For an acoustic heterogeneous medium, these are given by the scalar linear equation of motion: These methods solve for the propagation of the full seismic wavefield by discretising the elastodynamic equations of motion. They are able to capture a large range of physics, including the effects of undulating solid–fluid interfaces ( Leng et al., 2019), intrinsic attenuation ( van Driel and Nissen-Meyer, 2014 a) and anisotropy ( van Driel and Nissen-Meyer, 2014 b). Numerous methods exist for simulating seismic waves, the most popular in fully heterogeneous media being finite difference (FD) and spectral element methods (SEMs) ( Igel, 2017 Moczo et al., 2007 Komatitsch and Tromp, 1999). In planetary science, seismic simulations play a central role in understanding novel recordings on Mars ( Van Driel et al., 2019). In seismic inversion, they are used to estimate the elastic properties of a medium given its seismic response ( Tarantola, 1987 Schuster, 2017) and in full-waveform inversion ( Fichtner, 2010 Virieux and Operto, 2009), a technique used to image the 3-D structure of the subsurface, they are used up to tens of thousands of times to improve on estimates of a medium's elastic properties. In global geophysics, they are used to obtain snapshots of the Earth's interior dynamics by tomography ( Hosseini et al., 2019 Bozdağ et al., 2016), to decipher source and path effects from individual seismograms ( Krischer et al., 2017) and to model wave effects of complex structures ( Thorne et al., 2020 Ni et al., 2002). In geophysical surveying, they show how the subsurface is illuminated by different survey designs ( Xie et al., 2006). In oil and gas prospecting, they allow the seismic response of hydrocarbon reservoirs to be modelled ( Chopra and Marfurt, 2007 Lumley, 2001). In seismic hazard analysis, they are a key tool for quantifying the ground motion of potential earthquakes ( Boore, 2003 Cui et al., 2010). Seismic simulations are essential for addressing many outstanding questions in geophysics. We discuss further research directions which could address these challenges and potentially yield useful tools for practical simulation tasks. We find that are there are challenges when extending our methods to more complex, elastic and 3-D Earth models for example, the accuracy of both networks is reduced when they are tested on models outside of their training distribution. We test the sensitivity of the accuracy of both networks to different network hyperparameters and show that the WaveNet network can be retrained to carry out fast seismic inversion in the same media. The second network is significantly more general than the first and is able to simulate the seismic response in faulted media with arbitrary layers, fault properties and an arbitrary location of the seismic source on the surface of the media, using a conditional autoencoder design. The first network is able to simulate the seismic response in horizontally layered media and uses a WaveNet network architecture design. We present two deep neural networks which are able to simulate the seismic response at multiple locations in horizontally layered and faulted 2-D acoustic media an order of magnitude faster than traditional finite difference modelling. In this work, we investigate the potential of deep learning for aiding seismic simulation in the solid Earth sciences. Numerical methods such as finite difference (FD) modelling and spectral element methods (SEMs) are the most popular techniques for simulating seismic waves, but disadvantages such as their computational cost prohibit their use for many tasks. In geophysics the refraction or reflection of seismic waves is used for research into the structure of the Earth's interior, and man-made vibrations are often generated to investigate shallow, subsurface structures.The simulation of seismic waves is a core task in many geophysical applications. Velocity tends to increase with depth and ranges from approximately 2 to 8 km/s in the Earth's crust, up to 13 km/s in the deep mantle.Įarthquakes create distinct types of waves with different velocities when reaching seismic observatories, their different travel times help scientists to locate the source of the hypocenter. "The propagation velocity of the waves depends on density and elasticity of the medium. The correction in cryptocurrencies first comes to mind, or maybe the realization that a steepening yield curve is, after all, a real possibility? What would be the equivalent in today's markets? According to Wikipedia, "Seismic waves are waves of energy that travel through the Earth's layers, and are a result of earthquakes, volcanic eruptions, magma movement, large landslides and large man-made explosions that give out low-frequency acoustic energy."
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