An Empirical Correlation between the Residual Gravity Anomaly and the H/V Predominant Period in Urban Areas and Its Dependence on Geology in Andean Forearc Basins

Abstract

The study of site amplification effects is crucial to assess earthquake hazards that can produce great damage in urban structures. In this context, the gravity and the ambient noise horizontal-to-vertical spectral ratio (H/V) are two of the most used geophysical methods to study the properties of the subsoil, which are essential to estimate seismic amplification. Even though these methods have been used complementarily, a correlation between them has not been thoroughly studied. Understanding this correlation and how it depends on geology could be important to use one method as an estimator of the other and to make a distinction between the seismic and gravimetric basement. In this research, a comparison between the residual gravity anomaly and the H/V predominant period is performed using a long dataset from different projects on sedimentary basins in a group of the most important cities in Chile. To simplify the geological information, a seismic classification is used for soils, which considers the Vs30 and the predominant period of vibration (T0). The results of this comparison show a direct correlation between both parameters, the higher the negative residual gravity anomaly the higher the H/V predominant period. This correlation improves when only soft soils are considered, increasing the R2 value in more than a 50% in all the individual cities with respect to the overall correlation. When all the cities are considered, the R2 value for soft soils increases up to 0.87. These results suggest that the ideal geological background for this correlation is when a soft soil layer overlies a homogeneous bedrock. Heterogeneities in the bedrock and in the soil column add dispersion to the correlation. Additionally, the comparison between the depth to basement inferred by both methods show differences of less than 15% in soft sites; in denser sites, the difference increases up to 30% and the definition of a clear H/V peak is more difficult. In general, the gravimetric basement is deeper than the seismic one. However, gravimetric depths to basement can be under/over-estimated in zones with a heterogeneous soil column.

1. Introduction

Geophysical techniques used to study the subsoil properties have been widely applied due to their relative low cost compared to direct in-situ tests (e.g., boreholes). Additionally, these methods are less invasive and able to reach great depths. Therefore, they are specially adapted for urban environments where it is not possible to carry out deep invasive exploration or deploy heavy machinery.

Among the great variety of geophysical methodologies, gravity and ambient noise horizontal-to-vertical spectral ratio (H/V) are two of the most used because they are relatively easy to perform and they do not require very complex logistics in the field. Even though their physics are very different, they describe complementary variables. The gravimetric method measures the variations in the gravity field caused by the density contrast within the soil domain and with respect to the bedrock underneath [1]. Following this simple principle, gravimetric surveys have been used in many fields such as hydrogeology, e.g., [2,3,4], mining exploration, e.g., [5,6], or geometric characterization of sedimentary basins, e.g., [7,8], among others.

On the other hand, among the seismic methods, the H/V method, introduced by Nogoshi and Igarashi [9] and widespread by Nakamura [10], consists in determining the ratio between the Fourier spectra amplitudes of the horizontal and vertical components of microtremors [11]. According to these authors, the frequency peak of the H/V curve correlates with the predominant frequency of vibration at the site. Following this idea, many publications have used the H/V method to study the dynamic properties of the subsoil, e.g., [11,12,13,14,15,16]. In addition, the ellipticity from the Rayleigh waves obtained from the H/V curve, e.g., [17,18], can be used in a combined inversion with other seismic constrains (e.g., shear wave dispersion, autocorrelation curves) to improve the resolution of the deeper layers in the shear wave velocity profile [19].

In the study of sedimentary basins, many authors have combined both methods with others geophysical measurements, to conduct an integrated interpretation of their geometry and dynamic properties, and to estimate their seismic response, e.g., [7,8,20,21,22,23,24]. In this context, the parameter in common between both methods is the inference of the depth to rocky basement. However, the definition of basement given by each technique is different and it is very important to understand this distinction. The gravity methods, in the study of sedimentary basins, result in the depth of the basement, as compared to the negative anomaly produced by the low-density infill sediments versus bedrock. On the other hand, the H/V information can also be used directly as an infilling sediment thickness estimator under certain conditions assuming 1-D wave propagation and using the shear-wave velocity information [25]. Nevertheless, this method defines a mechanical or seismic bedrock in terms of a predominant impedance contrast, which does not necessarily imply rock. Thus, the location of both basements is not always the same, which can lead to wrong interpretations.

Consequently, it is very important to understand the connection between both methodologies and to define conditions in which both results can be correlated. A correlation between the methods could be beneficial in terms of the geophysical survey. Firstly, each gravity measurement requires less time than the H/V, so this possible correspondence could lead to better spatial coverage in less time. Secondly, the H/V results can help to discern between zones with different density contrast through the form of the curve. Finally, in cases when both methodologies are available, they can be complementary. However, a correlation between both methods, if it exists, has not been thoroughly studied, and thus very little information is available on whether one method could be an estimator of the other. A large part of available studies deals with the relationship between H/V frequency and depth to the basement derived from other techniques, such as boreholes or other seismic data [26,27,28,29,30,31,32]. Some other authors incorporate gravity information in their studies, to estimate the sediment thickness, e.g., [21,23,24], but these studies are not orientated to determining a correlation between both techniques, but rather they use the information to reach other objectives. Additionally, they do not explore how any potential correlation depends on geology.

Therefore, the motivation of this work is to define in what geological conditions both methodologies are consistent and if they can be used indiscriminately with respect to each other. In other words, in what conditions it would be possible to use gravity to estimate where the impedance contrast occurs (predominant frequency) and vice versa. Understanding this relation can be very important in future studies. Not only in cases where is not possible to apply one of the methodologies, but also to constrain and validate the results of each other. Additionally, another objective is to make a distinction between the gravimetric and the seismic basement, as was described before.

To achieve these objectives, a group of Chilean cities was selected as a case study. These cities (Arica, Iquique, Mejillones, Viña del Mar, Santiago and Concepción) cover a great portion of the country and collect different geological conditions, which is crucial to understand possible correlations (see Figure 1). Together, these cities account for approximately 50% of the country’s population [33]. These sedimentary basins include practically all the different types of soils present in the fore-arc of the Chilean Andes. The dataset was collected from different projects, which are described in Section 2 and whose main objective was to assess the seismic hazard in the country. Even though we are not including data from other main cities in the Andes of Peru and Ecuador, our observations are representative of almost all the tectonic and depositional settings of the fore-arc Andean domains of the whole region, dominated by intercalation of fluvial, volcanic and mountain erosional deposits [34,35].

2. Study Area and Dataset

As mentioned before, the case study in this research considers a group of important Chilean cities located over sedimentary basins. These basins are, in general, infilled by Quaternary deposits, but with different soil types. The sample chosen was to try to cover the full spectrum of typologies in order to provide a broad picture of likely scenarios for the relationship, if any, between gravity and H/V. The geology of all these sites is shown and described in Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6 and subsections below.

2.1. Arica

This city is located in the extreme north of the country in the coastal plain. As can be seen in the left panel of Figure 2. The basement in the zone corresponds to mostly andesite volcanic and volcano-sedimentary rocks from the Jurassic and Paleogene, respectively [36,37]. The basin infillings are quaternary deposits distributed into three areas [37,38]. The southern soils (dark yellow in left panel of Figure 2) are fluvial deposits composed mainly of semi-consolidated coarse gravels. In the northern flank of the city, we find a thick sequence of unconsolidated marine deposits composed of fine sands. Finally, there are some alluvial deposits to the north-east portion of the city. The geophysical campaign in this zone consisted in gravity and seismic measurements. The seismic survey was developed by Becerra et al. [14] and a detailed description is available in their research while the gravimetric campaign was carried out by the FONDEF project D10I1027 [39]. The right panel of Figure 2 shows the main results of these campaigns, including the residual gravity (colored map) and H/V results (colored and different size circles). This data set will be discussed in the following sections.

2.2. Iquique

This city is also located in northern Chile, 300 km further south from Arica (Figure 3). The basement of this zone corresponds to a widespread distribution Cretaceous volcanic rocks, mostly andesites, and in the northeast portion, Jurassic intrusive rocks (granodiorites) from the Jurassic [40,41]. In the urban area of Iquique, it is possible to observe two different types of soils. In the northwest portion, a thin layer of quaternary alluvial and marine deposits overlies the basement [40]. To the south of the Iquique urban area, there are fine sands of eolian and marine origin [40,41]. Finally, in the urban area of Alto Hospicio in the southeast portion of the area, the sedimentary cover includes Paleogene gravels (blue section of left panel in Figure 3). The seismic geophysical campaign in this zone is also available in the work of Becerra et al. [14], while the gravimetric survey is part of the FONDEF project D10I1027 [39] and the work of Garcia-Perez et al. [42]. The main results can be seen in the right panel of Figure 3, including the residual gravity (colored map) and H/V results (colored and different size circles).

This city is located in the Mejillones Peninsula northern Chile (Figure 4). The peninsula geology corresponds to Paleozoic metamorphic basement accreted to the margin ~ 440 Ma [43], in contact with a Jurassic basement, mostly volcanic andesites and intrusive outcrops of diorites and gabbro. The basin infilling are mainly Quaternary conglomerates in a sand matrix over deposits composed of sands, silts and diatomaceous soils [44].

2.3. Mejillones

Specifically in this city, there is a thick sedimentary infill, composed of diatomites and some sands and silts, which is a particularly different condition compared to the rest of the northern cities in the country [45]. According to Maringue et al. [8] the thickness of the sedimentary deposits reaches ~800 m with soil densities around 1.5 g/cc. The whole geophysical campaign in this zone is available in Maringue et al. [8] and the main results are shown in the right panel of Figure 4 including the residual gravity (colored map) and H/V results (colored and different size circles).

2.4. Viña del Mar

This city is located in the coastal central region of Chile (Figure 5). The basement in the zone is composed of Jurassic and Paleozoic intrusive rocks, mostly granites and granodiorites, outcropping both in the northern and southern parts of the city [36]. The sediments overlying the rock are mainly Quaternary fluvial medium density soils, composed of sand silt and some gravels [46]. The detailed geophysical campaign and the main results are available in the work of Podestá et al. [24], but a summary of gravity and H/V results are shown in the right panel of Figure 5 (the residual gravity (colored map) and H/V results (colored and different size circles). For simplicity, we will indicate this city as “Viña” in the legends of the following figures.

2.5. Santiago

Santiago is the capital of Chile, with a population of 6 million inhabitants. Santiago is located over an irregular sedimentary basin with maximum soil thicknesses of around 500 m and a mean depth of 300 m, e.g., [7,47]. The basement rocks of the basin are heterogenous. Those from the east correspond to the western foothills of the Andean Cordillera, mostly late Cenozoic volcano-sedimentary sequences, including andesites and basalts, with some Miocene plutons in the southern part [36,48,49]. To the west, the basement corresponds to the eastern flank of the Coastal Cordillera, composed mainly of Cretaceous volcanic (mostly andesites) and intrusive rocks (diorites) [36,50]. The infill soils of the basin are mainly quaternary fluvio-alluvial and fluvial deposits composed of medium to high density sandy gravels (dark yellow in the left panel of Figure 6) [36,51]. However, in the northeast flank of the basin, two other significant soil typologies are present: (1) fine soils, composed mainly of silts and clays (light yellow in left panel of Figure 6) and (2) pyroclastic deposits (Pl3t unit in Figure 6) of around 20 m thick of volcanic ash, mainly located in the western part of the city [47]. These last two domains concentrated the main structural damages after the 2010 Maule Mw 8.8 earthquake [52]. The main results of the geophysical campaign in the zone are presented in the right panel of Figure 6, including the residual gravity (colored map) and H/V results (colored and different size circles). The gravimetric survey is described in Yañez et al. [7], while the details of the seismic measurements can be found in Fondef project D10I1027 [39].

3. Analysis of Geophysical Data

The objective of this research is to determine possible relations between gravimetric and H/V method, and to understand the geological conditions in which these connections are valid. To achieve this objective, a long dataset of both methods in many Chilean cities (references in Section 2) is considered. Both methodologies are briefly explained here; a detailed description is beyond the scope of this research and can be found in specific literature for each method, e.g., [9,10] for H/V and [1] for gravity.

The gravimetric method is a passive technique that measures the gravity acceleration in different points of the earth. The density contrast between basement and coverage produces measurable anomalies in the gravimetric field. The infilling sediments have lower densities compared to bedrock, producing a negative gravity anomaly. To isolate the effect of the shallow soils in the gravity anomaly, it is necessary to subtract the rest of instrumental and geological sources that contribute to the results. In general, the data reduction in all the cities followed the standard procedure described in Telford et al. [1]. This includes the subtraction of tidal variations and instrumental drift, and topographic, latitude, altitude and Bouguer corrections. Additionally, a regional effect produced by deep geological structures was eliminated specifically for each site. More details can be found in the respective references mentioned in Section 2. Once isolated the effect of the infilling sediments (residual gravity anomaly) by performing all the previous corrections, the result can be inverted to obtain the depth to basement through estimating the density of the different units, where complex settings are most likely the rule (i.e., heterogeneous basement and sedimentary facies varying laterally and with depth). This complexity implies a particular treatment of each locality; for the sake of simplicity, the use of residual gravity anomaly is preferred to find correlations with the H/V method instead of the thickness resulting from the inversion process. The residual gravity anomaly is still a first order predictor of the depth to the geological basement, where larger negative values indicate higher depths to basement.

On the other hand, the H/V method consists in determining the spectral ratio between the horizontal and vertical components of the ambient vibrations [10]. The period of the peak of this spectrum can be associated with the predominant period of vibration of a soil deposit. However, this correlation depends strongly on the impedance contrast between the soils and the bedrock; it is possible to have curves with no clear peak or with more than one peak, e.g., [25]. We defined the predominant period as the one associated to the highest amplitude related to the high impedance contrast. Depending on the geology, this may or may not correspond to the peak associated with the longest period. Additionally, the resulting predominant period (T₀) can be used to estimate the thickness of the soil deposit (H) combined with the harmonic mean shear-wave velocity (V_s) of the site using the Equation (1) (e.g., [26]). This relation assumes 1-D wave propagation, and just as in the case of gravity inversion, it involves a particular treatment in each city.

$$H=\frac{T_0 \times V_s }{4}$$

(1)

The detailed description of the geophysical campaigns for each city can be found in the references mentioned in Section 2. However, all these campaigns were made with the current acquisition standards. In the case of the gravimetric survey, a Scintrex CG5 gravimeter was used together with a differential GPS Trimble C5 to have a net error lower than 0.05 mGal and altitude errors lower than 30 cm. Furthermore, all regional effects were removed by applying regional and low-pass filter techniques. For the H/V campaigns, a 3-component 4.5 Hz Tromino^® instrument was used to measure the ambient vibrations for at least 20 min, except for the case of Mejillones where a low frequency SARA^® triaxial seismometer was used and measurements of more than one hour. In this investigation, the analysis was carried out following a variation of the Nakamura method [53]. This approach considers a fixed window of 60 s for the S-transform application [54] at each window. S-transform uses a mobile and scalable window for the analysis. This achieves a frequency-dependent resolution, longer/shorter windows for low/high frequencies. This optimizes the signal response, obtaining smoother results at high frequencies and a more robust mean

Considering the shortcomings of both depth estimates, the depth-to-geological basement derived from gravity observations, and the depth-to-seismic/mechanic basement derived from H/V observations, in this work, only the raw results of each method were used to seek for possible correlations. The right panels of Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6 show the main results of these methodologies in terms of residual anomaly (gravity) and predominant period of vibration (H/V). In general, the green zones in the residual gravity anomaly illustrate the infilling sediments and the red zones show where the rock is shallow or where it outcrops. In all the figures, it is possible to see that negative residual gravity anomalies correlate with the quaternary deposits shown in the geology, indicating the presence of low to medium density soil deposits.

In terms of H/V, the predominant periods are summarized by colored and different size circles in the right panels of Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6. The circle color indicates the range of the predominant period, while the size indicates the amplitude of the H/V peak (A0 values). In general, higher periods indicate higher soil thickness, although this result will depend on the average velocity of the site and possible 2-D or 3-D effects [25]. The amplitude cannot be related with the site amplification factor, although, it is related with the site impedance contrast [11,25]. Higher amplitudes normally correlate with a higher impedance contrast between the infilling sediments and apparent bedrock. Finally, the black dots illustrate those sites where it is impossible to find a clear peak (flat curves). The H/V results show that the blue and green circles are located mainly in the zones with lower gravity residuals, which are mainly zones with higher sediment thicknesses, whereas the yellow and purple circles (lower periods) are located near the rock outcrops and red zones in the gravimetric results. Additionally, the bigger circles (higher amplitudes) are located mainly in two different zones. First, they appear in zones with large negative gravity residuals implying thick soil columns. Secondly, they are located in zones near the red gravity areas where the bedrock is probably at shallow depths, indicating a high impedance contrast between them and soil coverage. Finally, the flat curves (black dots in Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6) are located in zones where there is rock, however there are a lot of points that are over the green zones in the gravity residuals. This apparent contradiction highlights the differences, in some cases, between mechanical and geological sedimentary thickness. We will address this particular case in the discussion Section 4.

3.1. Seismic Classification of the Soils

To simplify the characterization of different types of infilling sediments throughout all the studied cities, a seismic classification is used. The seismic classification chosen in this work corresponds to a variation of the current Chilean seismic code NCh 433, mod DS 61 2011 [55], which defines five types of sites from A to E (from rock to soft soils) depending on the parameter V_s,30 (harmonic mean of the vs. in the upper 30 m). In this case, the new classification, modified from Verdugo et al. [56], incorporates the predominant period (T₀) as a way to include information deeper than 30 m. Additionally, it incorporates the parameter V_s < 900 (the harmonic mean of vs. is in the upper 30 m or until reaching a material with V_s < 900 m/s) to avoid the misrepresentation of V_s,30 when the bedrock is shallower than 30 m. This classification is shown in

Table 1. Seismic classification (modified from Verdugo et al. [56]).

Category	First Criterion: Vs,30 or Vs < 900 (m/s)	Second Criterion: T0 (s)	Site Type
A	≥900	<0.15 or flat HVSR	Rock, cemented soil
B	≥500	<0.30 or flat HVSR	Soft or fractured rock, very dense/firm ground
C	≥350	<0.40 or flat HVSR	Dense/firm soil
D	≥180	<1 or flat HVSR	Moderately dense/firm soil
E	<180		Medium compactness/consistency soil

. The first criterion is the V_s,30 or V_s < 900, but if the predominant period of the site is higher than the category limit, the site is penalized, taking the next lower classification.

This classification is used to study possible correlations between gravity and H/V results using a common criterion among the different geological sites. In general, lower classifications indicate the presence of soft soils, which are related mostly with fine soils (clays or silts) or low-density sands. On the other hand, higher classifications indicate more dense soils such as very dense sands, gravels or rock. The results of V_s,30 or V_s < 900, which are necessary for the results of the next section, are not presented in this research for simplicity, but they can be retrieved from the references provided in Section 2.

3.2. Gravity and H/V Correlation

In this section, the residual gravity anomaly is compared to the H/V predominant period in each site to define possible correlations. As a first approximation, the geology of the soils is incorporated using the seismic classification presented in Table 1. A more detailed analysis of the geology, including the basement rocks, is presented in the discussion Section 4.

Figure 7 shows this comparison in the city of Viña del Mar. This city presents the ideal conditions in terms of geology, where a relatively homogeneous medium density soil layer overlies the rock. Therefore, the results in this city are used as a reference to evaluate the correlations in the other cities. The upper panel of Figure 7 shows the sites classified according to the seismic classification of Table 1 in colored squares, while the red continuous line represents the linear trend between the gravity residual and the predominant period. The lower panel shows the same comparison but only considering the soft soils with a seismic classification of D or E. The results in both panels show a very clear tendency between both properties, where larger negative gravity residuals occurred in zones with higher predominant periods. In the upper panel, only two sites are far from the tendency, both classified as dense to very dense sites (B and C classification). This generates a lower R² in the tendency, which increases up to 0.82 when only the soft sites are considered. Furthermore, the slope of the trend increases when only soft sites are considered.

A less satisfactory case in terms of correlation between both parameters is Iquique city. Figure 8 shows the same comparison in this city, which presents a totally different geology background compared to Viña del Mar. Here, the geology is very heterogeneous. The rock is very shallow in a great portion of the city, e.g., [14], and outcrops in different zones of the basin. Additionally, the soils presented in the city are dense with a lower impedance contrast with the basement, and stiffer seismic classifications. In Figure 8 it is possible to see that most of the soils are A, B or C, and only five sites are classified as D. In this case, there is not a clear tendency between the properties, with an R² almost equal to zero. The analysis with soft sites is not reasonable here because there are only five sites in this condition.

On the other hand, Santiago appears as the more complete case study because of the high number of measurements and the presence of different types of infilling sediments in a complex geology background. The results of the comparison between gravity residual and H/V predominant period are shown in Figure 9, following the same properties of Figure 7 and Figure 8. The upper panel shows all the soil categories, while the lower panel shows only sites type D and E. The red line represents the linear trend in this case. As in the case of Viña del Mar, there is a negative relation between period and gravity residual, although in Santiago the results are more disperse with a lower R². However, the correlation is better for soft sites. The trend’s slope also increases when these soft sites are considered.

Additionally, the linear trend in Viña del Mar is presented in both panels of Figure 9 as a black continuous line, while the black dashed line corresponds to the same trend translated (−1.5 mGal) to better fit with the results in Santiago. From this figure, it is possible to see that the slope of Viña’s trend also fits well with the results of Santiago, although it is higher than the calculated linear regression (red continuous line). Nevertheless, the black line is displaced in respect to the Santiago data. This situation is possibly related with some regional gravity effect that gives a different level to Viña del Mar (located in the Chilean coast) compared to Santiago (located in the Chilean central valley).

Finally, Figure 10 shows the comparison between all the cities grouped in this work, divided into two panels as in the other figures (upper panel: all the soils categories; lower panel: only soils type D and E). In this case, the colored squares in the upper panel represent the different cities, as shown in the legend. In this figure, the data from Concepción was added to strengthen the relationship. Concepción is one of the biggest cities in Chile, located in the central-south portion of Chile (see location in Figure 1). Unfortunately, information about all of these same variables was not available from Concepción; therefore, it was not possible to process and present it in the same way as for the other cities. However, given its relevance, we consider it pertinent to present the H/V predominant periods and gravity in the present analysis and compilation (extracted from Montalva et al. [23]). From the Figure, it is possible to see that the Mejillones results (black squares) are located in higher periods compared to other cities, indicating the high thickness of the infilling sediments in the zone. Nevertheless, the trend between gravity and period is still negative and similar to the other figures showing that, in general, the higher the period the higher the gravity residual. The linear correlation, considering all the cities, is satisfactory, and it improves when only soft sites are considered, increasing from an R² of 0.79 to an R² of 0.87. The trend line increases its slope when only soft sites are considered as in the last cases.

3.3. Seismic and Gravimetric Basement Depth Inversion

The mechanical basement derived from seismic H/V measurements and the geological basement derived from gravity modeling are not necessarily the same. One of the goals of this research is to clarify the precise meaning of each basement definition, and how this understanding impacts the geological conditions in which the relation between predominant period and gravity residual is valid. Therefore, in this section we discuss the comparison between the depth-to-basement derived only from H/V measurements and the one derived from the 1-D gravity residual inversion in some sites of interest, considering different geological settings. Even though these inversions can be made in a more regional way considering data distributed in space (2D or 3D inversions), we perform only local 1D inversions to simplify the comparison of results.

The seismic basement derived from H/V is obtained through an inversion using the ellipticity of the Rayleigh waves [17]. The ellipticity corresponds to the ratio between the horizontal and the vertical particle motions and gives valuable information of the whole sedimentary layer [19]. Hobiger et al. [18] gives a detailed description of the methods to obtain this parameter. In this work, the ellipticity is obtained using the H/V TFA tool available in the software Geopsy^® [57]. However, the ellipticity curve cannot be used alone in the inversion because different soil structures can produce the same curve [19]. As a result, the inversions were complemented using dispersion curves from active seismic arrays available in the corresponding projects for each city. Hobiger et al. [19] gives recommendations about the portions of the curve to be included in the inversion through the analysis of synthetic and real data; according to their work, the right flank of the ellipticity peak contains the most important information, although the left flank can be used to constrain the peak frequency, if necessary. These recommendations were used in this work, although, some portions of the curve are unconstrained during the inversion. The focus of these inversions is to estimate the depth to the basement and not its shear wave velocity. This result is compared with the sediment thickness (H) obtained from the 1-D relation shown in Equation (1), that correlates H with the predominant period (T₀) and the harmonic mean shear-wave velocity (V_s). This relation can lead to wrong interpretations under 2-D environments, however, in this work it is only used as a way of comparison between independent results.

On the other hand, the gravimetric basement is calculated assuming a 1-D model consisting only in one soil layer overlying the rock. Assuming a unique density contrast between soil and bedrock, it is possible to obtain the thickness of the soil column through Equation (2) [1] for a semi-infinite horizontal slab.

$$\Delta g \left(\mathrm{mGal}\right)=0.0419\times \Delta \rho \left(\mathrm{ton}/{\mathrm{m}}^3\right)\times H \left(m\right)$$

(2)

With $\Delta g$ the gravity anomaly, $\Delta \rho$ the density contrast between the soil and the rock and H the sedimentary layer thickness.

The comparison between both basements is made using four different sites. Three sites (Figure 11, Figure 12 and Figure 13) are located in soft sites with seismic classification of D, according to Table 1, while the fourth site is located in a site with dense soils (Figure 14). In dense soils most of the sites show an H/V curve with no peak or with a peak of low amplitude, where it is difficult to define a predominant period (some examples are in Figure 15). For that reason, in many of them it is not possible to perform an inversion using ellipticity or using the Equation (1).

Figure 11 shows the results of the seismic inversion in one site located in the fluvial deposits of Viña del Mar (Figure 5). This site has a seismic classification of D, with an H/V predominant period of 0.72 s and a V_s,30 of 242 m/s. The soils in this site are medium density sands and silts [46]. The panel (a) of Figure 11 shows the adjustment of the ellipticity between the observed curve (black line) and the best inversion models. Here, both flanks of the peak were used in the inversion. Panel (b) shows the same results for the dispersion curve, where active and passive curves were used as input to constrain the ellipticity curve inversion. Finally, panel (c) displays the shear-wave velocity models, where the colors are related with the misfit bar below. Here the black line corresponds to the best model with a misfit value slightly lower than 0.11. From this figure, it is possible to see a very good agreement in the dispersion and ellipticity curves between the observed data and the resulting models. The resulting inversion profile shows a deposit of soil of about 250 m/s of shear wave velocity and then, at 48 m depth, a stiff material appears with a shear wave velocity over 2000 m/s, associated with the seismic bedrock. This value of seismic bedrock velocity is only tentative, since no information is available on the dispersion curve at low frequencies, nor is the peak of the H/V curve being used. However, regardless of the exact value of the impedance contrast, the thickness of the soil layer is well defined. The Equation (1), using the values previously mentioned in this site, gives a depth to the basement of 44 m, which is very close to the inversion. In terms of gravity, the residual anomaly in this site is −1.72 mGal. Podestá et al. [24] estimates a density contrast between the soils and bedrock in the zone of 0.7–0.8 ton/m³. Using a mean value of 0.75 and the Equation (2), the gravimetric basement results in 55 m.

Figure 12 shows the same results of the seismic inversion in Figure 11 but in one site located in the Quaternary marine sediments in Mejillones (Figure 4). This site has a seismic classification of D, with an H/V predominant period of 5.9 s and a V_s,30 of 390 m/s. The minimum misfit value in this inversion is around 0.12. From this figure, it is possible to see good agreement in the dispersion and ellipticity curves between the observed data and the resulting models. The resulting inversion profile shows a thick deposit with velocities increasing from 200 to 550 m/s and then, from 570 m appears a layer with a velocity around 1200 m/s, associated with the seismic bedrock. The Equation (1), using the values previously mentioned in this site, gives a depth to basement of 575 m, which is very similar to the inversion. In terms of gravity, the residual anomaly in this site is −29.2 mGal. Maringue et al. [8] estimates a density contrast between the soils and bedrock in the zone of 1.2 ton/m³. Using this value and Equation (2), the gravimetric basement in this site results in 580 m.

Figure 13 shows the same results for a site located in Santiago, specifically in the northern area with fine soils. This site has a seismic classification of D, with an H/V predominant period of 0.68 s and a V_s,30 of 288 m/s. The minimum misfit value in this inversion is around 0.088. Here, there is also a good agreement in the dispersion and ellipticity curves between the observed data and the resulting models. The resulting inversion profile shows a layer of almost 1000 m/s at 50 m deep, associated with the seismic bedrock. Equation (1), using the values previously mentioned in this site, gives a depth to basement of 49 m, which is almost the same as the inversion. In terms of gravity, the residual anomaly in this site is −1.15 mGal. From the work of Yañez et al. [7], it is possible to estimate a density contrast between the soils and bedrock in the zone of around 0.7 ton/m³. Using this value and Equation (2), the gravimetric basement in this site results in 40 m.

On the other hand, Figure 14 shows the same results, although for a dense soil in Iquique. This site has a seismic classification of C, with an H/V predominant period of 0.25 s and a V_s,30 of 380 m/s. The minimum misfit value in this inversion is around 0.141. The resulting inversion profile shows a layer of almost 3000 m/s at 28 m deep, associated with the seismic bedrock. The Equation (1), using the values previously mentioned in this site, gives a depth to basement of 24 m, which is close to the inversion. In terms of gravity, the residual anomaly in this site is −1.2 mGal. From the work of Garcia-Perez et al. [42], it is possible to estimate a density contrast between the soils and bedrock in the zone of around 0.7 ton/m³. Using this value and Equation (2), the gravimetric basement in this site results in 40 m.

Finally, Figure 15 shows three different examples of H/V curves obtained in Santiago, specifically in the southern part of the city (see black dots in the right panel of Figure 6. Santiago. Left panel: Simplified geology of the city adapted from Chilean geological map 1:1,000,000 [36]. Right panel: Main results of the geophysical campaign [7,36,39]. The color grid shows the gravity residuals in mGal. The color points show the H/V results. Color indicates the predominant period (T0) in seconds and the size indicates the amplitude (A0) of the H/V curve.). All these sites are located over dense gravels with a seismic classification of B or C, according to Table 1. From this figure, it is possible to see that there is not a clear peak in any of them, showing a flat curve along the whole frequency range. This situation occurs in a great part of the soils in all the cities located over dense soils (B or C seismic classifications), showing the low impedance contrast with the bedrock. Consequently, it is not possible in these sites to carry on an inversion using ellipticity or to use the 1-D approximation from the Equation (1).

Table 2. Summary of the comparison between seismic and gravity basement for the four sites studied.

Site (Fig.)	H/V T0 (s)	Seismic Classification (Table 1)	Vs (m/s)	H/V Amplitude (A0)	Gravity Residual (mGal)	Seismic Basement Depth (m)	Gravity Basement Depth (m)
Viña (Figure 11)	0.72	D	242	7.2	−1.72	48	55
Mejillones (Figure 12)	5.9	D	390	1.2	−29.2	570	580
Santiago (Figure 13)	0.68	D	288	5.5	−1.15	50	40
Iquique (Figure 14)	0.25	C	380	2.9	−1.2	29	40

shows the summary of the comparison between the depth to the basement derived from seismic and gravimetric methods for the sites shown in the previous figures. The seismic basement is obtained from the inversion using ellipticity, while the gravimetric basement comes from Equation (2). The H/V amplitude column is an indicator of the impedance contrast between the soil column and the bedrock. The higher the amplitude, the higher the impedance contrast. In general terms, the differences between the estimated soil thicknesses range from −27% to +25%, depending on the case. In the case of Mejillones (great thickness of light soils), the values are almost identical.

4. Discussion

The results presented in Section 4 try to determine possible correlations between the H/V predominant period and the gravity residuals. Figure 7, Figure 8, Figure 9 and Figure 10 show, in general, that there is a direct correlation between both parameters: the higher the period, the higher the negative gravimetric anomaly. However, the robustness of this correlation depends on particular geological/morphological conditions.

Considering each city individually, the best results are obtained in Viña del Mar (Figure 5) as can be seen in Figure 7. The whole sedimentary basin in the city is infilled by the same unconsolidated fluvial sediments, composed mainly of fine sands overlying a well-defined and quite homogeneous bedrock (Jurassic granitoid) [46]. In these conditions, there is a clear trend between both parameters with a very low dispersion. This trend improves when only the soils with seismic classifications of D and E are considered (lower panel of Figure 7). The reduced difference between both data sets can be attributed to the fact that more than the 80% of the soils in the city correspond to type D and E. Soils with classifications D and E are soils with low shear-wave velocities (lower than 350 m/s at least in the upper 30 m) or with predominant periods higher than 0.4 s. This indicates that they have a high impedance contrast with the rock (see Table 2, where the A0 from H/V is higher in the three fine soils than in the dense soil of Iquique).

On the other hand, the worst results are obtained in sites such as Iquique, where only a 10% of the soils are classified as D or E. In this city, the soils are more rigid, composed mainly of dense gravels, with velocities over 350 m/s and a very shallow bedrock in a great part of the city. This situation decreases the impedance contrast between soil and rock, and consequently, decreases the quality of the correlation between predominant period and gravity residuals. Figure 8 shows that there is no correlation at all between both parameters. Additionally, the presence of a heterogeneous bedrock can lead to some errors in the estimation of the gravity in which part of the signal is in fact the response of a mass defect/excess of the basement, and not an increase/decrease of the sedimentary thickness. This could add some noise, affecting the correlation with the period, as well.

This last situation is observed in Santiago, which is the biggest and extended city in the country and encompasses the largest number of measurements in this study (around 300 sites). Even though the negative correlation between gravity and H/V predominant period exists, the results are more disperse than in Viña del Mar. The correlation improves when only relatively soft sites are considered, although with a lower R² than in Viña (0.22 compared to 0.82). This higher dispersion can be explained, first, by the heterogeneous basement that induces some errors in obtaining the gravity residuals, as explained earlier. As in Iquique, the basement in Santiago is complex, including rock with different lithologies and from different ages and sources. These rocks can have densities from 2.3 to 2.9 ton/m³ [7], implying the heterogeneous nature of the basement. Secondly, the deeper basement (300–400 m) can increase the dispersion in the correlation. The deeper the source is, the less contribution to the signal as a result of the 1/r² or 1/r amplitude dependence with the source-sensor distance (r) [1]. Thus, lower signals imply larger influence of noise over the observations. This can be seen in Santiago and Mejillones (see Figure 10) where the depth to the basement is much higher than in the other cities, and the dispersion is also higher. Finally, the infilling sediments present different facies over the whole basin, and thus most likely, affecting in a heterogeneous velocity and density sedimentary distribution. This can lead to local effects in gravity that can be misunderstood or to more than one peak in the H/V curve, making it difficult to select a predominant period.

Even though the previous discussion on the gravity-H/V correlation shows a predominant trend, some differences are evident, and two first order aspects must be considered: (1) variability in the proportionality constant (or slope), and (2) the variance of the correlation. Both aspects are related to the degree of heterogeneity in the geological process that conform the basement and the infilling coverage. In small basins such as Viña del Mar and Mejillones, where a single basement and a unique sedimentary process took place, the variance in the correlation is minimal. However, the proportionality constant differs in a factor of two between them. This is most likely attributed to the very large density contrast between the basement and the sedimentary cover in the case of Mejillones as discussed in the previous paragraph. On the other hand, the case of Santiago is the opposite case, with a large basin evolving during the buildup of the Andes in the last 20 Ma [49,58], implying a heterogeneous basement and cover [7]. This geological heterogeneity mostly affects the gravimetric signal, amplifying the dispersion or variance in the correlation with the H/V data. The lower magnitude of the correlation factor in this case is probably the result of a mixture of fine and coarse sediments in the sedimentary column (superimpose sedimentary facies) that reduces the density contrast and consequently the amplitude of the gravity signal.

In terms of the slope of the linear regressions obtained, it is possible to see that there is not a common value among the cities. The slope of the best linear regression in Viña, considering only soft soils, is around −2.5 (Figure 7), while in Santiago it is around −1.4 (Figure 9). This difference can be explained because of the intercalation of fine soils and gravels in Santiago expressed in the previous paragraph, which directly affects the estimation of the gravity residual. However, as can be seen in Figure 9, Viña’s trend also can reasonably fit the measurements in Santiago, especially when it is translated, because of the higher dispersion of the results. When all the cities are considered together, the slope increases to around −4.4 mainly influenced by the higher periods and deep basement present in Mejillones. In this last case, the correlation is quite good, with an R² of almost 0.9.

The comparison between seismic-mechanic and gravimetric basement is also related to the geological conditions of the site. As can be seen in Figure 11, Figure 12 and Figure 13, the results in soft sites (with a seismic classification of D) show very good agreement between the bedrock from the ellipticity inversion and from Equation (1), evidencing a high impedance contrast between soils and rock. The higher difference between both basements is less than 10% in all the inversions in soft sites. In denser soils, such as in Iquique, the results are also good, as can be seen in Figure 14. However, the difference between both seismic basements is around 20%, and the H/V peaks have low amplitudes. This comparison is difficult to do in denser soils because they normally have flat H/V curves or there is not a clear peak (for example in Figure 15). Not having a predominant period, they cannot be correlated with the gravity results, and makes it impossible to perform an inversion and to obtain a seismic basement when the other seismic arrays do not reach rock. In the case of the southern Santiago, where the soils are mainly dense gravels, almost all the H/V curves are considered flat (see right panel of Figure 6). In the rest of the cities, the flat curves are present in Arica and Iquique where the soils are dense, while there are few flat curves in Viña del Mar and Mejillones, where the infilling sediments are mainly relatively soft soils.

In regards to the gravimetric basement, this is very similar to the seismic bedrock in the case of soft sites. The difference between them is lower than 15%, while in Iquique the difference is around 30%. Normally, the gravimetric basement is deeper than the seismic bedrock. This can be explained because of the soil confinement increases more the stiffness than the density in granular soils. The site in Santiago shown in Figure 13 is an exception. Here the gravimetric basement using a constant density contrast of 0.7 ton/m³ is at 40 m depth, shallower than the seismic one at 50 m. In this case, the reason could be the intercalation of a denser soil under the surface soft soils; if so, the smaller density contrast could account for a larger sedimentary thickness. In fact, Yañez et al. [7] estimates a soil density in the site location (Figure 13) around 1.9 ton/m³, while the typical fluvial gravels of the south of Santiago have densities up to 2.1 ton/m³. Therefore, if there are gravels under the soft soils in the site, the estimated density contrast of 0.7 could decrease to around 0.5, to account for a 50 m thickness.

5. Conclusions

This work presents a comparison between the gravity residual anomaly and the H/V predominant period from a long dataset that includes a group of the most important cities in Chile. This comparison is made to find relations between both parameters, and it is analyzed through the geology presented in each site. Key elements found in this analysis are the role played by the local geology characteristics (soil/basement type) and the potential differences between seismic and gravimetric bedrock.

The results of the comparison between gravity residuals and H/V predominant period show a direct correlation between both parameters, where the higher the period the higher the negative gravimetric residual. However, this correlation is better when only soft sites are considered, increasing the R² value in more than 50% in cities such as Viña del Mar or Santiago, compared to all the sites together. These soft sites are those with seismic classifications of D and E (shear wave velocities lower than 350 m/s or periods higher than 0.4 s), and they correspond, in general, to loose to medium density sands or fine soils such as clays or silts. Considering all the results, we conclude that the ideal conditions for this relation is when a soft soil layer overlies a homogeneous bedrock.

Even though this correlation is better over soft sites, the results on these sites present differences in the trend slope and in the variance of the correlation depending on the heterogeneity of the geological background and the depth to the basement. The results show that in zones where there is a heterogeneous basement or soil column, the dispersion of the correlation is higher than in zones where a unique sedimentary process took place. On the other hand, the dispersion is also higher over basins with higher sediment thicknesses, such as Santiago and Mejillones. The linear trend considering all the sites in the study with soft sites presents a good correlation with an R² of 0.87. The variability in the trend of every particular site is a function of the soil-bedrock mechanical and geological contrast, thus a general empirical rule cannot be established.

Finally, the seismic depths-to-basement obtained through the inversion of the ellipticity curve and through the 1-D relation of Equation (1) are very similar, although the difference is higher (around 20%) when denser soils are considered. The same occurs when the seismic basement is compared with the gravimetric one, where the differences are less than 15% in depth for soft soils and increase up to 30% in denser soils. These results show that both basements can be compared in places with high impedance contrast between soil and bedrock (soft sites). In denser sites with lower impedance contrast, the great part of the H/V curves does not present a clear peak or the peak has a low amplitude; this makes it impossible to estimate a seismic depth-to-basement from this method, as well as to make the comparison with gravity. In general, the gravimetric basement is deeper than the seismic one. However, gravimetric depths-to-basement can be under/over-estimated in zones with a heterogeneous soil column.