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This topic deals with the fundamentals of physics and numerical simulation of wave propagation in anisotropic, anelastic and porous media, including the analogy between acoustic waves (in the general sense) and electromagnetic (EM) waves. The emphasis is on geophysical applications for hydrocarbon exploration, but researchers in the fields of earthquake seismology, rock physics, and material science, -- including many branches of acoustics of fluids and solids (acoustics of materials, non-destructive testing, etc.) -- may also find the subject useful. Moreover, the topics include seismic and EM modeling, with an account of the numerical algorithms for computing the synthetic seismograms and radargrams, involving applications in the field of geophysical prospecting, seismology and rock physics, such as detection of oil and gas in sandstones, limestones and source rocks (mainly shales), evaluation of methane hydrate content, upscaling techniques, detection of overpressure, Antarctic and permafrost exploration, exploration of the Earth's deep crust, time-lapse for monitoring of CO2 injection, etc.