1 Introduction

Inferring seismic response from ambient noise has become a widely established technique which renders quick acquisition as well as cost-effectiveness. Numerous literatures are available which directly deals with effectiveness of quantification of ambient vibrations for delineating local seismic response (e.g. Nakamura 1989; SESAME 2004; D'Amico et al. 2008; Albarello and Lunedei 2011; Gallipoli et al. 2011 ; Paolucci et al. 2015; Farrugia et al. 2016). Local site settings play a major role in enhancing seismic damage; although, there are contributions from proximity of source location as well as path effect. In general terms, local site effects may be well-defined as amendment of features of receiving seismic wavefield, arising due to specific characteristics of site geology. There are two ways to quantify site effects; firstly, by using seismic array arrangement (multi-station) (Maranó et al. 2017) and secondly, by simply using a single-station deployment (e.g., Mucciarelli 1998; Parolai et al. 2005; Picozzi et al. 2005; Foti et al. 2011). Related to the latter category, ambient noises are accrued through three component sensor. From accrued noise, a division of amplitude of spectral ratios (HVSR) of horizontal (H) component by vertical (V) component is executed. As per reports of Field and Jacob (1993), Bindi et al. (2000), and Lunedei and Albarello (2010), shape of HVSR possesses no direct link with amplification. It is mention worthy that HVSR shape is dependent on frequency. Even, one cannot infer direct information of subsoil formation, as affirmed by Lachet and Bard (1994), Bard (1999) and Haghshenas et al. (2008). All these facts relate a complex nature of HVSR curve (e.g., Fäh et al. 2001; Albarello and Lunedei 2011 ; Sanchez-Sesma et al. 2011, Lunedei and Malischewsky 2015). Nonetheless, it is argued that the HVSR curve produces a sharp peak owing to existence of a sharp impedance contrast (e.g., Malischewsky and Scherbaum, 2004; Bonnefoy-Claudet et al. 2006). Again, the HVSR peak amplitude is linked to impedance contrast, giving rise to resonance (e.g., Albarello and Lunedei 2011). As pointed out by Lunedei and Malischewsky (2015), there is now two trending research lines. One interprets H/V curve by associating vibration of ambient wave field while the latter one deals with Rayleigh ellipticity. As such, seismic resonance phenomena can be effectively assessed by HVSR. Since VS profile is directly dependent on fr (resonance frequency), HVSR also yields significant attributes that affect the regional response, caused by an earthquake. Although, one cannot infer conclusive seismic amplification solely on it, it can be tuned to yield more exhaustive studies.

Single-station noise assessments are most preferred to quick acquisition of data for microzoning analysis. Recently, several HVSR measurements were executed in the context of Microzonation studies all over the globe. In this regard, Albarello et al. (2015) opined that this method can be regarded as an essential mean to locate the occurrences of resonance mechanism and to limit geometry of main seismic impedance contrasts in an examined area. However, complications arise when the amplitude is affected by more multifaceted local geological settings. For such ground settings, direct inspection is the best tactic to perceive knowledge of local site settings. For regions with a high seismicity, such execution is not achievable. The direct inspection is costly, time-consuming, and also not realistic at all times. Furthermore, the geological complexity and absence of acceptable reference locations impose restrictions on a varied range of approaches, employed to apprehend the role of geology, topography, and soil properties on earthquake ground motion. In this respect, the practice of microtremors is proven to be effective, as no additional data is mandatory for approximating the influence of surface geology on the seismic motion. This technique provides an accurate assessment of shallow and deep seismic structures and several geotechnical belongings of soils (Liu et al. 2000; Bard 2008; Kühn et al. 2011; Nardone and Maresca 2011; Biswas and Baruah 2011, 2016; Biswas and Bora 2017; Biswas et al 2014, 2015, 2018a, b; Singh et al. 2017).

The current study involved techniques including ambient noise of urban area whose objective is to determine vigorous soil response in this geologically multifaceted area. Keeping identical wavefield, we try to associate prevalent geotechnical/geological evidence to attain subsurface profile, aided by simulation techniques. Within the scope of this work, seventy (70) survey points were taken in the study area. Exploiting similarity of HVSR curves, the data have been clustered, thereby enabling robust interpretation of typical geophysical properties of the geological foundations and their seismic response.

Besides, the secondary objective of this work is aimed at designing a 3D shear wave velocity model of the subsurface, by combining the estimated shear velocity profiles with existing geotechnical information. This will help us to deduce the type of the sedimentary infill throughout this populated city, thereby permitting an enhanced understanding of the depositional procedures involved in the development of city deposit. Besides, eventual identification of areas capable of magnifying soil shaking at the time of probable high magnitude earthquake can also be executed.

2 Description of the Study Area

Geotechnical site characterization is of prime importance so far seismic hazard is concerned. It becomes crucial for a region exhibiting active seismicity. Northeast India is characterized by active seismotectonics. It has already witnessed two devastating earthquakes having magnitude 8.7(MS) (1897) and 8.6(MS) (1950) (Bora et al. 2018). In recent years, there has been a rise in the number of felt tremors which has become a potential challenge for geoscientists, seismologists so far earthquake hazard is concerned. It is a matter of concern that most of the populous cities of north-east India are located in alluvial sediments and nearer to river banks. There has been instrumental records of twenty-five felt earthquakes having magnitudes of 3.1–5.4 (Mw) till now. Furthermore, the active Kopili fault zone (Bora and Biswas 2017, 2018; Bora et al. 2017, 2018, 2020) is in close proximity to this study area (Fig. 1b). The proposed study area is a prominent commercial hub and a tourist spot with a considerable population density ~ 5000/km2. During last 10 years, more than seventy moderate earthquakes had jolted this area and its vicinity. Of late, there has been a considerable rise in the no. of earth tremors. Out of that, more than five earthquakes had its epicenter in and around this study region, having the highest magnitude of 4.5. All of them were felt earthquakes. Another 5.5 (Mw) earthquake jolted (maximum intensity felt III as per USGS) the area and its vicinity on November 6, 2013(IMD). The epicenters of the event was merely 80 km from it. As per reports, it caused damages to buildings. Very recently, another earthquake of magnitude 4.9 (Mb) at depth of 10 km (IMD), was felt (maximum intensity felt V as per USGS) at a distance of approximately 30 km from this study area on 11 June 2018 (https://earthquake.usgs.gov). Bureau of Indian Standards (BIS, 2002) categorized this city under zone V having a peak ground acceleration (PGA) of 0.36 g. It is worthy to mention here that potential threat in terms of damage may occur when there is a prolonged duration of ground shaking, regardless of the small magnitude of earthquakes. Particularly, settlements, where there is a predominance of Holocene sediments, are largely influenced by ground motion compared to more competent bedrock strata. The study area is no exception. Over the years, the city has expanded tremendously. As a matter of fact, more multistoried structures are being built due to rising population. Looking at this recent rise of small to moderate felt ground motions, it is customary to look into the hazard aspect.

Fig. 1
Fig. 1
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a, b Simplified geological map North east India. c Geological map of the Sonitpur District and the black square box represent the region chosen for this study

3 Data Used

70 single-site measurements were conducted in the urban area [Fig. 2a, red circle]. Out of which, only 47 measurements were chosen for the conclusive inspection, thereby eliminating those with no clear H/V peaks. Towards acquisition, a 500 m × 500 m grid was deployed. However, there are some restrictions while taking the survey in an urban settlement, based on equispaced grid formulation. Due to lack of some logistics, we were not able to carry out the survey at some points. However, our goal was to cover the entire urban area of the study region. As shown in Fig. 2a, the spatial locations of survey sites are not uniformly distributed. Along the Brahmaputra River area, sufficient survey points were taken as we expected deep sediments profile in that area.

Fig. 2
Fig. 2
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a Urban map of the investigated area displaying the location of survey points. The demarcated cross-sections are also specified. b Topographical profile of Tezpur city chosen for this study. Color bar represent the elevation in meters

All measurements were done in such a way that impact of near-source man-made noise were ineffective to the maximum possible extent. The recording was done for 40 min at each site, using a Reftek 130, 3 component broadband seismograph (Trillium 120P seismometer) with a natural frequency range (0.0083 Hz–20 Hz) coupled with a digitizer (100 samples per sec). It was ensured during recording process that there was good soil-sensor coupling. The data acquisition period was extended up to one hour for those areas where manmade activities were more severe. Moreover, to evade probable low-frequency disturbances triggered by wind, the data acquisition was performed in good environment. We had processed the obtained data by adopting Geopsy software package (https://geopsy.org). After dividing the entire waveform into 40-s window, we utilized the Fourier transform method to each window. We select such window lengths to have maximum number of cycles for the lowest frequency analyzed, which helps to have a stable mean over H/V ratio. The other applied conditions to the window are a 5% tapering and a smoothing factor of 40 (Konno and Ohmachi 1998). The HVSR processing parameters are as follows: STA of 1 s, LTA of 30.00 s, with minimum and maximum STA/LTA of 0.2 and 3.0, respectively. Subsequently, the HVSR estimates were executed as per SESAME (2004) guidelines.

4 Methods Used

4.1 H/V Technique

This method has attained good popularity and is commonly practiced, outsmarting other geophysical passive methods. According to Okada (2003), this method is based on assessment of ambient vibration, engaging low energy and amplitude levels. This has been proven to be one of the most acceptable procedures among others for estimating fr of soft deposits. The H/V method is not connected to any reference site. It comprises of estimating resonance frequency in the frequency domain along with a relative amplification, recorded at a station by calculating the average ratio of the horizontal to the vertical component of amplitudes of the recorded noise (Lermo and Chavez-Garcia 1993; Cartiel et al. 2006; Perton et al. 2016). Further, Lermo and Chavez-Garcia (1994), reported that spectral properties and polarization of seismic noise show a solid correlation with site geological sceneries.

Due to surface wave entrapment in layers, resonance effects can be observed in a planar-layered stratigraphy with varying levels of impedance contrast. It may include ruptured layers of covering bedrock or soft sedimentary layers. The fr of the upper level thus resembles ratio between average velocity (VS) and thickness (h) which is expressed as.

$$f_{r} \, = \,V_{s} /4 h$$
(1)

Castellaro and Mulargia (2009), observed that, if iri is the central frequency of the ith peak in the H/V-frequency curve, a natural peak (i.e., a peak analogous to a possible reflector or seismic-stratigraphic level) is undoubtedly signified by “eye-shaped” detachment in spectral curves of horizontal components from the vertical one centered at fri (SESAME 2004). Along with it, a H/V curve having amplitude of < 1 around 2fri also appeared. In practice, H/V curves show numerous peaks that are affected by existence (at variable depths) of several discontinuous layers of diverse lithology rather than by the presence of horizontal stratification in identical layers (Nakamura 1989; Fäh et al. 2001; Herak 2008). It is interesting to note that, the so-called osculation points of the Rayleigh dispersion curves have an influence on the behavior of the H/V curve (Lunedei and Malischewsky 2015). Even in the simple model "Layer over Halfspace (LOH)", two peaks of H/V can occur which are usually attributed to a much more complicated configuration. Moreover, the peak of average H/V amplitude curve is related to impedance contrast between upper and lower strata (Moisidi et al. 2012). Once the layer depth or its VS is known, it is feasible to regenerate the seismic stratigraphy and subsurface model, and as a result, there is a translation from H/V-frequency domain to the depth-VS domain (Lane et al. 2008; Castellaro and Mulargia 2009; Biswas et al. 2018b).

4.2 H/V Inversion Using DFA Theory

Sánchez-Sesma et al. (2011) have recommended that ambient noise forms a diffuse wave field comprising all types of body (P and S) and surface waves (Love and Rayleigh). Multiple random uncorrelated sources near to or at the earth surface generate this noise wave field. The wave field may contain the multiple scattering effect of various elastic mode. Within DFA, it is assumed that the relative power of each seismic phase is agreed with the energy equipartition principle. Under this hypothesis, the auto-correlation in frequency domain, at any point of the medium is proportional to the imaginary part of the Green's function.

Perton et al. (2009) showed that for a pure 3D-diffuse, equipartitioned, harmonic displacement vector field ui(x, ω) within an elastic medium, the average auto-correlation of motions at points xA and xB can be written as

$$\langle {u}_{i}\left({x}_{A},\omega \right){u}_{j}^{*}\left({x}_{B},\omega \right)\rangle \propto Im\left[{G}_{ij}\left({x}_{A}, {x}_{B},\omega \right)\right]$$
(2)

where \({G}_{ij}\left({x}_{A}, {x}_{B},\omega \right)\) is the displacement Green's function at xA in the direction i produced by a unit harmonic point force at xB in direction j, ω is the circular frequency.

For a diffused wave field, if both source and receiver coincide (i.e., xA = xB = x), and the corresponding components are same, the autocorrelation average corresponds to the directional energy density Ei(x, ω) at point x as

$${E}_{i}\left(x,\omega \right)=\rho {\omega }^{2}\langle {u}_{i}\left({x}_{A},\omega \right){u}_{i}^{*}\left({x}_{A},\omega \right)\rangle \propto Im\left[{G}_{ii}\left({x}_{A}, {x}_{A},\omega \right)\right]$$
(3)

where \(\rho\) is the mass density.

For a diffused wave field, the H/V can be represented in terms of directional energy densities assuming source and receiver having same location x on the earth surface as

$$\frac{H}{V}\left(x, \omega \right)=\sqrt{\frac{{E}_{1}\left(x, \omega \right)+{E}_{2}\left(x, \omega \right)}{{E}_{3}\left(x, \omega \right)}}$$
(4)

where, E1, E2 and E3 are the directional energy densities for the two horizontal (E1 and E2) and the vertical (E3) degree of freedom.

$$\frac{H}{V}\left(x, \omega \right)=\sqrt{\frac{Im\left[{G}_{11}\left(x, x,\omega \right)\right]+Im\left[{G}_{22}\left(x, x,\omega \right)\right]}{Im\left[{G}_{33}\left(x, x,\omega \right)\right]}}$$
(5)

The DFA model, assumes that the horizontal directions are indistinguishable e.g.,

$$Im\left[{G}_{11}\left(x, x,\omega \right)\right]=Im\left[{G}_{22}\left(x, x,\omega \right)\right]$$
$$so, \frac{H}{V}\left(x, \omega \right)=\sqrt{\frac{2Im\left[{G}_{11}\left(x, x,\omega \right)\right]}{Im\left[{G}_{33}\left(x, x,\omega \right)\right]}}$$
(6)

This last equation links the function H/V with the subsoil mechanical properties; thus, the resulted H/V curve from the DFA model might allow its inversion without considering any supplemented information (dispersion curve).

The inversion was done based upon the recently established inversion scheme developed by García-Jerez et al. (2016) and Piña-Flores et al. (2016). The blind inversion can be quite cumbersome because it may associate a huge search within parameter space and the convergence can require long time or even can't be reached. In order to hasten the search of solutions, it is convenient to delineate upper and lower bounds of target values, by means of a priori information (e.g. borehole, geology and geophysics information) or examining the form of the experimental H/V itself. In order to obtain the formerly demarcated parameter space, a large number of pseudo-random models are produced. S- and P-wave velocity, layer thickness and density of soil are the required parameters. The Poisson's ratio is fixed in between 0.2 and 0.5 (standard values for soils and rocks).

As per Scherbaum et al. (2003), by merely using H/V ratio, we cannot decipher main trade-off amongst layer thickness and shear velocity. For this reason, it is crucial to use some of these parameters from existing independent sources. Therefore, we used existing SPT data and earlier geotechnical measurements to delimit parameter space, i.e. number of layers and thickness and shear-wave velocity ranges. In our study, borehole information is used to define the initial layer associated with soft sediments.

Each H/V spectral ratio is attained from forward calculations of corresponding sampled models, and is compared with the experimental H/V curve utilizing a misfit function (Piña-Flores et al. 2016). This comparison reveals the proximity of the created model to the empirical H/V curve. Therefore, a number of S-wave velocity profiles were obtained by following this process and were compared with identical H/V curves via misfit values.

Fäh et al. (2001, 2003) opined that H/V ratio of ambient vibration is influenced by Rayleigh wave ellipticity of fundamental mode, incurred by an enormous impedance contrast amongst sediment deposits and bedrock. The applied frequency band mainly consists of the initial lowest values of the mean H/V curve and the resonant frequency of the deposited cover. Within this frequency band, the nature of the curve generally rests on depositing sediments.

For our study, we have picked the frequency band for the inversion process close to the main resonant peak, which is mainly within the range of 0.5 Hz–10 Hz. The frequency band was increased only when we detect a secondary peak, which might yield some information regarding other existing velocity contrasts.

5 Results and Discussion

5.1 H/V Analysis

Figure 3 shows some typical examples of obtained H/V curves using the popular GEOPSY software. The dashed lines describe the Standard Deviation of mean H/V values whereas the black solid line signifies mean H/V curve. The obtained results from the 47 survey points, randomly distributed within the study area, varied considerably. Overall, three types of H/V curves were acquired: (i) clear H/V peaks as shown in Fig. 3 (point TZ_44), (ii) two or more peaks as shown in Fig. 3 (point TZ_18), and (iii) broad flat curves with less amplitudes as shown in Fig. 3 (point TZ_09).

Fig. 3
Fig. 3
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a–e H/V curves computed using Geopsy software for few selected sites as indicated in top corner. f–j Corresponding directional analysis on H/V curves. Frequency is plotted along x-axis while direction (the position is calculated clockwise from North) is plotted along y-axes. The amplitude of H/V curves is represented by the color scale

The analysis exhibits a predominant frequency range within 0.5 Hz (e.g. Site TZ_18) to 3 Hz. A clear low-frequency range (as indicated by Site TZ_18) is evident mainly in a pocket region of the city. This low frequency is resulting from the largest energy at a low frequency of the horizontal ground motion compared to the vertical one. There is a zone having predominant frequency within the range 0.5–1.5 Hz moving from north-west to the south-east (Fig. 4a); although this moderate frequency zone has dissimilar amplitude levels (Fig. 4b). The amplitude of the H/V hump around this predominant frequency is higher in the north-west part (within the range 4–5.5) as compared to the central part (within the range 1.5–2.5) of the city.

Fig. 4
Fig. 4
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a Terrain map of study area with Contour map showing fundamental frequency (f0) in Hz in the Tezpur City b Contour map showing H/V spectral amplitude in the Tezpur City (c) Contour map showing Vs30 profile estimated using Madera (1970) formula

There is always a doubt regarding influences of body wave and surface wave over H/V curves. If we presume that surface wave overlook the H/V curve, then the foremost parameters responsible for the H/V peaks and troughs are the velocity contrast and Poisson's ratio of the soft soil deposit (Bonnefoy-Claudet et al. 2006; Lunedei and Albarello 2010; Tuan et al. 2012). The disparity in the position of predominant frequency and in the amplitudes of the H/V hump, moving from north-east to south-west, could be theoretically linked to a thickness transition from soft-to-bedrock edge. This can also be attributed to an adjustment of velocities and Poisson's ratio of soft deposits concerning those section of the city.

Likewise, we find broad H/V peaks. Low amplitude H/V or broad flat curves are usually associated to stiff soils (high shear wave velocities) in sites with low impedance contrast with the underlying bedrock. This may be a hint of prevalence of a dipping underground interface amongst softer and rigid layers at depth. It seems that underground configuration of the city reveals conspicuous lateral disparities, with plausible generation of two or three dimensional effects (Perton et al 2017). Such wide peak of H/V curves are indeed observed on various basin or valley edges. In our previous work using coda wave H/V spectral ratio (Bora and Biswas 2019), we reported a high shear wave velocities at deeper depths bellow strong motion recording stations for this region. However, we refrain from inferring resonance frequency from such types of peaks without having earthquake data.

The presence of secondary peaks in some survey areas may indicate the existence of shallower impedance contrast beneath. As shown in Fig. 3 (site TZ_09), we found two peaks; the lower peak could be selected as the fundamental one, whereas the higher one could be connected to the presence of shallower impedance contrast such as recent alluvium and old alluvium.

Figure 3f–j also illustrate the directional behavior of H/V ratio, as a function of azimuth as well as frequency. The North and the East direction are designated as an angle of 0° and 90°, respectively. Such plots visibly specify that resonance frequency is practically independent of azimuth, nullifying 2-D effects. Only longitudinal polarization behavior of the wave field is observed which is highlighted by the highest H/V amplitude values at angles within the normal range from 0° to 90°. Besides, the smallest value is observed at < 80° at sites TZ_33, TZ_18, while, in other sites, it is less evident.

As seen in Fig. 4b, for a major part of the study area, the obtained H/V spectral ratios show values varying from 1–2.5. This moderate amplification of H/V having a predominant frequency range from 0.5 to 1.5 Hz could be associated with the presence of velocity inversion between the underlying soil layers which are discussed in the following portions.

There is an anomaly observed in the riverside of this region where larger amplitudes observed. In this part, it is noticed that (from Fig. 4a, b) it exhibits higher values of H/V amplitudes in the high-frequency range (within 2.5 Hz–3.5). For these peaks, the obtained amplitude of the H/V varies between 3.5 and 8. This is probably due to the presence of outcropping bedrock. As per Mora et al. (2001), these higher frequency peaks possibly indicate resonance within the individual thin layers, arising from enormous impedance contrast with the adjacent material.

It is already established that, during an earthquake, the seismic ground motion can be amplified by the regional soil settings along with geo-morphological anomalies. The situation would be useful to authenticate if the strong fundamental resonance of the study area can be considered as a topographic effect. A joint outcome of theoretical as well as experimental results is that uppermost sites show amplification of ground motion with respect to those at the base. Few components of topographic feature, mainly the horizontal irregularities (e.g. mountain width), are comparable with incident wavelengths. As reported by Kamalian et al. (2008), the topographic effect is trivial for elongated wavelengths. Ashford et al. (1997) demonstrated that the frequency due to topographic effect is equivalent to VS/5H for a steep slope of elevation H. The value of H for this region is about 48 m (Fig. 2b), and VS is of the order of 200–375 m/s (Chopra et al 2018). Accordingly, we have calculated the topographic frequency as 0.8–1.6 Hz which tally well with the perceived resonance frequency for a major part of this study area (Fig. 4a).

5.2 Estimation of Liquefaction Vulnerability

From the above discussions, it is clear that the estimated resonant frequencies and amplifications are in best approximation to the geotechnical data, as obtained from existing borehole. This leads us to estimate the soil vulnerability index of this region. Nakamura (1996) suggested the Kg value (liquefaction vulnerability index) to compute vulnerability of soil, concerning liquefaction. Kg values are assessed using empirical relationship between amplification (A0) and fundamental frequency (f0), as given by Kg = A02/f0 (Nakamura 1996). It can be seen from Fig. 5 that the Kg value varies from 5 to > 50. A few points along the Brahmaputra River and some pocket regions of the city show high Kg values (Fig. 5). The larger Kg values are also supported by the lower f0 and higher A0 estimates (Fig. 4a, b). It is important to cite that, the entire city is developed above the alluvial deposits and falls in soil type of class B (Chopra et al 2018). In general, such types of soil have low Kg (< 10) values, with few exceptions at few areas. Several reprted works concur that sites, with Kg values greater than 10, undergo liquefaction during strong ground motions (e.g., Nakamura 1996; Singh et al. 2017). The estimates of Kg attained for our study imply that the whole area has less probable damage due to liquefaction except for few pocket regions where we estimate high values.

Fig. 5
Fig. 5
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Terrain map of study area with Contour map showing liquefaction vulnerability index in the Tezpur City

5.3 Velocity Profile from Inversion

Since phase velocities are more sensitive to the S-wave velocity arrangement than to the P-wave velocity and density arrangement, as such, we present only the shear-wave velocity profiles for this city. A three-layer model over a half-space (may be a sedimentary deposit) was anticipated as the preliminary model for the inversion, based on existing lithological and geological evidence (Fig. 6).

Fig. 6
Fig. 6
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Available geological borehole data for the study region. The position of the logs is indicated

Herein, a global-search inversion procedure (e.g., Yamanaka and Ishida 1996), mainly the genetic algorithm method, was implemented due to the lack of prominent a priori data. This is simply a Monte Carlo method that enables the user to search the entire parameter space (which includes a group of layer densities, velocities, thickness and Poisson's ratio). For such inversion process, we can't obtain a solo solution; therefore, a large number of simulated models are produced within the parameter space. Using this algorithm, each H/V curves are inverted for subsurface S and P-wave velocity profiles within a frequency band of 0.5–10 Hz. In Fig. 7, we have shown a variety of velocity models. As an illustration [Fig. 7a], we have obtained a decent match of the experimental H/V.

Fig. 7
Fig. 7
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a, b, c, d Represent the estimated shear wave velocity profiles at survey points Tz_P08, Tz_P29, Tz_p33, and Tz_P43. The black line represents the experimental H/V curve, red line represents the calculated H/V curve while the dashed line represents the SD of the experimental H/V curve [In the left panel]. The best fitted inverted velocity profile is shown in solid black line [in the right panel]

With a view to assess the appropriate parameterization, we have verified numerous iterations with diverse limitations to find the best fit of the experimental curve. Since available geotechnical profile shows only 3 distinct layers for the study area, hence we reduced the number of layers up to 3, excluding the half-space. Few of the estimated velocity profiles were exemplified in Fig. 7. For each survey points, we have shown two panels. On right one, we display the inverted best-fitting velocity model (in black). On the left panel, the red line represents the calculated H/V curve while the black solid line represents the experimentally obtained H/V curve. The dashed line represents the SD of the experimental H/V curve. The areas are typically categorized as a three-layer profile. The minimum misfit values validate the good correlation between empirical and experimental information. The eminence of the profiles may also be appreciated by verifying the inconsistency of models lying within the range of ‘minimum misfit’ + 10% concerning the finest one. Though, it is highly dependent on the precise features of the respective site, such inconsistency rises with buried depth. Last deposited layer for each generated model may be associated with presence of basement materials or a layer having higher VS values. The depth of this layer varies significantly from one point to another. Above basin basement rocks, one or two layers may be found within the sedimentary fill depending on the profile considered.

In order to compare our retrieved shear wave velocities, we used the well-known Madera (1970) formula, which can be expressed as

$${V}_{{S}_{avg}}=\frac{\sum_{i=1}^{n}{h}_{i}{V}_{{S}_{i}}}{\sum_{i=1}^{n}{h}_{i}}$$

where, hi is the thickness of individual layer having shear wave velocity Vsi. The calculated average velocities up to 30 m depth are almost comparable with the site resonance frequency and cation (Fig. 4c).

5.4 Fundamental Peak Frequency and Relationship with Irregular Subsurface Structures

To examine the variation between the sediment depths of the subsurface structure and the peak frequency, we have selected six cross-sections. This is demarcated by solid lines in Fig. 2a. Figure 8 displays six unique 2D cross-sections of the study region (see the position in Fig. 2a) up to a depth of 100 m.

Fig. 8
Fig. 8
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Cross-section of the study area along 6 distinct sites as shown in Fig. 3a, Four layers are segregated: The uppermost layer (demarcated by dark area), the intermediate layer (demarcated by light area), the third layer (delimited by dashed straight lines) and the basement formation

It has already been reported that fundamental frequencies f0 of H/V curve and distributions of VS30 are well connected with confined geology and topography (Di Giulio et al 2014; Leyton et al. 2013; Paolucci et al. 2015; Stanko et al. 2016). Based on thickness of sediment deposits above bedrock, we have estimated the VS30 profile by using VS30 = 4f0*h (where h = 30 m for simplicity) (Pitilakis 2007; Paolucci et al. 2015; Stanko et al. 2016). Figure 8 displays six cross-sections; each of them having four distinct layers. Firstly, the uppermost one is associated with recent new alluvium (having VS values within 208–272 m/s); secondly, one mid layer is associated with existence of old alluvium (having velocity range 128–192 m/s). Thirdly, one buried layer is possibly associated with early sedimentary deposits of the basin fill (with VS values within 220–316 m/s). Finally, the basement conformation exists (279 < VS > 471 m/s). Usually, with age and burial depth, the value of VS increases, which is also observed in our study. The divisions have been also juxtaposed and finalized with available lithology and accessible superficial geological evidence (as revealed in Fig. 6.).

For simplicity, we consider the fourth layer as our basement (mainly a sedimentary deposits). So, by combining the first three layers, we can calculate the basement depth. We can see that the frequency profiles are not linearly dependent with the basement depth. In Fig. 8d, the obtained subsurface profile for DD′ shows a linear dependency with the fundamental frequency. It is noticeable that there is a decreasing fundamental frequency with increasing basement depth. But in other profiles, there is no dependency. This can be attributed to presence of a few high-velocity pocket region within the subsurface layer. It is noticed from this estimated cross-sections that there is a rise in basin thickness towards the Brahmaputra River area (as seen from AA′, EE′ and FF′ in Fig. 8a, e, f). From Fig. 8 b, c, f, it has been observed that, while moving along BB′, CC′ and F′F, the thickness of the third layer varies considerably than the remaining cross-sections. This may be linked with basement uplift which also affects the deep layer. In Fig. 8c, we have noticed that, along the SW part, the basement attained its highest depth with respect to the remaining cross sections.

Though we used a wide velocity range for each layer, the attained VS values are compatible with the borehole data (Fig. 9). Despite having inadequate borehole data, it was observed that the available two borehole data, being in close proximity to survey points Tz_P10 and Tz_P45, are comparable with the retrieved velocity profiles to a considerable extent. Accordingly, it can be asserted that the obtained layers can be validated using such borehole profiles. These results also may reveal the presence of a horizontal discrepancy of VS values for this region due to variations in the subsurface configuration. This is again affected by the deposited soils from Brahmaputra River which is inter-stratified at various places. These consequences and the shear wave velocity variations within the layers are in good conformity with the borehole. The width of the soil profile differs considerably within the city which is supported by the additional information obtained from boreholes. It was revealed from the borehole that the whole area comprised of alluvial soil with alternate deposits of clays of dissimilar plasticity, silty clayey, clayey sand and occasionally clayey mixed with fine sand with the standard penetration test. Due to lack of borelogs deeper than 30 m, we are unable to estimate the thickness of the weathered sandstone.

Fig. 9
Fig. 9
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Comparison of the inferred velocity profile up to top 30 m for two survey points having borehole drilling data. The color represents the same legend as in Fig. 6

Figure 10 displays the obtained VS values in a histogram form for each layer. The figures are clear demonstration of variation of VS values within each layer. Accordingly, a normal distribution with predominant velocity at 300–400 m/s was noticed for the layer above the basement (3rd layer). The basement also reveals a reasonable distribution of VS at 300–400 m/s. However, there is also high-velocity distribution available for this basement. In the intermediate layer (2nd layer), highest proportion is available within 200–300 m/s. In the surface layer (1st layer), VS at 200–300 m/s is clearly predominant, but there, we have also observed another velocity range within 300–400 m/s. The estimated VS values for each layers may be useful for future ground response study, which will facilitate understanding of how these parameters varies with the deposited soil layers. This large variability may indicate that the layer is not a single geological unit, but rather it consists of several types of soils.

Fig. 10
Fig. 10
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Histogram represents the estimated VS values for individual layer. The estimated VS values are sorted in 100 m/s steps. The vertical axis represents the percentage of occurrence frequency

In order to confirm the consistency of these findings, it is advisable to double check geophysical data with geological data. Accordingly, borehole logs were also compared with the obtained depth profile. As shown in Fig. 6, the thickness was correlated to the available borehole data and it was found that the borehole did not encounter bedrock within the upper 30 m. in our study region.

5.5 Estimating 3D-VS Model

Finally, in order to apprehend the underneath subsurface structure, we have attempted to develop a 3D velocity model for this region. We have utilized the results, obtained from the inversion based on DFA methods. Then, we export the data from all the available velocity-Depth contour map and try to obtain a dependable and robust 3D profile without losing its resolution. Furthermore, different parameterization procedure were also applied. On the basis of obtained data points and assuming the near-surface velocity and thickness to be the important factors, the optimum result was acquired by using a 2 Ã— 2x5-m (along with x-, y-, and z-axes) grid spacing on a linear interpolation pattern with values at every 2 m. We also tried to reduce grid spacing further, but while doing this the survey points and the depth profiles estimated using the DFA scheme were distributed unevenly, and the resulting model exhibited undesirable velocities. Herein, we have eventually selected a grid spacing of 2 Ã— 2 Ã— 5-m for interpretation. The resulting 3D velocity-depth models show a vertical velocity variation analogous to the deposited arrangements available for this area. We used Kriging approximation technique, as an interpolation scheme (i.e., Molinari et al. 2012). The usual Kriging interpolation method allows one to describe a strange spatially continuous, random function with some geographical distribution from the samples in a neighborhood of any unsampled location (i.e., Davis 2002).

Figure 11 represents obtained 3D Velocity profiles of the study area. Figure 12b, c, d represent the iso-volumes having VS values 150 m/s, 200 m/s and 400 m/s, respectively. It is obvious that major part of the area is dominated by VS value (= 200 m/s) as seen in Fig. 11c. From Fig. 11b, we can see that there are certain pocket regions in the area with low velocities, as compared to the neighboring sites. These may be attributed to presence of low-velocity medium, as explained in previous sections. Significant lateral velocity variations are also prominent and lateral varying lithology may be the plausible reason for this observation.

Fig. 11
Fig. 11
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3D shear wave velocity profile obtained from interpolation of the inverted Vs values of this study area. a Shows the 3D plot of predominant frequency. b 3D Vs profile showing the iso-volume for Vs = 150 m/s. c 3D Vs profile showing the iso-volume for Vs = 300 m/s. The black arrows indicate the north direction for the estimated volume plot. d 3D Vs profile showing the iso-volume for Vs = 400 m/s. Latitude and longitude are in km and depth in meter scale. The color scale represents the Vs values in m/s

Fig. 12
Fig. 12
Full size image

3D cross-section of the obtained volume profile. a, b, c represents the cross-sections along latitude, longitude, and depth respectively. The color scale represents the VS values in m/s

The resulting 3D velocity model indicates higher average crustal velocities in the southern part. Likewise, a homogeneous velocity (150–300 m/s) for the whole upper crust is contemplated in the well-resolved area of the north-eastern part. Figure 11d shows that depth and velocity distribution are also relatively uniform; except for the iso-velocity surface deepening with some anomaly (represented by the dark blue color region). Similar features are also observed in Fig. 12, where the cross-section of the obtained 3D profile is shown. It is clearly evident from Fig. 12a, b, c; that the 800–1000 m/s velocity zone is only present especially along the southern part of the city. This is an implication of rock volume under that part. From field investigation, such anomaly supports the validity of the velocity model by resembling the general near-surface geology. We have noticed that in these part, a hilly area with outcropping bedrock is located. This is isolate hillocks of the Precambrian basement and is well-foliated medium to coarse-grained granitic gneisses; where, the existence of basement crystalline rock below such alluvial plain is already known (unpublished report).

6 Conclusions

By adopting horizontal to vertical spectral ratio (H/V) and diffused field theory, we have made a systematic imaging of subsurface up to an average depth of 100 m. The results implicate an anomalous pattern of shear wave velocity in the entire region. This finding is well substantiated by available site geology. Some of the conclusive salient features of this work are appended below:

  1. (1)

    The analysis reveals the predominance of single H/V peaks. The resonance frequencies for this area varies between 0.5 and 3 Hz. Throughout, frequency distribution is totally diverse and the estimates are proved to be azimuthally independent. The variation of frequency is seen to tally with the geomorphological signatures in the city and thus the high rise structures are found to be seismically vulnerable in some pocket regions where we estimate high Kg values.

  2. (2)

    The obtained shear velocity from inversion of H/V curve provides evidence of complex nature of the subsurface geological structures.

  3. (3)

    From the inferred S-wave velocity profiles, we have acquired a four layers model depicting local soil geology. This is achieved in synchronization of VS profiles with available borehole logging and superficial geology. Accordingly, 2D cross-sections characterized by six distinct profiles of the entire city are demarcated. From this, a low-velocity intermediate layer was obtained having velocity ranging from 128–192 m/s, while a relatively high-velocity layer (279–471 m/s) can be considered to be as basin basement.

  4. (4)

    Finally, the retrieved 3D shear wave velocity profile give an excellent match with estimated frequency distribution and its corresponding links with depth wise strata.

  5. (5)

    Using the invasive method (drilling), the underground assessment is generally very expensive. Therefore, by using this method, on-site assessment could help to estimate the basement boundary and also save both time and cost.

In summary, we can conclude that there is considerable scope of imaging subsurface to the best reliable extent through diffuse wave field theory, accompanied by HVSR characteristics. Although the results are convincing, yet with further inclusion of more sophisticated geophysical instrumentation, there is scope of attaining high resolution sub-surface profiles. We strongly believe that these results will pave the way to more rigorous analysis.