Characterizing the seismic response and basin structure of Cusco (Peru). Implications for the seismic hazard assessment of a World Heritage Site

doi:10.21203/rs.3.rs-3859742/v1

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Characterizing the seismic response and basin structure of Cusco (Peru). Implications for the seismic hazard assessment of a World Heritage Site

https://doi.org/10.21203/rs.3.rs-3859742/v1

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published 06 Sep, 2024

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Known worldwide for its rich and well-preserved pre-Columbian and Spanish architecture, the city of Cusco (Peru) is listed as a World Heritage Site since 1983. However, less well known is the seismic hazard, which represents a major threat to the 400,000 Cusco’s inhabitants and city’s cultural outreach. Despite the moderate magnitudes recorded in the area, macroseismic data inferred from historical earthquakes (1650, 1950) argue for strong amplification effects of the unconsolidated sediments of the Cusco Basin during ground motion. In order to address this aggravating factor for the first time, we conducted a large-scale passive geophysical survey in the historic city center of Cusco combining Microtremor Horizontal-to-Vertical Spectral Ratio (MHVSR) measurements and Microtremor Array Measurements (MAM). A subsurface wave velocity model and an evaluation of the depth of the engineering bedrock are proposed through joint data inversion. In addition to the characterization the soft sediment thickness, the site response analysis suggests the existence of a strong geological discontinuity beneath the city center of Cusco, consistent with the trace of the Cusco fault. Moreover, the results highlight the complexity of the earthquake site amplification assessment in dense urban areas. Our work paves the way for a comprehensive seismic microzonation of the entire Cusco Basin and opens up new perspectives on the potential of the MHVSR method for blind fault detection.

site effects

sedimentary basin

HVSR

blind fault

heritage preservation

Cusco

Major earthquake disasters such as Mexico City (1985), Kobe (1995) and more recently Turkey-Syria (2023) have demonstrated the increase in hazard caused by the amplification of seismic waves in soft soils (e.g., Kramer, 1996). However, this topic remains in its infancy in the Andes, limited almost exclusively to the capital cities (Santiago: Pilz et al., 2009; Lima: Calderon et al., 2014; Quito: Pacheco et al., 2022). As a fast-growing touristic town with uncontrolled planning, the city of Cusco turns out to be a crucial case study. The city, located at an altitude of 3,400 meters on the boundary between the Eastern Cordillera and the Altiplano, is settled in a Quaternary sedimentary basin bordered to the north and south by numerous active faults belonging to the Cusco-Vilcanota fault system (Cabrera et al., 1991). Although the seismic hazard in the region is considered moderate – compared with Peru's Pacific margin – the city of Cusco has suffered greatly from the regional seismic activity before the instrumental-digital era. The 1650 (Mw > 6; Combey et al., 2022; Silgado Ferro, 1978) and 1950 (5.6 < Mw < 5.9; Combey et al., 2022; Ericksen et al., 1954) earthquakes devastated Cusco, causing extensive damage to many historical buildings. Apart from these disasters, other violent tremors have punctuated the city's history, notably in 1744 (Seiner Lizárraga, 2016), 1941 (Silgado et al., 1952), 1986 (Cabrera and Sébrier, 1998) and 2018 (https://cnnespanol.cnn.com/2018/11/11/sismo-peru-cusco-pisac-magnitud-temblor/ Accessed: 10/01/24).

Although data on Cusco’s historical seismicity remain scanty and incomplete (Combey et al., 2022), macroseismic data inferred from the 1650 and 1950 earthquakes advocate for a significant role of local site conditions and site effects in the distribution and extent of damage. Unfortunately, we have little information on the characteristics of the Cusco subsurface geology. No boreholes have ever been drilled in the basin, and the use of this method now seems hampered by the dense urbanization of the entire valley. While the city still only occupied the north-western edge of the basin at the beginning of the 20th century, it has undergone rapid and uncontrolled demographic expansion since the 1950s (Fig. 1). The population living in the Cusco Basin has more than tripled since 1972, and now accounts for more than 400,000 inhabitants (Census INEI 2017: https://censos2017.inei.gob.pe/redatam/ Accessed: 10/01/24). Hence, there is an urgent need to characterize the mechanical properties and response of Cusco's subsoil in order to better assess the hazard and risk in the event of strong ground shaking. Non-invasive passive geophysical methods such as Microtremor Array Measurements (MAM) and single-station Microtremor Horizontal-to-Vertical Spectral Ratio (MHVSR) are particularly suitable for urban environments because they are quick and easy to deploy. Particularly effective in estimating subsoil S-wave velocity structure and mapping soil/rock interface, those methods constitute thus the first step towards a comprehensive seismic microzonation and the identification of potential soil-structure interactions. Listed as a World Heritage site by UNESCO since 1983 for the integrity and authenticity of its architectural heritage, the historic City Center of Cusco (CCC) has a rich Inca and colonial built heritage whose exposure to earthquakes needs to be urgently assessed (Brando et al., 2019).

That is why we carried out a large-scale passive seismic survey in the old city center, combining multichannel and single-station measurements. Through the joint inversion of both ambient vibration signals, this work aimed to characterize the response of the sediments beneath the city and their thickness. To that end, we first outline the geological setting of the Cusco Basin. We then present the different geophysical methods used as part of this seismic survey. Next, we describe the main results of the microtremor analysis and inversion for estimating bedrock depth. In the Discussion section, we first address the spatial heterogeneity of the subsurface response at Cusco and its potential relationship with the presence of a fault within the basin. Secondly, we will focus on the influence of the urban environment on measurements and its implications for the assessment of local seismic response. Finally, we conclude with the perspectives opened up by this case study for reevaluating the seismic hazard of World Heritage sites in developing countries.

In the southern High Andes, most of the current deformation is accommodated at the interface between two lithospheric blocks (Carlier et al., 2005; Ma and Clayton, 2014). These blocks are separated by a significant pre-existing structure, known as the Cusco Vilcanota Fault System (CVFS). Within the Cusco region, this system delineates the Eastern Cordillera from the Altiplano (Carlier et al., 2005) and manifests as a complex network of faults trending in a NW-SE direction (Fig. 2). Originally categorized as thrust faults, these structures have exhibited a transition to normal faulting since the Pliocene, approximately 5 Ma ago (Cabrera, 1988; Mercier et al., 1992; Suárez et al., 1983). Abundant evidence now supports the Holocene activity of these faults, providing substantial insights into quantifying the present-day extensional regime.

Besides the existence of fresh scarps and offset moraines that constitute good geomorphological markers (Benavente Escobar et al., 2013; Cabrera et al., 1991; Rosell et al., 2023) and allow us to estimate a current rate of deformation of the order of 1 to 4 mm/year (Wimpenny et al., 2020), palaeoseismic trenches revealed events of moment magnitude (Mw) greater than 6 over the last 10,000 years (Cabrera and Sébrier, 1998; Palomino Tacuri et al., 2021; Rosell et al., 2023). Finally, the installation of a temporary seismological network to the north of Cusco recorded localized seismicity along the Qoricocha and Tambomachay fault planes (Fig. 2; Guardia and Tavera, 2015).

These tectonic structures and the current extensional phase led to the formation of intra-cordilleran basins. These semi-graben structures include the Cusco Valley, which was occupied by the vast Lake Morkill in the Pleistocene (Gregory, 1916). The basin is now filled by a large quantity of fluvio-lacustrine and alluvial sediments that compose the San Sebastian formation (SBF). The Cusco City Centre (CCC) is located at the north-western end of the sedimentary basin. It is located at the confluence of three seasonal rivers (Chunchullmayo, Huatanay-Saphy and Tullumayo; Fig. 3), now channeled, which are responsible for a significant sediment input during the rainy season (Nuñez Peredo, 2021) and a shallow piezometric level (INDECI-PNUD, 2003). Unfortunately, very little information is available on the exact nature, distribution, thickness and water saturation of the sediments of the SBF since no borehole has ever been drilled and, to our knowledge, only few geotechnical studies has been undertaken. It includes a characterization of the soil types at the surface (Benavente Velásquez et al., 2004; Candia-Gallegos et al., 1993) and non-invasive geophysical surveys (Barrientos Guzmán, 2021; CISMID and UNI, 2013; INDECI-PNUD, 2003) imaging the Cusco Basin down to depths of ~ 150m. For all these studies, only part of the data seems to have been published, making them difficult to review. As it stands, the heterogeneous San Sebastian formation, composed of a succession of clay, gravel and unconsolidated sand horizons, is considered to be underlain by sandstones and conglomerates from the Paleocene (San Jerónimo group) as well as gypsum, limestone and shale formations from the Late Cretaceous (Yuncaypata group) outcropping to the north of the basin and dipping towards the southeast (Carlotto et al., 2011). The thickness of the Quaternary formation is thus probably gradually increasing to the south-east, in the downstream direction.

This lack of information is a major shortcoming regarding the characterization of the soil dynamic response and the subsequent seismic microzonation of the site. The active faults that run through the region represent a significant hazard, and the potential amplification phenomena within the basin have never been addressed. However, the most violent historical earthquakes (1650: Mw > 6; 1950: Mw ~ 5.7) point to the existence of violent site effects. Among the many Earthquake Environmental Effects (EEE; Michetti et al., 2007) reported in 1650 and 1950 (Fig. 2), many appear to be directly linked to the unconsolidated nature of the basin infill. These include liquefaction phenomena in the form of mud volcanoes (Silgado et al., 1952; Villanueva Urteaga, 1970) and a significant rise in the water table (Ericksen et al., 1954; Ladrón de Guevara, 1967). Interestingly, the highest seismic intensities in 1950 were mapped in the western part of the basin (Fig. 2).

In this tectonic-driven basin, the sedimentary infill also appears to cover unmapped fault segments, which would represent an additional risk for the population. A blind fault, known as the Cusco fault (Fig. 2), was suspected for the first time by Carlotto et al. (2011). Since then, electrical tomography (Benavente Escobar et al., 2013) and magnetotelluric studies (Antayhua et al., 2021) have demonstrated its existence and its highly branched nature. Nevertheless, the Holocene activity of this fault is not established and its exact trace remains to be defined.

In light of these concerns, two geophysical campaigns were carried out in April and July 2023 as the joint initiative of French public research institutions (IRD, CEREMA) and the Peruvian Institute of Geology (INGEMMET). The aim was to achieve complete coverage of the CCC using two distinct ambient vibrations-based methods: single-station recordings using a short-band velocimeter to compute Microtremor Horizontal-to-Vertical Spectral Ratio (MHVSR), and a multichannel seismic survey to analyze the propagation of surface waves (Rayleigh) using the Microtremor Array Measurement (MAM) technique. As the soil response depends mainly on the thickness of the layers, their geometry and their mechanical properties, it is directly linked to the propagation speed of shear waves (Vs). Cost-effective, non-invasive and non-destructive, these passive seismic methods are particularly well suited to the challenging urban context of Cusco (narrow streets, steep slopes, listed city). We first present the methodology of the single-station MHVSR survey, followed by a description of the multichannel array. Finally, we explain the joint inversion procedure for the results of the two previous methods.

3.1. MHVSR survey

Ambient vibration (or microtremor) based methods consist of recording background seismic noise (natural and anthropic) in order to assess the mechanical properties and nature of the ground subsurface. Among these, the Microtremor Horizontal-to-Vertical Spectral Ratio (MHVSR) computes the ratio between the quadratic average of the horizontal and vertical Fourier spectrum. This technique, popularized by Nakamura (1989), postulates that the frequency peak of the MHVSR correspond to the fundamental frequency and the amplitude could serve as a “proxy” for the amplification factor of the site.

It is considered a simple and effective technique to characterize subsurface features. However, this method remains the subject of intense debate due to 1) its relevance in a perfectly horizontally stratified media (1D; Mucciarelli and Gallipoli, 2001) and 2) the insufficient knowledge regarding the exact contribution of the different types of waves in the generation of the H/V peak (Lunedei and Malischewsky, 2015; Molnar et al., 2018). However, whether the peak is explained by the S-wave resonance frequency (e.g., Nakamura, 1989), Rayleigh wave ellipticity (e.g., Lachet and Bard, 1994), the Airy phase of Love waves (e.g., Konno and Ohmachi, 1998) or a mix of all three (Bonnefoy-Claudet et al., 2008), the method has demonstrated its usefulness and accuracy in investigating sedimentary basins and assessing the seismic site response, particularly in urban environments (Bonnefoy-Claudet et al., 2008; Lebrun et al., 2001; Pacheco et al., 2022; Pilz et al., 2009; SESAME, 2004). In practice, the MHVSR method is based on the assumption that there is a clear contrast of seismic impedance in the subsurface, unlike in the bedrock. The difference in amplitude between the horizontal and vertical signals in the upper layer is therefore expressed by a peak at the soil fundamental frequency (f₀). The amplitude of the peak (A₀) depends on the impedance contrast between the underlying layer and the layer of interest. Besides the effect of the velocity/density contrast in depth, the MHVSR may also be affected by Poisson ratio of superficial layers, the contact geometry and damping in the sediments (Lachet and Bard, 1994; Lunedei and Malischewsky, 2015).

We carried out 149 measurements throughout the CCC (Fig. 3; Table S1) using portable three-component velocimeters Lennartz 3Dlite MkIII (short-band) and Guralp CMG40T (medium-band). These seismometers with resonance frequencies close to 1Hz have proved to be suitable for retrieving MHVSR peaks down to 0.2Hz (Strollo et al., 2008). All acquisitions were carried out using a MiniShark datalogger (Keas), configured with a sampling rate of 200 Hz and a minimum recording length of 20 min. The sensors were oriented to the magnetic north and installed directly on the pavement (concrete or asphalt). The signals were then processed with the Geopsy software (Wathelet et al., 2020). To generate the MHVSR curves, windows of 40 seconds were used without overlap, tapered with a Tukey window. The spectral amplitudes were smoothed using the Konno and Ohmachi recording window with a relative width of 20% (b = 40). According to Picozzi et al. (2005), this data processing on recordings of at least 20 minutes guarantees stable and representative results. Regarding the sensor installation and signal analysis, we followed, as far as possible, the procedures and guidelines established by SESAME (2004) despite the inherent constraints of the urban context (i.e., inability to bury the sensor, proximity to buildings, vehicular traffic, etc.). In different parts of the city, we made sure to acquire data at different times of the day (4 am to 11 pm) and on different days in order to corroborate the stability of the results. No measurements were taken in strong winds. The occurrence of spurious peaks (coupling issues, anthropic sustained noise) was checked thanks to the analysis of the Fourier spectra before calculation of the MHVSR curves.

3.2. Multichannel seismic recordings

Besides single-point recordings, we also carried out multichannel acquisitions to estimate the propagation velocity of surface waves, and in particular to determine the shear wave velocity in the first 30 meters (Vs30). The propagation velocity characteristics of surface waves provides important information on the mechanical and elastic properties of the subsurface (Anderson et al., 1996). We designed linear arrays using a Geode (Geometrics) 24-channel seismograph and 24 Phasi 4.5 Hz geophones. The spacing between each geophone was 5 meters (total length of the line: 115 meters) but was reduced up to 3 meters (69-metres line) for the needs of some acquisitions. We used the equipment following the Microtremor Array Measurement (MAM) technique based on the SPAC method. The minimum recording time was 20 minutes and the sampling frequency of the geophones was set at 50 Hz. In order to avoid heavy vehicular traffic (particularly buses), measurements were preferably conducted during the quietest hours, at sunrise and late in the evening. In total, 50 seismic lines were recorded (Fig. 3; Table S2). The S-wave dispersion curves of the fundamental mode (Rayleigh wave phase velocity) derived from the recordings were plotted using the proprietary software SeisImager (Geometrics). Vs30 values for each linear array were then computed from the software Geopsy. In addition to the linear arrays, we designed a 100-m diameter circular array in the main square of Cusco (Plaza de Armas) using 6 Lennartz 3Dlite MkIII velocimeters and a Cityshark datalogger (Fig. 4a-b). Two 40-minutes recordings were made at a sampling frequency of 200 Hz. The dispersion curve was extracted using the F-K tool in Geopsy.

3.3. Calibrated joint inversions

Once the MHVSR and Rayleigh waves dispersion curves had been computed, the aim was to estimate the subsurface S-wave velocity structures and the sediment thickness beneath the CCC. To do so, we carried out joint inversions of the two datasets using the freely available software HV-inv (García-Jerez et al., 2016). By reducing the model search space, joint inversions allows for better fitting the observed data and for retrieving a more reliable model of the local velocity structure (e.g., Parolai et al., 2005; Picozzi et al., 2005b). We estimated the best-fitting model following 3,000 iterations and we allowed the model parameters to vary within ± 5% search space of the initial model (guided Monte Carlo method). Based on the geological data available (Carlotto et al., 2011; INDECI-PNUD, 2003), we considered 4-layers models with the following parameters:

1st layer: upper part of the soft Quaternary sediments from the SBF. Vs between 150 and 500 m/s, depth constrained to 100m and density between 1500 and 2000 kg/m3;
2nd layer: lower part of the soft Quaternary sediments from the SBF. Vs between 200 and 600 m/s, depth constrained to 100m and density between 1500 and 2000 kg/m3;
3rd layer: considered as a theoretical "engineering bedrock" with a Vs of 700 to 1200 m/s (Gupta et al., 2021), a maximum depth of 300m and a density of 2000 to 2500 kg/m3;
4th layer: Vs greater than 1000 m/s, infinite depth and a density of between 2200 and 2500 kg/m3.

We first inverted the passive seismic data recorded on the Plaza de Armas using two independent measurement techniques (different times and days). On one hand, we used the dispersion curve computed from the circular array and the MHVSR curve obtained from the station at the center (R1). On the other hand, we considered the data from a linear array cutting across the main square (L54) and the MHVSR point P36 (Fig. 4b). Given the stability and consistency of the results (Fig. 4c-d), we inverted the subsurface velocity model for 22 separate measurement points in the northern part of the CCC (Fig. 3, Table S3), where we were able to identify a strong MHVSR peak. For 17 of these, we performed the joint inversion of MHVSR and MAM data recorded at the same location, and for 5 others where no multichannel measurements were available, we used only the MHVSR curve.

4.1. Experimental data

For single-point measurements, we picked the frequency (f₀) and amplitude (A₀) of the MHVSR peak. In 119 out of 149 cases, we were able to identify a peak (Table S1), while in 7 cases, the MHVSR curve showed a ratio close to 1 over the frequency range 0.4–10 Hz. These points were interpreted as outcropping bedrock. Finally, for 22 measurement points, not randomly distributed, it was not possible to pick out a precise peak because of 1) a sharp increase in the MHVSR in the low frequencies (< 1 Hz) and/or 2) a "plateau" in the low frequencies ending more or less abruptly around 1 Hz (Fig. 5a-b). The curves of these points differ markedly from the 7 recordings interpreted as outcropping bedrock in their low-frequency content and are generally located in the middle of the Cusco Basin, making the hypothesis of an outcrop very unlikely.

Figure 6 shows the distribution of the fundamental frequency (f₀) using the Triangular Irregular Network (TIN) interpolation method from a QGIS algorithm. Despite the usually large standard deviation of MHVSR ratio for frequencies below 1Hz – probably related to the challenging context of the urban environment (ground coupling, diversity of noise sources) and the fact that short/medium-period sensors (1s) were used – the results of the f₀ picking show a very good spatial coherency. The f₀ value is generally associated with the depth at which strong impedance contrast exists (Molnar et al., 2018), such as the interface between unconsolidated Quaternary sediments and a more competent basement. In the case of the CCC, the results of the MHVSR survey are consistent with this hypothesis. The rapid decrease of the f₀ value (from 4 Hz to 0.6 Hz) from the edge of the basin in the north towards the middle of the valley in the south corresponds most probably to a deepening of this interface under the soft Quaternary sediment cover. Likewise, the outcropping bedrock is identified to the north-east of the CCC at the top of the steepest part of the study area, near the limit of the San Sebastian formation displayed by the geological map (Fig. 3; Carlotto et al., 2011). In the Santo Domingo sector, however, f₀ values appear to decrease more rapidly (Fig. 6), in accordance with a sudden deepening of the interface. In this respect, the 22 MHVSR measurements showing no peaks (red crosses in Fig. 6) and distributed along a line oriented more or less NW-SE, seem to delimit this area to the north. At first sight, these measurements suggest the disappearance of the impedance contrast at depth.

While f₀ is mainly related to the depth of the impedance contrast, the amplitude A₀ of the peak depends on the impedance contrast between the upper and underlying layers (Albarello and Lunedei, 2011). The higher the amplitude, the greater the impedance contrast. Unlike f₀, A₀ appears to have a much more heterogeneous and complex distribution (Fig. 7). The north-western part of the CCC has low amplitudes (A₀ ≤ 3), while sectors of the Plaza de Armas and Santo Domingo have higher amplitudes (A₀ > 5).

Finally, it should be noted that for 54 measurements, it was possible to identify a clear secondary peak (f1) corresponding to a harmonic of the natural frequency of the site or a shallower impedance contrast (Fig. 5c-d). The frequency exhibits very high variability, ranging from 1.5 to 19 Hz (Table S1). The amplitude of this second peak (A₁) remains low, usually less than 3.

Meanwhile, the Vs30 calculated from the 50 linear arrays range from 250 to 480 m/s (Table S2) suggesting the presence at the subsurface of significant "deposits of dense of medium dense sand, gravel, or stiff clay" (soil type C, Eurocode 8, 2005), consistent with the geological description of the SBF. Once again, there is a north-south trend, with a significant drop in velocity between the Plaza de Armas and the Santo Domingo sector (Fig. 6-inset).

4.2. Subsurface velocity model

Could the site response provide information about the structure and mechanical properties of the subsurface? We combined the results of the multichannel recordings with those of the MHVSR points to derive velocity models at several locations in the CCC. Firstly, we wanted to assess the consistency of the results by comparing the velocity models of the main square of Cusco using two different techniques. A first velocity model was obtained by the joint inversion of the S-wave dispersion curve resulting from the circular array and the MHVSR curve coming from the station at the center of this network (R1). A second model was based on the inversion of the dispersion curve of a linear array crossing the square (L54) from west to east and a nearby MHVSR point (P36). It must be noted that both data acquisitions were not done simultaneously. Figure 4 shows the design of the different geophysical surveys (b) as well as the outputs of the two inversions (c and d). Presenting both low and similar misfit values, the two inversions point to the same structure of the subsurface: two first layers with low Vs (< 500 m/s) followed by a more competent layer (Vs > 700 m/s) at a depth of around 70 m and with a significant thickness of 100 to 150 m (Fig. 4c-d). We then observe another significant velocity rise (Vs > 1500 m/s) at greater depths (> 150 m). With Vs greater than 700 m/s, the third layer will hereafter be referred to as the 'engineering bedrock' (EB; Gupta et al., 2021).

Given the consistency of the results at the Plaza de Armas, the same procedure was applied to 21 other points in the CCC, including 17 where both an MHVSR curve and a dispersion curve derived from a linear array were available. All the points were selected in the northern part of the city (Fig. 3). As the frequency of the MHVSR peak is higher there, the dispersion curves derived from the MAM were all the more relevant for constraining the inversion down to the first impedance contrast. By averaging the shear wave velocities and depths of each of the four layers from the best-fitting models, it is possible to generate a unidimensional CCC velocity model (Fig. 8a). The model thus obtained supports the existence of the first two layers with similar thicknesses (~ 30m) and relatively low shear wave velocities (Vs ~ 300 and 500 m/s respectively). Underneath, there is an initial rise in Vs corresponding to the EB (~ 800 m/s). This third layer, approximately 150 m thick, overlays a much more competent fourth layer, highlighted by a new rise in shear velocity (Vs > 1400 m/s). The results of the 22 inversions are therefore entirely consistent with the two models obtained at the Main square. Note the limited dispersion of the velocity values compared with the degree of freedom left to the models (Fig. 8a). As an illustration, the mean and standard deviation of the Vs of the engineering bedrock is 823 ± 94 m/s. Only the parameters of the fourth layer appear to be less well constrained. The explanation lies in the uncertainty and low resolution of the methods used at low frequencies (f ≤ 0.6 Hz). The EB depths obtained from the best-fitting models were then compared with the f₀ of the inverted MHVSR curves (Fig. 8b). The fitting of a power law function gives: Z = 86.34f₀ ^− 0.777 (R²=0.79), where Z refers to the depth of the EB, and f₀ to the fundamental frequency of the site. Although the power law relationship indicates some variability in the mechanical properties of the overlying layers (OL), the relationship proves to be close to the theoretical relationship f₀ = Vs/4H (Nakamura, 2000) or H_OL=(Vs/4)*f₀, where H_OL and Vs correspond to the thickness and S-wave velocity of the overlying layers. This demonstrates that the shape and frequency of the MHVSR peak is mainly driven by the first impedance contrast between the second (Quaternary sediments) and third layers (EB: Late Cretaceous and Paleogene formations). Despite the contrasts in terms of A₀ and Vs30 highlighted between the northern and southern parts of the CCC, we decided to assume a relative geological homogeneity throughout the Cusco city center. As a result, we computed the depth of the EB based on the above power function, wherever a value of f₀ was available. In other words, it enables to assess the variation in thickness of the unconsolidated sediments beneath Cusco. Figure 7 shows the EB isodepth contour lines based on the interpolation of the computed depth values using the Inverse Distance weighting (IDW) method (QGIS algorithm). Mirroring the f₀ distribution, the depth of the engineering bedrock increases towards the south. From 40 meters in the north, the EB is estimated to be more than 120 meters deep in the southern part of the CCC. In the sector of Santo Domingo, the EB seems to sink severely by almost 30 meters in less than 50m of horizontal distance.

5.1. Tracking the Cusco fault below the CCC

The velocity model (Fig. 8a) is in good agreement with the results of the electrical resistivity survey carried out previously in the south of the CCC (INDECI-PNUD, 2003). Their authors estimated the contact between soft sediments and more compact rocks belonging to the San Jeronimo Group (Eocene) at a depth of around 50-60m. Our results for the CCC indicate a similar structure: several horizons of the San Sebastian formation, at least 40m thick and constituting the basin infill, overlie Eocene formations visible to the south of the basin and/or Cretaceous formations outcropping to the north of the basin (Yuncaypata Group; Carlotto et al., 2011). In any case, based on Vs values, the EB would consist of significantly altered sandstone or limestone formations. Aside from this simplified geological model, the data from this geophysical survey highlights some particular features.

As pointed out in the previous section, the variations of natural frequencies seem to be strongly correlated with the geometry and depth of the first impedance contrast (Fig. 8b), referred to as the EB. In other terms, the quick and strong decrease of the f₀ that we observe in the southern part of the CCC suggests a sudden steepening of the EB close to the Santo Domingo sector (Fig. 7). The sudden thickening of the sediment cover in that area is hard to explain without the existence of geological structures or discontinuities. Several studies have provided evidence of the existence of a blind fault, named hereafter the Cusco fault, running parallel to the basin (Benavente Escobar et al., 2013; Carlotto et al., 2011; Wimpenny et al., 2020). While field observations report the presence of deformed Quaternary sediments within the basin (Benavente Escobar et al., 2013), electrical resistivity profiles reveal colluvial wedges (Benavente Escobar et al., 2013). Since then, magnetotelluric profiles carried out by Antayhua et al. (2021) have confirmed the tectonic origin of the Cusco Basin, and then suggest a branched structure with several fault segments connected at depth.

Our findings seem to attest to the presence of at least one fault segment beneath the CCC and thus offer interesting avenues for research into the influence of tectonic structures in modifying the local ambient noise wave-field. We base our analysis on the recent work of Garcia et al (in prep.), who mapped soil gas radon anomalies in the Cusco area and matched them to the active faults in the area. The authors found several well localized anomalies distributed linearly and parallel throughout the Cusco Basin (Garcia et al., pers. comm.). The authors therefore support the existence of several parallel fault segments, oriented NW-SE across the basin. It turns out that among the areas showing anomalous soil gas radon concentrations, several are located in the Santo Domingo sector and at the confluence of the Huatanay and Chunchullmayo rivers (Pumacchupan). The presence of a normal fault in the Santo Domingo sector is perfectly consistent with the results of this work. As shown in Fig. 7, the area of sudden deepening of the EB to the south of Santo Domingo agrees very well with the fault line proposed by Garcia et al (pers.comm.). The map also highlights the strong spatial agreement between the variations in amplitude of the MHVSR peak (A₀) and the breaks in slope of the EB. Given the influence of the impedance contrast’s geometry in the amplitude in the microtremor measurements (reflection, refraction, complex surface wave field; Irikura and Kawanaka, 1980), it is likely that a geological discontinuity, i.e. a fault zone, could affect locally the MHVSR peak (D’Amico et al., 2008; Mucciarelli et al., 1999; Tarabusi and Caputo, 2017). Indeed, it is in this zone of lower amplitude that most of the MHVSR curves for which no f₀ value could be picked are located. Regarding the higher uncertainty of the MHVSR measurements at these points, we should point out that the large standard deviation cannot be solely explained by the relatively short recording period (~ 20 min) and the non-stationary nature of the ambient vibrations. At various measurement points, a longer recording duration (40 min) gave similar results.

Looking at a N-S profile (Figs. 3 and 9), some of the MHVSR curves (2 and 4) show very local shrinkage (reduction of A₀) and/or broadening (plateau) of the peak, which makes more difficult to estimate the f₀. Strikingly, the areas in which these two points are located correspond to the assumed traces of two fault segments based on radon measurements (Figs. 7 and 9). The sectors between points 1 and 3 and between 3 and 5 also show a more or less sudden drop of f₀. The MHVSR method is not meant to identify faults. Although MHVSR surveys have already been used to identify and locate tectonic structures, the discussion was limited to sudden variations in f₀ (D’Amico et al., 2008; Khalili and Mirzakurdeh, 2019; Stanko et al., 2017; Tarabusi and Caputo, 2017) and wave polarization in the horizontal components (Lombardo and Rigano, 2006; Pischiutta et al., 2013). To our knowledge, no work has ever addressed a potential disturbance of the wave field in the vicinity of an active fault that would significantly affect the MHVSR curves, excluding the preliminary observation made by Mucciarelli et al. (1999) in Italy. In short, the microtremor measurements, combined with the inverted velocity model, reveal a geological discontinuity, consistent with the trace of one segment of the Cusco fault. The concordance of areas without a MHVSR peak with the sudden deepening of the bedrock argues for an effect of this structure on the mechanical properties of the sediments in these areas, potentially generating disturbances in the wave field. This fault with a normal component and dipping towards the south would displace the compact Eocene or Cretaceous formations but could also affect the overlying sediments, as evidenced by the disturbances in the MHVSR curves close to the discontinuity (colluvial wedge, fault gouge?).

5.2. Urban environment: a masking effect for soil response evaluation?

Several studies have demonstrated that the MHVSR technique tends to underestimate the amplitude of frequency peaks (Lebrun et al., 2001; Pilz et al., 2009; Rong et al., 2017) and might only be regarded as a lower bond of the actual site amplification (Bard, 1999; Bonnefoy-Claudet et al., 2008, 2006). Furthermore, the challenging nature of ambient vibrations-based surveys in urban environments (Pacheco et al., 2022) and the non-linear response of the ground during strong transient shaking should not be overlooked. Nevertheless, as the frequency of the MHVSR secondary peaks falls within the frequency range of engineering interest (~ 3–10 Hz), it is necessary to examine the distribution and amplitude of these peaks in order to identify potential soil-structure interaction phenomena. Because of the wide variability of the f₁ frequencies identified during the MHVSR survey, it is difficult to establish the origin of these peaks. They might be harmonics of the fundamental frequency f₀ or a shallow seismic interface within the Quaternary sediments of the San Sebastian Formation. Nevertheless, it is worth noting that the results of the joint inversion support the existence of a first (moderate) velocity contrast at a depth of around 30m compatible with the lowest f₁ (~ 5 Hz).

Given the densely urbanized environment in which the MHVSR measurements were carried out and the relatively small number of recordings showing an identifiable second peak (54, i.e., 1/3 of the total; Table S1), we are inclined to consider the role of shallow velocity inversions detailed by Castellaro and Mulargia, (2009). The authors highlight the dramatic effect that very thin and stiff artificial layers (concrete/pavements) can have on the MHVSR curves, lowering the peaks down to relative low frequencies (~ 2Hz). These shallow velocity inversions are frequently accompanied by MHVSR curves with an amplitude below 1 over a wide range of frequencies. We observe this phenomenon on some curves, such as P90 (Fig. 5b) and curve 2 in Fig. 9. However, as the measurements were all carried out on paved areas, we should expect a generalized alteration in the MHVSR curves throughout the entire CCC. Actually, the f₁ distribution does not seem to be random and the amplitudes (A₁) do not seem to be damped out homogeneously. There is a clustering of the lowest values of f₁ (≤ 5 Hz) on the margins of the city center, while most of the frequencies between 5 and 15 Hz are located in the core of the city (between the Tullumayo and Huatanay rivers). It should also be noted that the f₁ > 5 Hz generally has higher amplitudes than the f₁ ≤ 5 Hz, which are characterized by very low amplitudes (< 2). In addition, the highest amplitudes (> 3) are confined to two sectors of the CCC: Plaza de Armas (Fig. 5c-d) and Santo Domingo. These two areas exhibit the two largest open spaces in the CCC. With regard to this singular f₁ distribution, we formulate two hypotheses, not mutually exclusive:

A contribution of the Inca urban pattern in the differential response of the CCC;
A masking effect of the city building network on the local site response.

The CCC is located on the exact place where the capital of the Inca Empire was settled in the 15th and 16th centuries, of which many remains can still be admired. At that time, the city's residential sectors were mainly confined between the Tullumayo and Huatanay rivers (Bauer, 2018; Beltrán-Caballero, 2013; Vranich et al., 2014), while an extensive network of agricultural terraces and canals structured the surrounding area (Fig. 10). The plaza de Armas then represented half of a large open space known as Hawcaypata, while the sector of Santo Domingo consisted of a plaza to the north (Intipampa) and a terraced garden to the west, bordering the Huatanay river. Given the long period of occupation of the city of Cusco (at least since the 11th century; Bauer, 2018) and the great capacity of the Incas to transform their landscape (e.g., Wright, 2006), it seems very likely that the Inca city of Cusco was made up of a large number of man-made earthworks. These embankments and terracing projects, which were potentially more extensive and thicker in the residential area, are also documented by Spanish sources describing the large quantities of sand brought in from other regions of the Empire to prepare the Hawcaypata square (de Ondegardo, 1916). The higher frequencies observed in the city core would therefore indicate the persistence of significant anthropogenic backfills, while on the periphery the absence of such deposits sometimes highlights a deeper impedance contrast (f₁ < 5Hz) between natural Quaternary horizons (Fig. 10). The pre-Columbian urban planning and the past cultural practices could therefore be related, at least partially, with the f₁ distribution pattern. This hypothesis will have to be confirmed by further analysis of the archaeological data and stratigraphy.

A second hypothesis concerns the influence of the current urban layout on the site response. It has been established that buildings and their interaction with the ground can have a significant impact on nearby free-field measurements (Gallipoli et al., 2004). At the scale of an urban context, this "site-city seismic interaction" might significantly affect the site response in case of an earthquake. For Gueguen et al., (2002), the urban environment should not only be considered as a vulnerable entity but also as an active component of the seismic hazard. During an earthquake, building vibrations can be transferred back to the ground through the foundations (inertial soil-structure interactions), amplifying and prolonging the ground motion. In the case of the Mw 7.3 earthquake in Mexico (1995), the authors demonstrated that a high building-to-soil kinematic energy ratio usually implies high buildings, a high urban density and a correspondence between the site response and the building resonance frequencies. Although the previous work focuses on the “site-city interaction” during earthquakes, we can question the role of the urban layout of Cusco in contaminating the response of the site during a passive survey using MHVSR measurements. As proposed by Brûlé et al. (2017), cities can be regarded as metamaterials. In geophysics, such concept implies that the urban fabric might behave like a group of “Above-Surface resonators” (Brûlé et al., 2020), modifying thus the response of individual structures and acting as surface wave filters (Colombi et al., 2016; Gueguen and Colombi, 2016). It is striking that, despite the relative coherence of the frequencies of the secondary peak within the core of the city, the strongest amplitudes are restricted to the largest open spaces and therefore to the areas furthest away from the buildings (Fig. 10). In Cusco, most of the buildings that make up the historic center are large colonial complexes with patios, connected to each other and subdivided over time into multiple flats and lots. Clustering effects and interactions between the structures are therefore likely to be high, and the data collected so far as part of our research suggests that modes specific to an entire residential block could be identified. The long-period vibrations of these ‘meta-structures' could thus alter the apparent response of the ground (Fig.S1).

In short, the clustered distributions of f₁ and A₁ do not seem to be explained solely by a velocity inversion at very shallow depths. They also point to a decisive role for the urban layout (past and present) in the response of the site. Although these hypotheses remain to be ascertained, the strong contrast in frequency between the core and the periphery could be due to differences in the nature and thickness of the surface sediments. The higher frequencies in the urban core could be associated with anthropogenic deposits dating from the pre-Columbian period, which are absent from the outskirts. In parallel, the strong contrast in A₁ between the open spaces and the rest of the city suggests a significant influence of the city's buildings on MHVSR measurements at medium and high frequencies (> 3 Hz). If confirmed, the influence of these two parameters should be taken into account in a future microzonation of Cusco.

As the impact of earthquakes on World Heritage sites "is well beyond the direct economic losses" (Despotaki et al., 2018), a better assessment of the seismic hazard and risk are crucial concerns for a developing country like Peru. Established in a tectonic basin and prone to site effects, the “archaeological capital of the Americas”, Cusco, represents an emblematic case of vulnerable World Heritage city as well as of the many aggravating factors specific to Southern countries (fast-paced urbanization, few geotechnical studies, heterogeneity of buildings’ condition). The aim of this work was therefore to characterize the dynamic properties of the subsoil in the historic center of Cusco for the first time, and to pave the way for a microzonation of the city. To tackle the inherent challenges of the urban environment, we relied on passive seismic methods, which offer rapid, cost-effective and non-invasive solutions.

Joint analysis and inversion of data acquired by single-station and array measurements using the MHVSR and MAM techniques enabled us to characterize the geometry and mechanical properties of the subsurface. The results therefore provide a good assessment of the fundamental frequency of the site and the variation of the sediment thickness at the scale of the urban center. The results indicate a rapid thickening from north to south of the weakly consolidated Quaternary sedimentary cover (Vs < 400 m/s), from around 30 to almost 120 meters. All of the geophysical data, from the frequency and amplitude of the MHVSR peak to the Vs30 values, highlight a strong contrast between the northern and southern parts of the city center, supporting the existence of a geological discontinuity between the main square and the Santo Domingo sector. This discontinuity echoes the already documented presence of a blind normal fault running through the Cusco Basin. Moreover, a very good correspondence emerges between the discontinuity identified in this work and the fault traces inferred from recent soil gas radon measurements (Garcia et al, in prep.).

In addition, although the response of the Cusco subsoil seems to be mainly influenced by the interface between the bottom of the basin (engineering bedrock) and the sedimentary infill composed of fluvio-lacustrine sediments, the MHVSR survey suggests the existence of a second impedance contrast at a shallower depth (< 30m) in the core of the historic city of Cusco. Given the peculiar distribution of f₁, we assume that this secondary peak may be of human origin, corresponding to the earthworks carried out by pre-Columbian populations. The significantly higher amplitude of this frequency in the only two large open spaces also argue for a significant influence of buildings and the current urban layout on the elastic response of the subsoil.

These findings, though still hypothetical, could have a major impact on the assessment of seismic hazard. Further works are needed to better characterize the geometry and structure of the Cusco fault, its potential contribution to site amplification and distribution of past seismic damage. As the MHVSR method does not provide a reliable assessment of site amplification, this work was not intended to provide a quantification of site-effects amplifications. Nevertheless, the data acquired concerning the structure of the basin and the distribution of frequencies demonstrates the relevance of this approach for the necessary characterization of the subsurface of a UNESCO-listed city. Future monitoring initiatives are promising. In a city like Cusco, where the water table seems to be relatively close to the surface and subject to significant variations due to seasonal rainfall, it would be particularly interesting to set up long-term monitoring of the fundamental frequency of the site in order to monitor the piezometric level and saturation of the subsoil (Rigo et al., 2021; Seivane et al., 2022; Vassallo et al., 2022), i.e., major vulnerability factors in case of strong earthquake shaking. Finally, these future long-term MHVSR campaigns will make it possible to record seismic events, a prerequisite for properly estimating the site amplification and vulnerability of the Cusco built heritage.

Acknowledgements/Funding

This work would not have been possible without the collaboration of Architect Eliluz Palomino of the Gerencia del Centro Histórico de Cusco and Archaeologist Yeny Baca of the Dirección Desconcentrada del Ministerio de Cultura de Cusco. We also thank Fabrizio Delgado, Cristhian Baca, Julio Rojas, Enoch Aguirre for their precious assistance and expertise during the field campaigns. This work has been supported by the French government, through the UCA^JEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01. It was also supported by the Peruvian Ministry of Energy and Mines, through the Institute of Geology, Mining and Metallurgy (Geological Survey) and the Neotectonics project of the Department of Environmental Geology and Geological Risk. The project has received, as well, financial support from the UMR 7329 Geoazur Laboratory.

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contributions:

Conceptualization: A. Combey, E.D. Mercerat, C.L. Benavente; Methodology: A. Combey, E.D. Mercerat, J.E. Díaz, F.P. Pérez; Formal analysis and investigation: A. Combey, E.D. Mercerat, J.E. Díaz; Writing - original draft preparation: A. Combey; Funding acquisition: A. Combey, E.D. Mercerat, C.L. Benavente; Resources: B. García, A.R. Palomino, C.J. Guevara; Supervision: A. Combey, E.D. Mercerat, C.L. Benavente.

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Characterizing the seismic response and basin structure of Cusco (Peru). Implications for the seismic hazard assessment of a World Heritage Site

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Abstract

Figures

1. Introduction

2. The Cusco Basin, a tectonic-driven formation prone to site effects

3. Geophysical methods

3.1. MHVSR survey

3.2. Multichannel seismic recordings

3.3. Calibrated joint inversions

4. Results

4.1. Experimental data

4.2. Subsurface velocity model

5. Discussion

5.1. Tracking the Cusco fault below the CCC

5.2. Urban environment: a masking effect for soil response evaluation?

6. Conclusions

Declarations

References

Supplementary Files

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