Bistatic Radar Observations of Europa: Peering Beneath the Galilean Ice

Introduction: The Enigma of the Galilean Ice Worlds

Jupiter, the largest planet in our solar system, is orbited by a vast retinue of moons, but planetary science has historically focused on the three largest icy Galilean satellites: Europa, Ganymede, and Callisto¹. Among these, Europa represents a premier target for astrobiology and comparative oceanography due to compelling evidence that it harbors a global subsurface ocean of liquid water beneath a geologically young, tectonically deformed icy crust². While optical, ultraviolet, and infrared observations yield critical information regarding the chemical composition and geological features of Europa's outermost surface layers, these short electromagnetic wavelengths can only penetrate mere micrometers to millimeters into the ice².

To deduce the structural integrity, porosity, thermal dynamics, and purity of the bulk ice shell, researchers must employ longer-wavelength electromagnetic radiation, specifically radio waves, which can penetrate deeply into the subsurface². Geologic surface features provide clues regarding how the ice shell and the underlying ocean interact, but these features only hint at mechanisms occurring far below³. As Tunhui Xie, a researcher at the University of California, Los Angeles, noted, radar delves beneath what is easily visible because radio waves carry information about the internal structure and purity of the ice as they propagate².

Recently, planetary scientists concluded the most extensive Earth-based radar study of Europa to date. Spanning from 2011 to 2024, the campaign filled a three-decade gap in radar observations of the Galilean moons, building upon foundational studies conducted in the late 1980s and early 1990s². Presented at the 248th meeting of the American Astronomical Society, researchers Tunhui Xie and Jean-Luc Margot utilized a bistatic radar configuration pairing the National Aeronautics and Space Administration (NASA) Goldstone Solar System Radar with the National Science Foundation (NSF) Robert C. Byrd Green Bank Telescope². By bouncing 3.5-centimeter radio waves off the Jovian moon, the team gathered unprecedented insights into Europa's unusually strong and complex radar scattering properties².

This exhaustive report synthesizes the geophysical context of Europa's ice shell, the mechanical principles of bistatic planetary radar astronomy, the highly specific physics of the coherent backscatter opposition effect, the implications of radiation weathering on hemispheric asymmetries, and how these rigorous Earth-based constraints provide critical foundational data for upcoming orbital sounding missions such as NASA's Europa Clipper and the European Space Agency's (ESA) Jupiter Icy Moons Explorer (JUICE).

The Geophysical Context of Europa's Ice Shell

Before interpreting the complex radar echoes bouncing off Europa, it is crucial to establish the current physical models of its ice shell. Europa is slightly smaller than Earth's Moon, yet its surface is extraordinarily smooth and bright, largely devoid of the heavy impact cratering that characterizes ancient planetary surfaces⁴. The scarcity of craters implies a surface age of perhaps less than 200 million years, suggesting continuous resurfacing driven by internal tidal heating⁷.

Recent spacecraft encounters have refined our estimates of the ice shell's thickness and internal complexity. During a close flyby on September 29, 2022, NASA's Juno spacecraft approached within roughly 360 kilometers of Europa's surface⁹. Utilizing its Microwave Radiometer instrument to scan approximately half of the moon, the Juno team estimated that the cold, rigid, conductive outer layer of Europa's pure water ice shell is, on average, approximately 29 kilometers thick⁹. This estimate applies to a pure ice shell; if the ice contains a modest amount of dissolved salts, or if a warmer, convective inner layer exists beneath the rigid crust, the total thickness could vary, potentially reducing the rigid shell estimate by nearly 5 kilometers or increasing the overall total thickness⁹.

Furthermore, the Juno flyby identified shallow ice features termed "scatterers"—such as cracks, pores, and voids—located close to the surface⁹. These subsurface anomalies, estimated to be at most a few inches in diameter, scatter microwave radiation and are theorized to complicate the vertical transport of oxygen and nutrients from the surface down to the subsurface ocean⁹.

The dynamic nature of Europa's surface has also been a subject of intense debate regarding transient water vapor plumes. In 2014, a prominent analysis of Hubble Space Telescope data indicated the presence of intermittent water vapor plumes erupting from Europa's south pole¹⁰. However, a subsequent 2026 re-analysis by the same research team scrutinized Hubble data collected between 1999 and 2020. They concluded that while there is strong evidence for a persistent hydrogen exosphere originating from the water ice surface, the initial detection of localized water vapor plumes lacked sufficient statistical certainty, dropping below a 90 percent confidence threshold¹⁰. This underscores the necessity of deep-penetrating radar; if surface plumes cannot be reliably utilized to sample the subsurface ocean, instruments must peer through the thick, scattering ice shell directly.

Principles of Planetary Radar Astronomy

Planetary radar astronomy is a uniquely powerful active remote sensing technique. Unlike passive radiometry or optical astronomy, which measure the emission of thermal radiation or the reflection of incident sunlight, radar astronomy involves transmitting a high-powered, well-characterized beam of coherent microwave radiation at a target and analyzing the returning echo¹¹. The time delay of the echo provides precise distance measurements, while the Doppler frequency shift reveals the target's rotation and radial velocity¹¹. Most importantly for subsurface analysis, the intensity and polarization state of the returning echo provide profound insights into the target's surface roughness, porosity, density, and dielectric constant¹¹.

Monostatic vs. Bistatic Configurations

Radar observations can be conducted in two primary configurations: monostatic and bistatic. In a monostatic configuration, the same antenna is used to both transmit the outgoing signal and receive the returning echo. In this geometry, the phase angle (the angle between the transmitter, the target, and the receiver) is exactly zero degrees¹⁴.

Conversely, a bistatic configuration utilizes geographically separated facilities: one antenna transmits the signal, and a different antenna (or an array of antennas) receives the echo¹⁴. Because the transmitter and receiver are located at different positions on Earth, the radar waves form a very small but non-zero angle—known as the bistatic angle—when they bounce off the distant planetary target¹⁵. As the Earth rotates and the relative geometry between the Earth and the target changes, the bistatic angle subtly shifts. Measuring how the radar echo intensity fluctuates across varying bistatic angles is the only empirical method for characterizing the angular width of specific backscatter scattering peaks¹⁴.

Radar Albedo and Circular Polarization

The two paramount metrics utilized to characterize planetary surfaces via radar are the radar albedo and the circular polarization ratio¹¹.

Radar albedo is a measure of the target's intrinsic reflectivity. It is defined as the total radar cross-section of the body divided by its projected physical area¹¹. The observation results typically measure the radar albedo in a specific polarization state, but combining the orthogonal states yields the total radar albedo, providing a comprehensive image of the body's microwave reflectivity¹¹.

When researchers transmit a continuous radio wave toward a planetary body, the wave is typically circularly polarized, possessing either a right-handed or left-handed helicity. When this wave strikes a smooth, rocky, or metallic surface, the electromagnetic boundary conditions dictate that the reflected wave reverses its geometric handedness¹². Thus, a right-handed transmitted wave reflects predominantly as a left-handed wave. Radar receivers are designed with dual channels to measure this phenomenon: the "Expected" or Opposite Sense channel, and the "Unexpected" or Same Sense channel¹¹.

The ratio of the echo power received in the Same Sense channel to the power received in the Opposite Sense channel is known as the circular polarization ratio¹¹. A smooth planetary surface acting as a dielectric mirror will yield a circular polarization ratio near zero. As a surface becomes increasingly rough at scales comparable to the radar wavelength, multiple scattering events and reflections from blocky, angular structures (like corner reflectors) cause the wave to lose its original polarization state, increasing the ratio¹⁸.

Target Body	Typical Total Radar Albedo	Typical Circular Polarization Ratio	Primary Scattering Mechanism
Main-Belt Asteroids (e.g., Ceres, Pallas)	0.04 to 0.08	0.05 to 0.10	Specular reflection off smooth regolith
Earth's Moon	< 0.10	~ 0.10	Single-bounce surface reflection
Ganymede (Galilean Moon)	1.39	1.43	Moderate multiple volume scattering
Europa (Galilean Moon)	2.60	1.53	Intense multiple volume scattering

Table 1: Comparative radar scattering properties of rocky bodies versus the icy Galilean moons, demonstrating the extraordinary radar brightness and polarization inversion of Europa. Data derived from historical Arecibo observatory measurements¹².

For most terrestrial planets, the Moon, and main-belt asteroids, the total radar albedo is relatively low, and the circular polarization ratio rarely exceeds 0.3, reflecting standard specular and diffuse reflection off a rough, absorbing silicate surface¹². However, as Table 1 illustrates, the icy Galilean satellites exhibit properties that completely defy the expectations set by rocky worlds.

In foundational studies conducted between 1987 and 1991, planetary astronomer Steven Ostro and colleagues discovered that the icy moons possessed total radar albedos exceeding 1.0, with Europa reaching a staggering 2.60 at 13-centimeter wavelengths¹². This indicates that Europa reflects radio waves more efficiently than a perfectly conducting metallic sphere of equivalent size. Furthermore, the circular polarization ratios exceeded unity, meaning that against all conventional electromagnetic expectations, more energy was returned in the "unexpected" Same Sense polarization than in the "expected" Opposite Sense polarization¹².

The 2011-2024 Bistatic Observation Campaign

To rigorously investigate these historical anomalies and address a three-decade gap in the data, Xie and Margot initiated an exhaustive Earth-based radar campaign spanning from 2011 to 2024². The campaign leveraged advanced instrumentation that was vastly superior in sensitivity and bandwidth compared to the equipment available during the Voyager era¹².

The researchers utilized a bistatic configuration to probe Europa. The transmission source was NASA's Deep Space Station 14 (DSS-14), a massive 70-meter fully steerable parabolic antenna located at the Goldstone Deep Space Communications Complex in the Mojave Desert, California²¹. The Goldstone Solar System Radar is powered by dual 250-kilowatt klystron amplifiers—vacuum tube electron beam devices that interact with radio waves passing through resonant cavities²². These amplifiers combine to radiate approximately 450 to 500 kilowatts of continuous wave power at a center frequency of 8.56 gigahertz, which corresponds to an X-band wavelength of 3.5 centimeters²¹.

Campaign Specification	Details
Transmitting Facility	NASA Goldstone DSS-14 (California)
Receiving Facilities	Goldstone DSS-14 & NSF Green Bank Telescope (West Virginia)
Antenna Diameters	70 meters (Goldstone) / 100 meters (Green Bank)
Transmitter Output Power	~450 - 500 kilowatts
Operating Frequency	8.56 Gigahertz (X-band)
Radar Wavelength	3.5 centimeters
Observation Modality	Bistatic, Continuous Wave

Table 2: Technical specifications of the 2011-2024 Europa radar observation campaign¹⁴.

The echoes bouncing back from Europa were received simultaneously by the Goldstone antenna and the National Science Foundation's Robert C. Byrd Green Bank Telescope in West Virginia². The Green Bank Telescope is the world's largest fully steerable radio telescope, boasting a 100-meter-diameter collecting area²³. Its unblocked aperture and active surface—comprising over two thousand actuators that continuously adjust the aluminum panels to compensate for gravitational sagging—provide unparalleled sensitivity across microwave frequencies²³. Receiving the radar echoes at the 100-meter Green Bank Telescope substantially improved the signal-to-noise ratio compared to purely monostatic reception at Goldstone²⁵. Furthermore, the geographic separation between California and West Virginia provided the necessary geometric baseline to observe Europa across a range of narrow bistatic angles⁵.

The Physics of the Coherent Backscatter Opposition Effect

The UCLA researchers confirmed that Europa's radar albedo is substantially higher than typical planetary bodies and that the returning signal is dominated by the same circular polarization as the transmitted beam². These specific characteristics are the definitive hallmark of an optical and electromagnetic phenomenon known as the coherent backscatter opposition effect (CBOE)².

Multiple Scattering in a Low-Loss Medium

To understand CBOE, one must consider the interaction of microwaves with water ice. Unlike silicate rock, which is highly absorptive, cold, pure water ice is highly transparent to microwave and radio frequencies, possessing a very low dielectric loss tangent²⁶. When the 3.5-centimeter X-band radio waves strike Europa, a significant fraction of the electromagnetic energy penetrates the surface rather than reflecting off the top boundary²⁷.

As the wave propagates through the ice shell, it encounters an immense volume of subsurface heterogeneities. These include the precise features identified by the Juno spacecraft—fractures, voids, porosity variations, and embedded impurities like silicates or salts⁹. If these discrete scatterers are roughly comparable in size to the radar wavelength (a few centimeters), they trigger Rayleigh or Mie scattering¹¹.

The radio wave scatters multiple times, undertaking a chaotic random walk through the ice volume¹⁴. Eventually, a portion of this energy diffuses back toward the surface and escapes into space. For the vast majority of exiting trajectories, the scattered waves have traversed paths of differing lengths. Consequently, their electromagnetic phases are randomized, and they sum together incoherently, producing a standard, diffuse background level of radar return¹⁴.

Time-Reversed Paths and Constructive Interference

However, in the exact retro-reflection direction—straight back toward the transmitting antenna—the physics shift dramatically due to the principle of time-reversal symmetry¹².

For every multiple-scattering path a wave can take through the ice (for example, striking subsurface anomaly A, then B, then C, and exiting), there exists an exact time-reversed counterpart that traverses the identical path in reverse (striking C, then B, then A, and exiting)¹⁴. Because the physical path lengths of these conjugate pairs are perfectly identical, the phase shift accumulated by both waves is exactly equal²⁹. When these two waves exit the ice in the exact backward direction, the phase difference between them is identically zero, ensuring they interfere constructively¹⁴.

This constructive interference effectively doubles the intensity of the backscattered signal within a very narrow angular cone centered on the source, resulting in the dramatic spike in radar albedo observed on Europa¹⁴.

Polarization Memory and the Opposition Effect

The CBOE mechanism elegantly resolves the mystery of Europa's polarization inversion. When a circularly polarized wave undergoes a single specular reflection, its helicity is cleanly reversed¹⁸. However, when the wave undergoes multiple internal scattering events, the chaotic geometry of the subsurface structures causes a complex sequence of polarization vector rotations¹².

Theoretical physics demonstrates that the coherence of these time-reversed paths is largely preserved for waves that scatter back into the Same Sense polarization state, but the coherence is highly degraded or destroyed for waves scattering into the Opposite Sense state¹². This phenomenon, often referred to as "circular polarization memory," ensures that a heavily volume-scattered signal returns predominantly with the same geometric handedness it possessed upon transmission¹².

It is important to differentiate CBOE from another related phenomenon: the Shadow Hiding Opposition Effect (SHOE). SHOE occurs in porous regoliths when particles are large enough to cast sharp shadows. At exactly zero degrees phase angle, the particles hide their own shadows, causing a sudden surge in brightness¹⁴. However, SHOE is dominated by single-scattering events and does not produce the extreme polarization inversion seen on Europa¹⁴. CBOE explicitly requires a medium with a high single-scattering albedo and low absorption to allow for high-order multiple scattering, making cold planetary ice the perfect host¹⁴.

Terrestrial Analogs

To validate these scattering models, researchers have turned to terrestrial analogs. In recent years, radar engineers utilized bistatic radar systems to measure dry seasonal snowpacks and the accumulation areas of glaciers in the Swiss Alps¹⁴. Operating at the Ku-band (17.2 gigahertz) and X-band (9.65 gigahertz) frequencies, they successfully detected the coherent backscatter opposition effect in terrestrial snow, finding backscatter enhancements of 35 to 60 percent exactly at the zero bistatic angle¹⁵. These field experiments mathematically confirm that the presence of disordered, weakly absorbing water ice produces the exact radar anomalies detected millions of miles away on Jupiter's moons¹⁴.

Constraints on Ice Transparency and the Mean Free Path

The application of bistatic radar geometry in the 2011-2024 campaign yielded one of the study's most crucial constraints. In radar scattering theory, the angular half-width of the CBOE interference peak is physically linked to the transport mean free path of the medium¹⁵. The transport mean free path is defined as the average distance an electromagnetic wave travels through the ice before its trajectory is completely randomized by scattering events³¹.

If the ice is highly transparent with sparse scatterers, the wave travels very deeply before randomization (a long mean free path), which results in an exceedingly narrow backscatter peak¹⁵. Conversely, if the ice is densely packed with internal structures that intensely scatter the wave near the surface (a short mean free path), the interference peak becomes much broader¹⁵.

Because the researchers observed Europa using both the Goldstone and Green Bank telescopes, they were able to test how the coherent backscatter effect shifted as the bistatic angle between the transmitter, the moon, and the receiver varied². The team discovered that Europa's radar brightness remained roughly constant even when the bistatic angle increased².

This finding implies that the bright backscatter peak must be broader than the narrow range of angles they were able to sample². A broad peak demands a relatively short transport mean free path, allowing the team to place a strict limit on the depth to which the 3.5-centimeter radio waves diffused before being either absorbed or scattered out of the ice². This calculation serves as a new, definitive constraint on the absolute transparency of Europa's upper crust. It indicates that the top layers of the ice shell are intensely fractured, highly porous, and immensely complex at centimeter scales, preventing high-frequency microwaves from penetrating deeper than a few meters to tens of meters before severe volume scattering redirects the energy³.

Decadal Stability and Hemispheric Asymmetries

The 13-year observation window also allowed the UCLA team to evaluate the temporal stability of Europa's surface. By comparing their modern dataset to the legacy observations from the late 1980s and early 1990s, the researchers found strong statistical agreement⁵. Europa's disk-integrated radar properties—its extreme reflectivity and highly diffuse scattering—have remained entirely stable over a three-decade baseline⁵. This consistency increases confidence that the physical mechanisms driving the radar anomalies operate at depths or scales that are largely insulated from rapid, short-term surface weathering, providing a unified physical framework for interpreting future measurements⁵.

However, because the campaign monitored the moon across many years and viewing geometries, the team investigated whether Europa's radar brightness fluctuated with its rotation. While the overall disk-integrated properties remained nearly constant, dividing the data into leading and trailing hemispheres revealed a subtle hint of asymmetry. Although not yet statistically conclusive, the data suggests that the trailing hemisphere could be slightly brighter in one polarization state⁵.

The Role of Jupiter's Magnetosphere

This potential radar asymmetry aligns seamlessly with the profound optical and chemical dichotomy observed between Europa's hemispheres. Europa is tidally locked in a synchronous rotation, maintaining a constant leading hemisphere pointing in the direction of its orbit, and a trailing hemisphere facing backward⁷.

Jupiter boasts a massive, rapidly rotating magnetosphere that completes a revolution approximately every 10 hours⁷. Because Europa's orbital period is much slower (85.2 hours), the Jovian magnetic field lines continually overtake the moon from behind⁷. The magnetic field traps a dense plasma of energetic electrons, protons, and heavy sulfur and oxygen ions (the latter largely originating from the volcanic moon Io)³⁶. These charged particles relentlessly bombard Europa's trailing hemisphere⁶.

This high-energy radiation environment induces severe radiolytic processing. The energetic particles break the molecular bonds of the water ice, combining with the implanted sulfur to create hydrated sulfate salts, sulfuric acid, and other non-ice radiolytic products⁶. Consequently, the trailing hemisphere exhibits a distinct visually darker, "redder" spectral slope in optical and near-infrared wavelengths compared to the pristine, icy leading hemisphere⁶.

If the subtle radar asymmetry detected by Goldstone and the Green Bank Telescope is confirmed by future observations, it implies that this intense radiation weathering modifies not only the chemical composition of the outermost surface but also alters the physical macro-structure or dielectric properties of the ice at centimeter depths³⁴. The continuous bombardment of charged particles may modify the ice lattice, generate small-scale structural voids, or alter the distribution of the subsurface scatterers responsible for the coherent backscatter effect, subtly enhancing the volume scattering of radio waves on the trailing side³⁴.

Synergy with Orbital Sounding Radars: Europa Clipper and JUICE

The exhaustive Earth-based characterization of Europa's upper ice shell provides an indispensable foundation for the interpretation of data from upcoming orbital missions. Currently en route to the Jovian system are two ambitious robotic explorers: NASA's Europa Clipper and ESA's Jupiter Icy Moons Explorer (JUICE)¹. Both spacecraft are equipped with sophisticated ice-penetrating radar instruments designed to map the global structure of the icy shells and search for the elusive ice-ocean interface³⁷.

Instrument Architectures: REASON and RIME

NASA's Europa Clipper carries the Radar for Europa Assessment and Sounding: Ocean to Near-surface (REASON) instrument³⁹. REASON is a dual-frequency radar system operating at High Frequency (HF) 9 megahertz and Very High Frequency (VHF) 60 megahertz³⁹. The instrument utilizes a 16-meter dipole antenna for the HF band and four smaller antennas for the VHF band, which are mounted on the spacecraft's solar arrays⁴⁰. REASON's objectives include altimetry, deep sounding, and characterizing the distribution of putative non-ice materials (like brines) within the subsurface³⁸.

Concurrently, ESA's JUICE mission features the Radar for Icy Moon Exploration (RIME) instrument²⁶. RIME is optimized for the penetration of Ganymede, Europa, and Callisto up to depths of 9 kilometers²⁶. Like the HF channel on REASON, RIME operates at a central frequency of 9 megahertz utilizing a 16-meter dipole antenna²⁶.

Mission	Spacecraft	Radar Instrument	Operating Frequencies	Bandwidth	Primary Antenna
NASA	Europa Clipper	REASON	9 MHz (HF) & 60 MHz (VHF)	1 MHz / 3 MHz (HF)	16-meter dipole (HF)
ESA	JUICE	RIME	9 MHz (HF)	1 MHz to 3 MHz	16-meter dipole

Table 3: Comparison of the orbital sounding radar instruments en route to the Jovian system. Both prioritize a 9 MHz frequency to bypass the high-frequency surface scattering identified by Earth-based radar²⁶.

Bypassing Surface Clutter for Deep Sounding

The specific frequency selection for these orbital instruments is directly informed by the physical scattering constraints quantified by Earth-based radar studies. The 8.56-gigahertz (3.5-centimeter) X-band waves transmitted by Goldstone undergo extreme multiple scattering in Europa's upper crust, creating the brilliant coherent backscatter peak². For an orbiting radar attempting to look deep inside the moon, this highly active upper scattering layer represents "clutter"—a barrage of unwanted, early-arriving backscatter that can easily disguise the faint, deeper echoes returning from the ice-ocean interface¹³.

To bypass this clutter, REASON and RIME operate at 9 megahertz, which corresponds to a much longer wavelength of approximately 33 meters⁴³. These long radio waves are physically larger than the centimeter-scale fractures, voids, and impurities that cause the CBOE⁴³. Consequently, the 9-megahertz waves are relatively insensitive to surface roughness and buried small-scale scatterers, allowing the signal to penetrate cleanly through the highly porous upper crust and travel kilometers deep into the bulk ice shell⁴². The dual-frequency capability of REASON further mitigates risk; while the 9-megahertz signal probes the deep interior, the 60-megahertz signal offers higher vertical resolution for shallow subsurface features, such as perched meltwater pockets or tectonic fault lines⁴⁰.

The Earth-based constraint on Europa's transport mean free path and ice transparency directly feeds into the geophysical models utilized by the REASON and RIME science teams². By mathematically understanding exactly how much energy is scattered or absorbed in the top layers, mission engineers can better calibrate the orbital instruments, calculate the attenuation rate of the bulk ice, and optimize signal processing algorithms to filter out surface noise². Furthermore, the potential hemispheric variations in radar brightness driven by Jovian radiation will force orbital teams to adjust their dielectric models geographically, as changes in ice purity across the leading and trailing hemispheres will alter the wave's propagation speed and the perceived depth of the subsurface ocean⁶.

Conclusion

The 2011-2024 bistatic radar campaign observing Europa via the Goldstone Solar System Radar and the Green Bank Telescope stands as a triumph of planetary remote sensing. By leveraging immense transmission power and extraordinary receiver sensitivity to measure Europa's radar albedo and circular polarization ratio across varying bistatic angles, researchers have unequivocally demonstrated that the moon's anomalous radar brightness is driven by the coherent backscatter opposition effect².

The data confirms that Europa's outermost ice shell is incredibly pure yet highly structurally complex, riddled with wavelength-scale voids and fractures that trigger intense multiple volume scattering². The campaign's ability to map the angular width of the backscatter peak has provided a definitive, empirical constraint on the transport mean free path of the radio waves, establishing a hard limit on the transparency of the upper crust².

The unwavering stability of these scattering properties over a thirty-year baseline reassures scientists of the physical permanence of these subsurface structures, while tantalizing hints of hemispheric asymmetry highlight the dramatic, continuous weathering imposed by Jupiter's harsh radiation belts⁵. As the planetary science community prepares for the arrival of the Europa Clipper and JUICE spacecraft, these rigorous Earth-based constraints will be indispensable. By fully characterizing the dense, scattering clutter of Europa's frozen exterior, we clear the theoretical path for orbital instruments to sound the depths, bringing humanity one step closer to characterizing the vast, hidden ocean that lies beneath.

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