving different wave equation and training scales. To access the data, please click this link.

Acoustic

acoustic

Elastic

elastic

Real Earth

earth

▶ Acoustic Data Structure


                Acoustic wavefield:
                {
                'harmonics': (10000, 405), // Velocity structure parameters
                'X': (10000, 15, 16, 3648), // Spatial-temporal potential in wavefield
                'element_coords_cartesian': (16, 3648, 3), // Cartesian coordinates of wavefield points
                'timestep': (15,), // The propagation time of each snapshot
                }
                Acoustic Fourier wavefield:
                {
                'harmonics': (10000, 405), // Velocity structure parameters
                'X_coef': (10000, 15, 3648, 16), // Spatial-temporal Fourier potential in wavefield
                'element_coords_sz': (3648, 2), // Cartesian coordinates of wavefield points
                'timestep': (15,), // The propagation time of each snapshot
                }
                Acoustic seismogram:
                {
                'harmonics': (10000, 405), // Velocity structure parameters
                'disp': (10000, 37, 37, 3, 150), // Spatial-temporal displacement in seismograms
                'station_coords_cartesian': (37, 37, 3), // Cartesian coordinates of seismogram stations
                'station_coords_spherical': (37, 37, 3), // Spherical coordinates of seismogram stations
                'time': (150,), // Time points of seismograms
                }

▶ Elastic Data Structure


                Elastic wavefield:
                {
                'harmonics': (30000, 1215), // Velocity structure parameters
                'disp': (30000, 15, 16, 3648, 3), // Spatial-temporal displacement in wavefield
                'element_coords_cartesian': (16, 3648, 3), // Cartesian coordinates of wavefield points
                'timestep': (15,), // The propagation time of each snapshot
                }
                Elastic Fourier wavefield:
                {
                'harmonics': (30000, 1215), // Velocity structure parameters
                'disp_coef': (30000, 15, 3648, 16, 3), // Spatial-temporal Fourier displacement in wavefield
                'element_coords_sz': (3648, 2), // Cartesian coordinates of wavefield points
                'timestep': (15,), // The propagation time of each snapshot
                }
                Elastic seismogram:
                {
                'harmonics': (30000, 1215), // Velocity structure parameters
                'disp': (30000, 37, 37, 3, 150), // Spatial-temporal displacement in seismograms
                'station_coords_cartesian': (37, 37, 3), // Cartesian coordinates of seismogram stations
                'station_coords_spherical': (37, 37, 3), // Spherical coordinates of seismogram stations
                'time': (150,), // Time points of seismograms
                }
                Elastic source:
                {
                'source': (30000, 6), // Source parameters
                }

▶ Real Earth Data Structure


                Real earth wavefield:
                {
                'harmonics': (10000, 5427), // Velocity structure parameters
                'disp': (10000, 20, 16, 16470, 3), // Spatial-temporal displacement in wavefield
                'element_coords_cartesian': (16, 16470, 3), // Cartesian coordinates of wavefield points
                'timestep': (20,), // The propagation time of each snapshot
                }
                Real earth Fourier wavefield:
                {
                'harmonics': (10000, 5427), // Velocity structure parameters
                'disp_coef': (10000, 20, 16470, 16, 3), // Spatial-temporal Fourier displacement in wavefield
                'element_coords_sz': (16470, 2), // Cartesian coordinates of wavefield points
                'timestep': (20,), // The propagation time of each snapshot
                }
                Real Earth seismogram:
                {
                'harmonics': (10000, 5427), // Velocity structure parameters
                'disp': (10000, 19, 37, 3, 6000), // Spatial-temporal displacement in seismograms
                'station_coords_cartesian': (19, 37, 3), // Cartesian coordinates of seismogram stations
                'station_coords_spherical': (19, 37, 3), // Spherical coordinates of seismogram stations
                'time': (6000,), // Time points of seismograms
                }
                Real earth source:
                {
                'source': (10000, 9), // Source parameters
                }

Results

Forward modeling: given specific source and velocity structures, the goal is to predict the wavefield at various time steps and the resulting seismograms at surface stations.

Inversion: this process utilizes the seismograms as observational data to deduce the underlying velocity structures.