Case Study: Microtremor H/V Ratios and the 1985 Mexico City Earthquake Response

The 1985 Michoacán earthquake, a magnitude 8.0 event occurring on September 19, resulted in catastrophic structural failure within Mexico City, despite the epicenter being located approximately 350 kilometers away in the Pacific Ocean. The disproportionate level of damage observed in the capital highlighted the critical role of site-specific geological conditions in modulating seismic energy. Specifically, the soft, water-saturated lacustrine clay deposits of the former Lake Texcoco acted as a natural resonator, significantly amplifying seismic waves within a narrow frequency band.

Subsequent empirical studies utilized microtremor measurements—ambient seismic noise generated by human activity and atmospheric conditions—to analyze the dynamic response of these soil layers. By applying the Horizontal-to-Vertical (H/V) Spectral Ratio technique, researchers confirmed that the resonance frequencies of the subsurface stratigraphy directly corresponded to the spatial distribution of building collapses. This case study serves as a foundational example of how passive seismic data can be used to predict ground motion characteristics and inform seismic hazard assessments in complex urban environments.

By the numbers

• 8.0:The moment magnitude (Mw) of the primary earthquake event on September 19, 1985.
• 350 km:The approximate distance between the Michoacán subduction zone epicenter and Mexico City.
• 2 to 5 seconds:The dominant period range of ground motion resonance observed in the Lake Zone of the Valley of Mexico.
• 10 to 50 times:The factor by which seismic wave amplitudes were increased relative to firm ground sites.
• 6 to 20 stories:The height range of buildings that suffered the most extensive damage due to resonance matching.
• 100 meters:The approximate maximum depth of the highly compressible lacustrine clay deposits in the urban center.

Background

The Valley of Mexico is an endorheic basin situated in the Trans-Mexican Volcanic Belt. Historically, the basin was dominated by a system of lakes, the largest being Lake Texcoco. Over centuries, these lakes were drained to help urban expansion, leaving behind thick layers of highly porous, water-saturated volcanic silts and clays. These deposits possess unique geotechnical properties, including extremely low shear wave velocities (often below 100 m/s) and high plasticity. From a geophysics perspective, these layers represent a high-impedance contrast relative to the underlying consolidated sediments and volcanic bedrock.

When seismic waves enter the Valley of Mexico, they transition from the dense, high-velocity rock of the surrounding mountains into the soft, low-velocity sediments of the basin. This transition causes a significant decrease in wave speed, which, by the principle of conservation of energy, results in a massive increase in amplitude. Furthermore, the basin's geometry and the stratigraphy of the clay layers trap seismic energy, leading to the generation and persistence of surface waves. The 1985 earthquake demonstrated that the duration of shaking in the Lake Zone was significantly longer than in the surrounding Hilly Zone, often exceeding several minutes of perceptible motion.

The Mechanics of Site Amplification

Site amplification occurs when the natural frequency of a soil deposit matches the frequency content of incoming seismic waves. In the case of Mexico City, the clay layers acted as a filter, attenuating high-frequency signals while reinforcing low-frequency oscillations. This phenomenon is termed "constructive interference." Because the lacustrine deposits have a very high water content—sometimes exceeding 400% by weight—they behave more like a viscous fluid than a solid under certain loading conditions. The low damping ratio of these clays further allows for sustained resonance, which is particularly destructive to man-made structures.

Microtremor H/V Spectral Ratios (HVSR)

The analysis of site response traditionally required the recording of strong-motion data from actual earthquakes. However, the development of the microtremor H/V Spectral Ratio (HVSR) method, often attributed to the work of Yutaka Nakamura in the late 1980s, provided a passive alternative. This technique involves recording three-component ambient noise (two horizontal and one vertical) at a single station. The ratio between the horizontal and vertical Fourier spectra is calculated to identify the fundamental resonance frequency ($f_0$) of the site.

Empirical evidence from the Valley of Mexico suggests that the H/V ratio provides a reliable estimate of the site’s natural period. The peaks in the H/V curve correspond to the frequency at which the soil layer undergoes maximum displacement. In the context of the 1985 response, HVSR surveys conducted across the city revealed a direct correlation between the thickness of the clay deposits and the peak resonance periods recorded. Areas with 30 meters of clay typically showed periods around 2 seconds, while deeper deposits near the center of the lake bed reached periods of up to 5 seconds.

Spatial Distribution of Damage and Resonance

The damage pattern in 1985 was remarkably selective. While the outskirts of the city built on volcanic rock (the Hilly Zone) suffered minimal impact, the Lake Zone experienced total collapse of reinforced concrete structures. Intermediate zones, known as Transition Zones, showed varying degrees of damage. Research into microtremor resonance peaks has shown that the damage was most severe where the natural period of the buildings matched the resonance period of the ground.

Buildings of 6 to 20 stories generally possess natural periods ranging from 0.6 to 2.0 seconds. In the Lake Zone, the ground motion was dominated by energy in this exact range. Consequently, these structures entered a state of resonance with the soil, leading to excessive lateral displacements, P-delta effects, and ultimately, structural failure. Lower-rise buildings and very tall skyscrapers often survived more effectively because their natural frequencies were "out of sync" with the ground’s dominant vibration period.

Comparative Analysis: Ambient Noise vs. Strong-Motion Data

The validity of using microtremors to characterize seismic response was solidified through comparisons with data from the Mexican Strong Motion Network (Red Acelerográfica de México). Following the 1985 disaster, the network was expanded to include a high density of sensors across different geological units. Researchers compared the transfer functions derived from strong-motion recordings of aftershocks and subsequent earthquakes with H/V ratios obtained from ambient noise at the same locations.

The agreement between the fundamental frequency identified via microtremors and that identified during actual seismic events was remarkably high, particularly in the Lake Zone. While microtremors do not always accurately predict the absolute amplification magnitude during non-linear soil behavior, they provide an exceptionally precise map of the resonant frequency across the basin.

This comparison confirmed that passive seismic monitoring is a viable tool for microzonation. By mapping the fundamental period of the ground across an entire city, engineers can create "vulnerability maps" that dictate where specific building heights or construction types should be restricted or reinforced. The Mexican Strong Motion Network data corroborated that the soft clay deposits in Mexico City behave linearly for a wider range of strain than many other soil types, which is why the low-intensity ambient noise remains a faithful proxy for high-intensity earthquake response in this specific environment.

Implications for Inversion and Subsurface Imaging

Beyond identifying resonance, the H/V ratios from the Valley of Mexico have been used in inversion algorithms to determine the thickness and elastic moduli of the subsurface layers. By treating the microtremors as a combination of Rayleigh and Love waves, geophysicists can invert the dispersion curves to estimate the shear wave velocity ($V_s$) profile. This is essential for non-destructive testing and site characterization where invasive drilling is prohibited by cost or urban density.

Inversion of H/V data in the Lake Zone has allowed for the creation of 3D models of the basin's basement. These models show that the depth to the hard formation is not uniform, explaining the local variations in damage. Furthermore, the detection of microtremor anomalies has assisted in identifying buried utilities and localized