Seismic velocity structure

Seismic velocity structure is the distribution and variation of seismic wave speeds within Earth's and other planetary bodies' subsurface. It is reflective of subsurface properties such as material composition, density, porosity, and temperature. Geophysicists rely on the analysis and interpretation of the velocity structure to develop refined models of the subsurface geology, which are essential in resource exploration, earthquake seismology, and advancing our understanding of Earth's geological development.

History
The understanding of the Earth's seismic velocity structure has developed significantly since the advent of modern seismology. The invention of the seismogram in the 19th-century catalyzed the systematic study of seismic velocity structure by enabling the recording and analysis of seismic waves.

20th century
The field of seismology achieved significant breakthroughs in the 20th century.In 1909, Andrija Mohorovičić identified a significant boundary within the Earth known as the Mohorovičić discontinuity, which demarcates the transition between the Earth's crust and mantle with a notable increase in seismic wave speeds. This work was furthered by Beno Gutenberg, who identified the boundary at the core-mantle layer in the early to mid-20th century. The 1960s introduction of the World Wide Standardized Seismograph Network dramatically improved the collection and understanding of seismic data, contributing to the broader acceptance of plate tectonics theory by illustrating variations in seismic velocities.

Later, seismic tomography, a technique used to create detailed images of the Earth's interior by analyzing seismic waves, was propelled by the contributions of Keiiti Aki and Adam Dziewonski in the 1970s and 1980s, enabling a deeper understanding of the Earth's velocity structure. Their work laid the foundation for the Preliminary Reference Earth Model in 1981, a significant step toward modeling the Earth's internal velocities. The establishment of the Global Seismic Network in 1984 by Incorporated Research Institutions for Seismology further enhanced seismic monitoring capabilities, continuing the legacy of the WWSSN.

21st century
The advancement in seismic tomography and the expansion of the Global Seismic Network, alongside greater computational power, have enabled more accurate modeling of the Earth's internal velocity structure. Recent progress focuses on the inner core's velocity features and applying methods like ambient noise tomography for improved imaging.

Principle of seismic velocity structure
The study of seismic velocity structure, using the principles of seismic wave propagation, offers critical insights into the Earth's internal structure, material composition, and physical states. Variations in wave speed, influenced by differences in material density and state (solid, liquid, or gas), alter wave paths through refraction and reflection, as described by Snell's Law. P-waves, which can move through all states of matter and provide data on a range of depths, change speed based on the material's properties, such as type, density, and temperature. S-waves, in contrast, are constrained to solids and reveal information about the Earth's rigidity and internal composition, including the discovery of the outer core's liquid state since they cannot pass through it. The study of these waves' travel times and reflections offers a reconstructive view of the Earth's layered velocity structure.

Velocity structure of Earth
Seismic waves traverse the Earth's layers at speeds that differ according to each layer's unique properties, with their velocities shaped by the respective temperature, composition, and pressure. The Earth's structure features distinct seismic discontinuities where these velocities shift abruptly, signifying changes in mineral composition or physical state.

Crust

 * Average P-wave velocity: 6.0–7.0 km/s (continental); 5.0–7.0 km/s (oceanic)
 * Average S-wave velocity: 3.5–4.0 km/s

Within the Earth's crust, seismic velocities increase with depth, mainly due to rising pressure, which makes materials denser. The relationship between crustal depth and pressure is direct; as the overlying rock exerts weight, it compacts underlying layers, reduces rock porosity, increases density, and can alter crystalline structures, thus accelerating seismic waves.

Crustal composition varies, affecting seismic velocities. The upper crust typically contains sedimentary rocks with lower velocities (2.0–5.5 km/s), while the lower crust consists of denser basaltic and gabbroic rocks, leading to higher velocities.

Although geothermal gradient, which refers to the increase in temperature with depth in the Earth's interior, can decrease seismic velocities, this effect is usually outweighed by the velocity-boosting impact of increased pressure.

Upper mantle

 * Average P-wave velocity: 7.5–8.5 km/s
 * Average S-wave velocity: 4.5–5.0 km/s

Seismic velocity in the upper mantle rises primarily due to increased pressure, similar to the crust but with a more pronounced effect on velocity. Additionally, pressure-induced mineral phase changes, where minerals rearrange their structures, in the upper mantle contribute to this acceleration. For example, olivine transforms into its denser polymorphs, wadsleyite and ringwoodite, at depths of approximately 410 km and 660 km respectively, resulting in a more compact structure that facilitates faster seismic wave propagation in the transition zone.

Lower mantle
In the lower mantle, the rise in seismic velocity is driven by increasing pressure, which is greater here than in the upper layers, resulting in denser rock and faster seismic wave travel. Although thermal effects may lessen seismic velocity by softening the rock, the predominant factor in the lower mantle remains the increase in pressure.
 * Average P-wave velocity: 10–13 km/s
 * Average S-wave velocity: 5.5–7.0 km/s

Outer Core
In the outer core, seismic velocity significantly decreases due to its liquid state, which impedes the speed of seismic waves despite the high pressure. This sharp decline is observed at the core-mantle boundary, also referred to as the D '' region or Gutenberg discontinuity.
 * Average P-wave velocity: 8.0–10 km/s
 * S-waves: Do not propagate as the outer core is liquid

Furthermore, the reduction in seismic velocity in the outer core suggests the presence of lighter elements like oxygen, silicon, sulfur, and hydrogen, which lower the density of the outer core.

Inner core
The solid, high-density composition of the inner core, predominantly iron and nickel, results in increased seismic velocity compared to the liquid outer core. While light elements also present in the inner core modulate this velocity, their impact is relatively contained.
 * Average P-wave velocity: ~11 km/s
 * Average S-wave velocity: ~3.5 km/s

Anisotropy of inner core
The inner core is anisotropic, causing seismic waves to vary in speed depending on their direction of travel. P-waves, in particular, move more quickly along the inner core's rotational axis than across the equatorial plane. This suggests that Earth's rotation affects the alignment of iron crystals during the core's solidification.

There is also evidence suggesting a distinct transition zone ("inner" inner core), with a hypothesized transition zone some 250 to 400 km beneath the inner core boundary (ICB). This is inferred from anomalies in travel times for P-wave that travels through the inner core. This transition zone, perhaps 100 to 200 km thick, may provide insights into the alignment of iron crystals, the distribution of light elements, or Earth's accretion history.

Studying the inner core poses significant challenges for seismologists and geophysicists, given that it accounts for less than 1% of Earth's volume and is difficult for seismic waves to penetrate. Moreover, S-wave detection is challenging due to minimal compressional-shear wave conversion at the boundary and substantial attenuation within the inner core, leaving S-wave velocity uncertain and an area for future research.

Lateral variation of velocity structure
Lateral variation in seismic velocity is a horizontal change in seismic wave speeds across the Earth's crust due to differences in geological structures like rock types, temperature, and fluids presence, affecting seismic wave travel speed. This variation helps delineate tectonic plates and geological features and is key to resource exploration and understanding the Earth's internal heat flow.

Discontinuity
Discontinuities are zones or surfaces within the Earth that lead to abrupt changes in seismic velocity, revealing the composition and demarcating the boundaries between the Earth's layers.

The following are key discontinuities within the Earth:
 * Mohorovičić discontinuity: the boundary between the crust and the mantle, located approximately 30–50 km below the continental crust and 5–10 km beneath the oceanic crust.
 * 410 km discontinuity: a phase transition where olivine becomes wadsleyite.
 * 520 km discontinuity: a phase transition where wadsleyite becomes ringwoodite.
 * 660 km discontinuity: a phase transition where of ringwoodite to bridgmanite and ferropericlase.
 * Gutenberg discontinuity: the core-mantle boundary, at approximately 2890 km depth.
 * Lehmann discontinuity: marking the inner core boundary (ICB), at approximately 5150 km depth.

Velocity structure of the Moon
Knowledge of the Moon's seismic velocity primarily stems from seismic records obtained by Apollo missions' Passive Seismic Experiment (PSE) stations. Between 1969 and 1972, five PSE stations were deployed on the lunar surface, with four operational until 1977. These four stations created a network on the near side of the moon, configured as an equilateral triangle with two stations at one vertex. This network recorded over 13,000 seismic events, and the gathered data remains a subject of ongoing study. The analysis has revealed four moonquake mechanisms: shallow, deep, thermal, and those caused by meteoroid impacts.

Crust

 * Average P-wave velocity: 5.1–6.8 km/s
 * Average S-wave velocity: 2.96–3.9 km/s

The seismic velocity on the Moon varies within its roughly 60 km thick crust, presenting a low seismic velocity at the surface. Velocity readings increase from 100 m/s near the surface to 4 km/s at a depth of 5 km and rise to 6 km/s at 25 km depth. At 25 km depth, a discontinuity presence, at which the seismic velocity increases abruptly to 7 km/s. This velocity then stabilizes, reflecting the consistent composition and hydrostatic pressure conditions at greater depths.

Seismic velocities within the Moon's approximately 60 km thick crust exhibit an initial low of 100 m/s at the surface, which escalates to 4 km/s at 5 km depth, and then to 6 km/s at 25 km depth where velocities sharply increase to 7 km/s and stabilize, revealing a consistent composition and pressure conditions in deeper layers.

Surface velocities are low due to the loose, porous nature of the regolith. Deeper, compaction increases velocities, with the region beyond 25 km depth characterized by dense, sealed anorthosite and gabbro layers, suggesting a crust with hydrostatic pressure. The Moon's geothermal gradient minimally reduces velocities by 0.1-0.2 km/s.

Mantle
Research into the seismic structure of the Moon's mantle is hampered by the scarcity of data. Analysis of moonquake waveforms suggests that seismic wave velocities in the upper mantle (ranging from 60 to 400 km in depth) exhibit a minor negative gradient, with S-wave speeds decreasing at rates between -6×10−4 to -13×10−4 km/s per kilometer. A decease in P-wave velocities has also been postulated. The data delineates a transition zone between 400 km and 480 km depth, where a noticeable decrement in the velocities of both P- and S-waves occurs.
 * Average P-wave velocity: 7.7 km/s
 * Average S-wave velocity: 4.5 km/s

Uncertainty grows when probing the lower mantle, extending from 480 km to 1100 km beneath the lunar surface. Some studies detect a consistent decline in S-wave transmission, suggesting absorption or scattering phenomena, while other findings indicate that velocities for P- and S-waves may in fact rise.

Temperature increases with depth are believed to be the primary influence behind the observed drop in velocities within the upper mantle, suggesting a mantle heavily regulated by thermal gradients rather than compositional changes. The delineated transition zone implies a division between the chemically distinct upper and lower mantles, possibly explained by an uptick in iron concentration due to high pressure and thermal conditions at depth.

Deeper into the lower mantle, the debate over seismic characteristics continues, with theories of partial melting around the 1000 km depth mark to justify the attenuation of S-wave velocities. This molten state may cause a segregation of materials, resulting in a concentration of magnesium-rich olivine in the lower regions and potentially affecting seismic speeds.

Core
Understanding the seismic velocities within the Moon's core presents challenges due to the limited data available.

Outer core:


 * Average P-wave velocity: 4 km/s
 * S-waves: Do not propagate as the outer core is liquid

Inner core:


 * Average P-wave velocity: 4.4 km/s
 * Average S-wave velocity: 2.4 km/s

The sharp decline in P-wave velocity at the mantle-core boundary suggests a liquid outer core, transitioning from 7.7 km/s in the mantle to 4 km/s in the outer core. The inability of S-waves to traverse this zone further confirms its fluid nature with molten iron sulphate.

An increase in seismic velocities upon reaching the inner core intimates a transition to a solid phase. The presence of solid iron-nickel alloys, potentially alloyed with lighter elements, is deduced from this increase.

Current geophysical models posit a relatively diminutive Lunar core, with the liquid outer core accounting for 1-3% of the Moon's total mass and the entire core constituting about 15-25% of the lunar mass. While some lunar models suggest the possibility of a core, its existence and characteristics are not unequivocally required by the observed data.

Lateral variation of seismic velocity structure
Crustal velocity also varies laterally, particularly in impact basins, where meteoroid collisions have compacted the substrate, resulting in higher velocities due to reduced porosity.

Lateral variations in the Moon's seismic velocity structure are marked by differences in the crust's physical properties, especially within impact basins. The velocity increases in these regions are attributed to meteoroid impacts, which have compacted the lunar substrate, thereby increasing its density and reducing porosity. This phenomenon has been studied using seismic data from lunar missions, which show that the Moon's crustal structure varies significantly with location, reflecting its complex impact history and internal processes.

Velocity structure of Mars
The investigation into Mars's seismic velocity has primarily relied on models and the data gathered by the InSight mission, which landed on the planet in 2018. By September 30, 2019, InSight had detected 174 seismic events. Before InSight, the Viking 2 lander attempted to collect seismic data in the 1970s, but it captured only a limited number of local events, which did not yield conclusive insights.

Crust

 * Average P-wave velocity: 3.5–5 km/s
 * Average S-wave velocity: 2–3 km/s

The crust of Mars, ranging from 10 to 50 km in thickness, exhibits increasing seismic velocity as depth increases, attributable to rising pressure. The upper crust is characterized by low density and high porosity, leading to reduced seismic velocity. Two key discontinuities have been observed: one within the crust at a depth of 5 to 10 km, and another which is likely the crust-mantle boundary, occurring at a depth of 30 to 50 km.

Mantle
Upper mantle: Lower mantle:
 * Average P-wave velocity: 8 km/s
 * Average S-wave velocity: 4.5 km/s


 * P-wave: 5.5 km/s
 * S-waves: Not applicable (liquid)

The Martian mantle, composed of iron-rich rocks, facilitates the transmission of seismic waves at high speeds. Research indicates a variation in seismic velocities between depths of 400 and 600 km, where S-wave speeds decrease while P-wave speeds remain constant or increase slightly. This region is known as the Low Velocity Zone (LVZ) in the Martian upper mantle and may be caused by a static layer overlying a convective mantle. The reduction in velocity at the LVZ is likely due to high temperatures and moderate pressures.

Martian mantle research has also identified two discontinuities at depths of approximately 1100 km and 1400 km. These discontinuities suggest phase transitions from olivine to wadsleyite and from wadsleyite to ringwoodite, analogous to the Earth's mantle phase changes at depths of 410 km and 660 km. However, Mars's mantle composition differs from Earth's as it does not have a lower mantle predominated by bridgmanite.

Recent study suggested the presence of a molten lower mantle layer in the Mars which could significantly affect the interpretation of seismic data and our understanding of the planet's thermal history.

Core

 * Average P-wave velocity: 5 km/s
 * S-waves: Do not propagate as the outer core is liquid

Scientific evidence suggests that Mars has a substantial liquid core, inferred from S-wave transmission patterns that indicate these waves do not pass through liquid. The core is likely composed of iron and nickel with a significant proportion of lighter elements, inferred from its lower-than-expected density.

The presence of a solid inner core on Mars, comparable to Earth's, is currently the subject of scientific debate. No definitive evidence has yet confirmed the nature of the inner core, leaving its existence and characteristics as topics for further research.

Lateral variation of velocity structure
Lateral variations in the seismic velocity structure of Mars have been revealed by data from the InSight mission, indicating an intricately layered subsurface. InSight's seismic experiments suggest that these variations reflect differences in crustal thickness and composition, potentially caused by volcanic and tectonic processes unique to Mars. Such variations also provide evidence for the presence of a liquid layer above the core, suggesting a complex interplay of thermal and compositional factors affecting the planet's evolution. Further analysis of marsquake data may illuminate the relationship between these lateral variations and the Martian mantle's convective dynamics.

Velocity structure of Enceladus
Research on Enceladus's subsurface composition has provided theoretical velocity profiles in anticipation of future exploratory missions. While Enceladus's interior is poorly understood, scientists agree on a general structure consisting of an outer icy shell, a subsurface ocean, and a rocky core. In a recent study, three models—single core, thick ice, and layered core —were proposed to delineate Enceladus' internal characteristics.

According to these models, seismic velocities are expected to decrease from the ice shell to the ocean, reflecting transitions from porous, fractured ice to a more fluid state. Conversely, velocities are predicted to rise within the solid silicate core, illustrating the stark contrast between the moon's various layers.

Future plan
Seismic exploration of celestial bodies has so far been limited to the Moon and Mars. However, future space missions are set to extend seismic studies to other entities in our solar system.

The proposed Europa Lander Mission, slated for a launch window between 2025 and 2030, will investigate the seismic activity of Jupiter's moon, Europa. This mission plans to deploy the Seismometer to Investigate Ice and Ocean Structure (SIIOS), an instrument designed by the University of Arizona to withstand Europa's harsh, cold, and radiative environment. SIIOS's goal is to provide insight into Europa's icy crust and subterranean ocean.

In conjunction with its Artemis program to the Moon, NASA has also funded initiatives under the Development and Advancement of Lunar Instrumentation (DALI) program. Among these, the Seismometer for a Lunar Network (SLN) project stands out. The SLN aims to facilitate the creation of a lunar seismometer network by integrating seismometers into future lunar landers or rovers. This initiative is part of NASA's broader effort to prepare for continued exploration of the Moon's geology.

Methods
The study of seismic velocity structure is typically conducted through the observation of seismic data coupled with inverse modeling, which involves adjusting a model based on observed data to infer the properties of the Earth's interior. Here are some methods used to study seismic velocity structure:

Applications of velocity structure
Applications of seismic velocity structure encompass a range of fields where understanding the Earth's subsurface is crucial:

Limitation/Uncertainty

 * S-wave velocity of the inner Earth's core

Investigating Earth's inner core through seismic waves presents significant challenges. Directly observing seismic waves that traverses the inner core is difficult due to weak signal conversion at the core boundaries and high attenuation within the core. Recent techniques like earthquake late-coda correlation, which utilises the later part of a seismogram, provide estimates for the inner core's shear wave velocity but are not without challenges.


 * Isotropic assumptions

Seismic velocity studies often assume isotropy, treating Earth's subsurface as having uniform properties in all directions. This simplification is practical for analysis but may not be accurate. The inner core and mantle, for example, likely demonstrate anisotropic, or directionally dependent, properties, which can affect the accuracy of seismic interpretations.


 * Dimensional considerations

Seismic models are frequently one-dimensional, considering changes in Earth's properties with depth but neglecting lateral variations. Although this method eases computation, it fails to account for the planet's complex three-dimensional structure, potentially misleading our understanding of subsurface characteristics.


 * Non-uniqueness of Inverse Modelling

Seismic velocity structures are inferred through inverse modeling, fitting theoretical models to observed data. However, different models can often explain the same data, leading to non-unique solutions. This issue is compounded when inverse problems are poorly conditioned, where small data variations can suggest drastically different subsurface structures.


 * Data Limitations for the Moon and Mars Seismic Studies

In contrast to Earth, the seismic datasets for the Moon and Mars are sparse. The Apollo missions deployed a handful of seismometers across the Moon, and Mars's seismic data is limited to the InSight mission's findings. This scarcity restricts the resolution of velocity models for these celestial bodies and introduces greater uncertainty in interpreting their internal structures.