**3. Calculation of crust-corrected P-relative residual**

For picking P, the measured waveforms from our network are bandpass filtered using the inbuilt WWSSN filter of the seismic handler. This narrow frequency band allows us to study the uppermost mantle without caring about finite frequency effects [13]. In order to calculate relative residuals, only first strong and clear phase (peak or trough) are picked from different stations, with the help of high magnification on the computer screen. Since the sampling rate used for data recording is 50 sps, thus, phases could be picked manually with a precision of at least 0.08 s. Thus, the most of the estimated relative residuals are found to have an uncertainty of less than 0.1 s.

The analysis of broadband waveforms of teleseismic events are used here to estimate travel time residuals, as well as deviations in slowness and back azimuth about the standard earth model iasp91 [14]. A travel time residual can be defined as

**35**

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume…*

iasp91). Now, a systematic bias to rij could be resulted from following sources:

To isolate information underneath the receiver network, the average of all measurements (n) of a phase j is subtracted from the estimated relative residual

<sup>r</sup> = rij − (1/n)∑

Thus, the residual part, which is common in all measurements, is eliminated. Therefore, the remaining part of traveltime residual, which is caused by heterogeneity below the receivers, defines the relative residual. This normalization (Eq. (2)) produces an equal amount of positive and negative residual times per phase with a zero mean. Now, to use these relative residuals in tomographic inversions, a weighting scheme following Evans and Achauer [15] has been used here. The weights wij are assigned while picking the arrival times based on arrival time uncertainties (d) and SNR of the picks. We use four different weights (1, 2, 3, and 4): 1 = 1.0 for d ≤ 0.05 s, 2 = 0.2 for 0.05 s < d ≤ 0.1 s, 3 = 0.1 for 0.1 s < d ≤ 0.2 s and 4 for d ≤ 0.2 s. The picks with quality 4 are excluded from the further analysis.

After estimating relative travel time residuals using Eq. (2), these residuals are corrected from already known heterogeneous crustal anomalies and the travel time anomalies from the top sediments, which generally cause unwanted smearing effects of the residuals along the steep teleseismic ray paths [15, 16]. An available detailed crustal velocity model is used for this purpose and then these residuals are

<sup>m</sup> = tij

<sup>m</sup> − rij

It is well-established fact that significant travel time residuals can be caused by the heterogeneous continental crust. Further, large delays of the order of 1 s can be resulted from the low-velocity sediments in the rift basins (like Kachchh) or/either the Moho topography, which laterally replaces mantle (Vp ~ 8 km/s) and crustal (Vp ~ 6.5 km/s) material. Thus, the relative residuals should be corrected from such known crustal residuals to study the deep mantle structure. Therefore, these crustal anomalies should be determined a priori and subtracted [16, 17]. Following Martin et al.'s [16] approach, here the crustal corrections are applied using the iasp91 reference earth model consisting of a 20 km thick upper crust with a Vp of 5.8 km/s and a 15 km thick lower crust with a Vp of 6.5 km/s. To apply crustal correction, top

*i*=1 *n*

<sup>m</sup> − tij

i.the uncertainties in origin time and hypocenter location of the teleseismic events

m is the measured arrival time of a teleseismic phase j from an event at

is the theoretical arrival time derived from an earth model (e.g.,

<sup>t</sup> (1)

*rij* (2)

crust) relative to the background

crust (3)

*DOI: http://dx.doi.org/10.5772/intechopen.83738*

ii.the source side heterogeneity.

t

using the following equation,

rij

**3.1 Estimation of relative travel-time residual**

corrected from crustal travel time anomalies (rij

earth model using the relation:

**3.2 Crustal correction**

tij,c

where tij

ith station and tij

rij = tij

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume… DOI: http://dx.doi.org/10.5772/intechopen.83738*

$$\mathbf{r}\_{\vec{i}\vec{j}} = \mathbf{t}\_{\vec{i}\vec{j}}^{\text{m}} - \mathbf{t}\_{\vec{i}\vec{j}}^{\text{t}} \tag{1}$$

where tij m is the measured arrival time of a teleseismic phase j from an event at ith station and tij t is the theoretical arrival time derived from an earth model (e.g., iasp91). Now, a systematic bias to rij could be resulted from following sources:

i.the uncertainties in origin time and hypocenter location of the teleseismic events

ii.the source side heterogeneity.

*Forecasting Volcanic Eruptions*

**34**

than 0.1 s.

**Figure 2**

**3. Calculation of crust-corrected P-relative residual**

*shows our study area considered for our P-wave teleseismic tomography.*

For picking P, the measured waveforms from our network are bandpass filtered using the inbuilt WWSSN filter of the seismic handler. This narrow frequency band allows us to study the uppermost mantle without caring about finite frequency effects [13]. In order to calculate relative residuals, only first strong and clear phase (peak or trough) are picked from different stations, with the help of high magnification on the computer screen. Since the sampling rate used for data recording is 50 sps, thus, phases could be picked manually with a precision of at least 0.08 s. Thus, the most of the estimated relative residuals are found to have an uncertainty of less

*(a) Crust corrected relative P-residuals in Gujarat. (b) Directional mean of P-residuals by subtracting an average residual from the eight stations in Kachchh. Red open circles mark negative residuals while blue open circles show positive residuals. CRZ marks the Cambay rift zone, which is shown by dotted lines. Black dotted elliptical area mark the central Kachchh rift zone characterized by negative residuals. And, black square area* 

The analysis of broadband waveforms of teleseismic events are used here to estimate travel time residuals, as well as deviations in slowness and back azimuth about the standard earth model iasp91 [14]. A travel time residual can be defined as

To isolate information underneath the receiver network, the average of all measurements (n) of a phase j is subtracted from the estimated relative residual using the following equation,

$$\mathbf{r}\_{\text{ij}}\,^{\text{r}} = \mathbf{r}\_{\text{ij}} - \left(\mathbf{1}/\mathbf{n}\right)\sum\_{i=1}^{\text{pl}} r i j \,\tag{2}$$

Thus, the residual part, which is common in all measurements, is eliminated. Therefore, the remaining part of traveltime residual, which is caused by heterogeneity below the receivers, defines the relative residual. This normalization (Eq. (2)) produces an equal amount of positive and negative residual times per phase with a zero mean. Now, to use these relative residuals in tomographic inversions, a weighting scheme following Evans and Achauer [15] has been used here. The weights wij are assigned while picking the arrival times based on arrival time uncertainties (d) and SNR of the picks. We use four different weights (1, 2, 3, and 4): 1 = 1.0 for d ≤ 0.05 s, 2 = 0.2 for 0.05 s < d ≤ 0.1 s, 3 = 0.1 for 0.1 s < d ≤ 0.2 s and 4 for d ≤ 0.2 s. The picks with quality 4 are excluded from the further analysis.

#### **3.1 Estimation of relative travel-time residual**

After estimating relative travel time residuals using Eq. (2), these residuals are corrected from already known heterogeneous crustal anomalies and the travel time anomalies from the top sediments, which generally cause unwanted smearing effects of the residuals along the steep teleseismic ray paths [15, 16]. An available detailed crustal velocity model is used for this purpose and then these residuals are corrected from crustal travel time anomalies (rij crust) relative to the background earth model using the relation:

$$\mathbf{t}\_{i\mathbf{j},\mathbf{c}}^{\ \mathbf{m}} = \mathbf{t}\_{i\mathbf{j}}^{\ \ \ \mathbf{m}} - \mathbf{r}\_{i\mathbf{j}}^{\ \ \ \text{crust}} \tag{3}$$

#### **3.2 Crustal correction**

It is well-established fact that significant travel time residuals can be caused by the heterogeneous continental crust. Further, large delays of the order of 1 s can be resulted from the low-velocity sediments in the rift basins (like Kachchh) or/either the Moho topography, which laterally replaces mantle (Vp ~ 8 km/s) and crustal (Vp ~ 6.5 km/s) material. Thus, the relative residuals should be corrected from such known crustal residuals to study the deep mantle structure. Therefore, these crustal anomalies should be determined a priori and subtracted [16, 17]. Following Martin et al.'s [16] approach, here the crustal corrections are applied using the iasp91 reference earth model consisting of a 20 km thick upper crust with a Vp of 5.8 km/s and a 15 km thick lower crust with a Vp of 6.5 km/s. To apply crustal correction, top

sedimentary layer is assumed to be composed of Cenozoic sediments (Vpsed ~ 2.41–4.60 km/s) and Jurassic/Mesozoic sediments (Vpsed ~ 4.61– 5.58 km/s). The estimated corrections of the travel time residuals for such 1-D known crustal velocity models in the region vary from 0.29 to 0.79 s for P-waves.

A total of 241 teleseismic events (Mw 6.0–8.0) have been analyzed to estimate crust corrected P-residuals using Eq. (3), they are found to be stable for stations in the Kachchh network (**Figure 2**). From **Figure 2**, we notice that there is no clear anisotropic signal in the P-residuals in most of Kachchh region except the Motapaya (MTP) station, which is the northernmost station in Kachchh. **Figure 2** shows a plot of estimated crust corrected relative P-residuals at 14 stations as a function of slowness (p) (0–10 s/o along the radial axis) and back azimuth (BAZ 0–360°) to the event. In general, early P-arrivals are noticed for events in the east of the network while delayed P-arrivals are observed for events in the west. Most of the stations, which are lying in the Deccan basalt covered regions in the Kachchh and Cambay rift zones, show negative residuals. This could be attributed to the presence of significant crustal and lithospheric upwarping below these rift zones [18, 19]. At MTP, travel time residuals show images of the spatial variation of wave propagation anomalies of P-waves, which can be attributed to an anisotropy structure of the mantle domains (**Figure 2a**). This anisotropic nature of P-waves is not seen for other stations due to fewer numbers of observations.

The directional term of relative crust-corrected P-residuals is calculated by dividing the 0–360 to 18 quadrants, and then we calculate the average residuals of stations falling in a particular quadrant. And finally, we estimate the arithmetic mean of the average residuals of stations falling in all 18 quadrants. Subsequently, this mean of residuals is being subtracted from the relative crust-corrected P-residuals for different stations for estimating the directional term of relative crust-corrected P-residuals. Following the above procedure, we also computed directional term of relative crust-corrected P-residuals, which are plotted in **Figure 2b**. The directional mean of P-residuals, which are obtained by subtracting average residuals of all stations in Kachchh, is shown in **Figure 2b**. While **Figure 2b** represents the directional mean of P-residuals, which are calculated by subtracting average residual of 8 stations in Kachchh. Most interestingly, two distinct zones of negative P-residuals associated with Kachchh and Cambay rift zones are noticed from **Figure 2b**. These zones of negative P-residual probably mark the regions of marked lithospheric thinning. This model gets further support from available estimates of crustal and lithospheric thicknesses, suggesting a marked crustal and lithospheric thinning below the Kachchh and Cambay rift zones [18, 19].

### **4. P-wave teleseismic tomography**

The teleseismic tomography code developed by Weiland et al. [20] and later modified by various investigators [21–24] has been used here to estimate the 3-D P-velocity structure down to 250 km underlying the Kachchh rift zone (KRZ). The data collected by the digital networks of NGRI (Hyderabad, India) and ISR (Gujarat, India) are combined, resulting in a dataset from a total of 59 stations (**Figure 2b**). Here, the P-wave teleseismic tomography is performed using relative crust-corrected P-residuals as estimated above. First velocity perturbations in this method are calculated in the orthogonal net of nodes approximating the volume under consideration. And, the trilinear interpolation is used to calculate velocity at adjacent nodes [25]. The initial velocity model of the upper mantle and theoretical travel times are set according to a reference Earth model IASP91 [14]. We run the tomographic code with three-dimensional ray tracing implemented by the Simplex

**37**

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume…*

method [25]. The kernel matrix is inverted by Singular Value Decomposition (SVD). The basic equation of the inversion of the tomographic code (i.e., TELINV)

where **mes**t and **G** are estimated model parameters (i.e., velocity perturbations) and matrix of partial derivatives with respect to the model parameters, respectively. **W**D is weighting matrix of data, where weights are set according to

factor and a unit diagonal matrix, respectively. And, **d** is data vector (i.e., relative residuals) [26]. Several iterative cycles are performed for satisfying assumptions behind the linearization of the inversion. New ray-paths inside of the area studied are traced at each cycle using the improved velocity model retrieved in the previous step. Here, four iteration cycles are applied to reach such data variance which does not decrease with further iterations noticeably and stay above the twice the

The primary study area extends about 320 km in E-W and 240 km in N-S, which covers the E-W trending Kachchh rift zone (**Figures 1a** and **2b**). Here, the volume below the central study area is approximated by the 3D (i.e., x, y and z directions) grid of nodes (17 × 18 × 15). For teleseismic tomography, a much large area covering 10,000 km × 10,000 km × 530 km, is assumed to stabilize the velocity perturbation outside the main study region. Seventeen X-nodes are distributed at distances of −5000 −240 −200 −160 −120 −80 −40 0 40 80 120 160 200 520 560 600 5000 km while eighteen Y-nodes are located at distances of −5000 −360 −320 −280 −240 −200 −160 −120 −80 −40 0 40 80 120 160 200 240 5000 km. And, fifteen nodes in Z directions are at depths of −5 10 70 50 90 130 170 210 250 290 330 370 410 450 490 km. The center of the array is assumed to be at latitude 23.3° and longitude 70.3°. Here, the teleseismic tomographic inversion is performed using a total of 1788 P-residuals, which are estimated using vertical component of broadband seismograms of 241 good teleseismic events (with epicentral distances between 30° and 90°) recorded at 59 stations. Here, the travel time residuals range from −2.276 s to 2.096 s. This study results in an average data error of 0.062 s. For the present study, a travel-time residual

minimize effects of potential inaccuracies of the 3D crustal model applied in the inversion, the first inverted layer of nodes is assumed at 50 km depth. Several different vertical parameterizations with irregular and smaller spacing are being tested, but the variance reduction, as well as the diagonal terms of the resolution matrix, decreased rapidly. In total, the inversion is performed for 980

The crustal structure cannot be resolved through teleseismic tomography due to the sub-vertical directions of the incoming rays. However, the heterogeneous, complex crustal structure can affect the inverted travel-times significantly [27–29]. Further, the size of crustal heterogeneities is often exceeded by the spacing between stations. Therefore, crustal corrections are inevitable to apply on the travel-time residuals, before inverting the residuals for the upper mantle velocity structure. Here, following the standard procedure [17, 29] crustal corrections as discussed above are applied to the dataset. Modeled dVp (%) tomograms at different depths are shown in **Figure 3a**–**d**.

damping factor of 100 is used for the inversion. To

−1

**G**TWD **d** (4)

and **I** are a damping

2

*DOI: http://dx.doi.org/10.5772/intechopen.83738*

**m**est = (**G**<sup>T</sup>**W**D**G** + ε<sup>2</sup> **I**)

quality factors assigned to individual arrival time picks. ε

can be written as:

average data error.

**4.1 Model parameterization**

of 2.5 s is used while a ε

model parameters.

2

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume… DOI: http://dx.doi.org/10.5772/intechopen.83738*

method [25]. The kernel matrix is inverted by Singular Value Decomposition (SVD). The basic equation of the inversion of the tomographic code (i.e., TELINV) can be written as:

$$\mathbf{m}\_{\text{est}} = \left(\mathbf{G}^{\text{T}}\mathbf{W}\_{\text{D}}\mathbf{G} + \varepsilon^{2}\mathbf{I}\right)^{-1}\mathbf{G}^{\text{T}}\mathbf{W}\_{\text{D}}\mathbf{d} \tag{4}$$

where **mes**t and **G** are estimated model parameters (i.e., velocity perturbations) and matrix of partial derivatives with respect to the model parameters, respectively. **W**D is weighting matrix of data, where weights are set according to quality factors assigned to individual arrival time picks. ε 2 and **I** are a damping factor and a unit diagonal matrix, respectively. And, **d** is data vector (i.e., relative residuals) [26]. Several iterative cycles are performed for satisfying assumptions behind the linearization of the inversion. New ray-paths inside of the area studied are traced at each cycle using the improved velocity model retrieved in the previous step. Here, four iteration cycles are applied to reach such data variance which does not decrease with further iterations noticeably and stay above the twice the average data error.

#### **4.1 Model parameterization**

*Forecasting Volcanic Eruptions*

sedimentary layer is assumed to be composed of Cenozoic sediments (Vpsed ~ 2.41–4.60 km/s) and Jurassic/Mesozoic sediments (Vpsed ~ 4.61– 5.58 km/s). The estimated corrections of the travel time residuals for such 1-D known crustal velocity models in the region vary from 0.29 to 0.79 s for P-waves. A total of 241 teleseismic events (Mw 6.0–8.0) have been analyzed to estimate crust corrected P-residuals using Eq. (3), they are found to be stable for stations in the Kachchh network (**Figure 2**). From **Figure 2**, we notice that there is no clear anisotropic signal in the P-residuals in most of Kachchh region except the Motapaya (MTP) station, which is the northernmost station in Kachchh. **Figure 2** shows a plot of estimated crust corrected relative P-residuals at 14 stations as a function of slowness (p) (0–10 s/o along the radial axis) and back azimuth (BAZ 0–360°) to the event. In general, early P-arrivals are noticed for events in the east of the network while delayed P-arrivals are observed for events in the west. Most of the stations, which are lying in the Deccan basalt covered regions in the Kachchh and Cambay rift zones, show negative residuals. This could be attributed to the presence of significant crustal and lithospheric upwarping below these rift zones [18, 19]. At MTP, travel time residuals show images of the spatial variation of wave propagation anomalies of P-waves, which can be attributed to an anisotropy structure of the mantle domains (**Figure 2a**). This anisotropic nature of P-waves is not seen for

other stations due to fewer numbers of observations.

below the Kachchh and Cambay rift zones [18, 19].

**4. P-wave teleseismic tomography**

The directional term of relative crust-corrected P-residuals is calculated by dividing the 0–360 to 18 quadrants, and then we calculate the average residuals of stations falling in a particular quadrant. And finally, we estimate the arithmetic mean of the average residuals of stations falling in all 18 quadrants. Subsequently, this mean of residuals is being subtracted from the relative crust-corrected P-residuals for different stations for estimating the directional term of relative crust-corrected P-residuals. Following the above procedure, we also computed directional term of relative crust-corrected P-residuals, which are plotted in **Figure 2b**. The directional mean of P-residuals, which are obtained by subtracting average residuals of all stations in Kachchh, is shown in **Figure 2b**. While **Figure 2b** represents the directional mean of P-residuals, which are calculated by subtracting average residual of 8 stations in Kachchh. Most interestingly, two distinct zones of negative P-residuals associated with Kachchh and Cambay rift zones are noticed from **Figure 2b**. These zones of negative P-residual probably mark the regions of marked lithospheric thinning. This model gets further support from available estimates of crustal and lithospheric thicknesses, suggesting a marked crustal and lithospheric thinning

The teleseismic tomography code developed by Weiland et al. [20] and later modified by various investigators [21–24] has been used here to estimate the 3-D P-velocity structure down to 250 km underlying the Kachchh rift zone (KRZ). The data collected by the digital networks of NGRI (Hyderabad, India) and ISR (Gujarat, India) are combined, resulting in a dataset from a total of 59 stations (**Figure 2b**). Here, the P-wave teleseismic tomography is performed using relative crust-corrected P-residuals as estimated above. First velocity perturbations in this method are calculated in the orthogonal net of nodes approximating the volume under consideration. And, the trilinear interpolation is used to calculate velocity at adjacent nodes [25]. The initial velocity model of the upper mantle and theoretical travel times are set according to a reference Earth model IASP91 [14]. We run the tomographic code with three-dimensional ray tracing implemented by the Simplex

**36**

The primary study area extends about 320 km in E-W and 240 km in N-S, which covers the E-W trending Kachchh rift zone (**Figures 1a** and **2b**). Here, the volume below the central study area is approximated by the 3D (i.e., x, y and z directions) grid of nodes (17 × 18 × 15). For teleseismic tomography, a much large area covering 10,000 km × 10,000 km × 530 km, is assumed to stabilize the velocity perturbation outside the main study region. Seventeen X-nodes are distributed at distances of −5000 −240 −200 −160 −120 −80 −40 0 40 80 120 160 200 520 560 600 5000 km while eighteen Y-nodes are located at distances of −5000 −360 −320 −280 −240 −200 −160 −120 −80 −40 0 40 80 120 160 200 240 5000 km. And, fifteen nodes in Z directions are at depths of −5 10 70 50 90 130 170 210 250 290 330 370 410 450 490 km. The center of the array is assumed to be at latitude 23.3° and longitude 70.3°. Here, the teleseismic tomographic inversion is performed using a total of 1788 P-residuals, which are estimated using vertical component of broadband seismograms of 241 good teleseismic events (with epicentral distances between 30° and 90°) recorded at 59 stations. Here, the travel time residuals range from −2.276 s to 2.096 s. This study results in an average data error of 0.062 s. For the present study, a travel-time residual of 2.5 s is used while a ε 2 damping factor of 100 is used for the inversion. To minimize effects of potential inaccuracies of the 3D crustal model applied in the inversion, the first inverted layer of nodes is assumed at 50 km depth. Several different vertical parameterizations with irregular and smaller spacing are being tested, but the variance reduction, as well as the diagonal terms of the resolution matrix, decreased rapidly. In total, the inversion is performed for 980 model parameters.

The crustal structure cannot be resolved through teleseismic tomography due to the sub-vertical directions of the incoming rays. However, the heterogeneous, complex crustal structure can affect the inverted travel-times significantly [27–29]. Further, the size of crustal heterogeneities is often exceeded by the spacing between stations. Therefore, crustal corrections are inevitable to apply on the travel-time residuals, before inverting the residuals for the upper mantle velocity structure. Here, following the standard procedure [17, 29] crustal corrections as discussed above are applied to the dataset. Modeled dVp (%) tomograms at different depths are shown in **Figure 3a**–**d**.

#### **Figure 3**

*P-wave velocity perturbations at horizontal slices imaged at (a) 50, (b) 90, (c) 130, and (d) 170 km depths, by the P-wave tomography using the crust corrected relative P-residuals***.** *Major faults (solid white lines): ABF—Allah bund fault; IBF—Island belt fault; KMF—Kachchh mainland fault; KHF—Katrol hill fault; NPF—Nagar Parkar fault; BF—Banni fault. And, NWF (north Wagad fault), the causative fault for 2001 Bhuj earthquake and Gedi fault, are shown by dotted white lines. Locations of mobile broadband stations are marked by gray open triangles. A black dotted elliptical area mark the central KRZ.*

#### **4.2. Resolution analyses**

Resolution analyses of tomographic models are essential for distinguishing real structures from artifacts caused by methods used and for identifying well-resolved model parameters. The reliability of tomographic images have been analyzed by performing a checkerboard test, which is performed with the ray geometry of the Kachchh network, with 3D ray-tracing, and with the damping factor of 100.

To verify sensitivity in the whole volume studied, a checkerboard test is performed [30]. For this, a net of alternating anomalies of +5% and −5% in nodes is constructed at depths of 50, 90, 130, and 170 (**Figure 4a**–**d**), leaving the layers in between them unperturbed as well as in the remaining parts of the model [30]. The input anomalies are recovered well at depths ranging from 50 to 170 km (**Figure 4e**–**h**). The low-velocity anomalies in the central part are not resolved successfully at ~210 km depth, which could be attributed to the well-known vertical smearing dominated in the inversions of teleseismic data.

**39**

**Figure 4**

**5. Results and discussions**

Large negative travel time residuals associated with the central Kachchh rift zone are detected (marked by a black dotted elliptical area shown in **Figure 2b**), suggesting relatively thin lithosphere underlying the central KRZ while surrounding

*Input 3-D synthetic P-wave velocity model with alternative grids of high (±5%) and low (−5%) velocity for the checkerboard test at (a) 50, (b) 90, (c) 130, and (d) 170 km depths***.** *Results of checkerboard test showing* 

*retrieval of synthetic velocity perturbations at (e) 50, (f) 90, (g) 130, and (h) 170 km depths.*

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume…*

*DOI: http://dx.doi.org/10.5772/intechopen.83738*

*P-Wave Teleseismic Tomography: Evidence of Imprints of Deccan Mantle Plume… DOI: http://dx.doi.org/10.5772/intechopen.83738*

#### **Figure 4**

*Forecasting Volcanic Eruptions*

**38**

**4.2. Resolution analyses**

**Figure 3**

Resolution analyses of tomographic models are essential for distinguishing real structures from artifacts caused by methods used and for identifying well-resolved model parameters. The reliability of tomographic images have been analyzed by performing a checkerboard test, which is performed with the ray geometry of the Kachchh network, with 3D ray-tracing, and with the damping factor of 100. To verify sensitivity in the whole volume studied, a checkerboard test is performed [30]. For this, a net of alternating anomalies of +5% and −5% in nodes is constructed at depths of 50, 90, 130, and 170 (**Figure 4a**–**d**), leaving the layers in between them unperturbed as well as in the remaining parts of the model [30]. The input anomalies are recovered well at depths ranging from 50 to 170 km (**Figure 4e**–**h**). The low-velocity anomalies in the central part are not resolved successfully at ~210 km depth, which could be attributed to the well-known vertical

*P-wave velocity perturbations at horizontal slices imaged at (a) 50, (b) 90, (c) 130, and (d) 170 km depths, by the P-wave tomography using the crust corrected relative P-residuals***.** *Major faults (solid white lines): ABF—Allah bund fault; IBF—Island belt fault; KMF—Kachchh mainland fault; KHF—Katrol hill fault; NPF—Nagar Parkar fault; BF—Banni fault. And, NWF (north Wagad fault), the causative fault for 2001 Bhuj earthquake and Gedi fault, are shown by dotted white lines. Locations of mobile broadband stations are* 

*marked by gray open triangles. A black dotted elliptical area mark the central KRZ.*

smearing dominated in the inversions of teleseismic data.

*Input 3-D synthetic P-wave velocity model with alternative grids of high (±5%) and low (−5%) velocity for the checkerboard test at (a) 50, (b) 90, (c) 130, and (d) 170 km depths***.** *Results of checkerboard test showing retrieval of synthetic velocity perturbations at (e) 50, (f) 90, (g) 130, and (h) 170 km depths.*
