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When earthquakes occur, they emit energy that travels through the Earth as seismic waves, providing a glimpse into the planet's internal structure. These waves come in two main types: primary (P-waves) and secondary (S-waves).

P-waves are compressional waves that can travel through both solids and liquids. They are the fastest type of seismic wave and are the first to be detected by seismographs after an earthquake. As they move through the Earth, their speed can change, and they can refract or bend, much like light waves passing through different materials.

S-waves, on the other hand, are shear waves that can only move through solid materials. If they encounter a liquid, they are absorbed and do not continue to propagate, which is a critical observation for understanding the Earth's core. The behavior of S-waves and their inability to pass through liquids led scientists to a crucial discovery about the Earth's internal composition.

The propagation characteristics of P-waves and S-waves differ significantly as they travel through the Earth's layers. The way these waves spread out and arrive at seismic stations allows us to infer the Earth's layered structure.

Investigating P-waves reveals how they accelerate when passing through denser material, such as the transition from the Earth's mantle to the outer core. Conversely, S-waves, which do not travel through liquids, have been instrumental in detecting the liquid nature of the Earth's outer core. Analysts observe a zone, known as the 'S-wave shadow zone,' where S-waves are not detected after an earthquake. This absence is due to the S-waves being stopped by the core's liquid layer.

As an added layer of complexity, P-waves also exhibit a shadow zone, but for different reasons. Their altered paths, including reflection and refraction phenomena, signal varied densities and states of the materials they encounter, leading to the theory of a solid inner core surrounded by a liquid outer core.

The Earth's core is composed of two main parts: the solid inner core and the liquid outer core. The study of seismic waves has been fundamental in reaching these conclusions about the core's structure.

The inner core is believed to be primarily made of iron and nickel, existing in solid form despite its extremely high temperature. This is due to the immense pressures found at the Earth's center, which prevent the core from melting. The liquid outer core surrounds the inner core and is responsible for the Earth's magnetic field.

The existence of the core and its properties are inferred from the seismic wave behavior previously described. The P-wave shadow zone and S-wave absence in particular regions have allowed researchers to construct a model of the core that has both a liquid and a solid phase. This understanding of the core structure not only explains geophysical observations but also sheds light on magnetic field generation and the dynamic processes at work in the Earth's interior.