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Chapter 3

Minimum 1-D Velocity Model: Using joint determination of

hypocenters and velocity

3.1 Introduction

This chapter deals with the estimation of a new 1-D velocity model in the Kumaon-

Garhwal Himalaya region, based on travel times using the Joint hypocenter and velocity

determination (JHD) method. A one-dimensional P- and S- wave velocity structures of the upper

crust beneath the Kumaon-Garhwal Himalaya region is determined by simultaneously inverting

the hypocentral locations as well as the velocity structure of the study region. Seismic velocity

structure of a region not only provides a window to its deeper geological setting but constitutes

basic information required for analyzing seismograms generated at its various sites. In particular,

it is indispensable to accurate mapping of hypocentral locations of earthquakes that, in turn,

illuminate ambient strain concentrations as well as distribution of interactive fault systems, to

model earthquake hazard and design mitigation works such as the formulation of building codes

and design of advanced warning systems. Also, with the use of known hypocentral parameters,

we can estimate the seismic velocities beneath the area under investigation. One, therefore, tries

to determine the hypocenters and the velocity structure simultaneously.

Results of local earthquake tomography highly depend on the initial reference model

(Kissling et al., 1994). Kissling (1988); Kissling et al. (1994) introduced the concept of the

minimum 1-D model in local earthquake tomography that can be use as a initial reference model.

The minimum 1-D model itself is a result of a series of simultaneous inversions of hypocentral

parameters, 1-D velocity models (VP & VS), and station corrections. Besides serving as an initial

reference model, the minimum 1-D model will provide high precision hypocenter locations for

use in 3-D local earthquake tomography.

Initial earthquake locations with computer code HYPOCENTER using an earlier known

velocity model is presented in the first section of this chapter. This is followed by joint inversion

of P- and S- wave velocity model and the earthquake hypocenter. For the purpose we use well

documented software VELEST. Finally, model errors are estimated by means of different

reliability tests for the derived model.

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3.2 Initial Hypocenter locations

A total 1250 local earthquake records, which had registered a minimum of 5 P- and 3 S-

arrivals, were selected for inversion of their hypocenters by using HYPOCENTER program.

With the availability of the GPS timing system, reliability of the internal clock system was

always better than a few microseconds. We assigned a time uncertainty to each interval; for

events inside the network time uncertainties of P- wave arrivals ranges from 0.05 to 0.50 s and

for S- wave arrivals 0.1 to 1.5 s.

For locating earthquakes we used Nepal Himalayan velocity model (Monsalve et al.,

2006) shown in Table 3.1, and an average VP/VS ratio (1.73) abstracted from the P- and S- wave

arrival time data from our network using the Wadati diagram (Fig. 3.1). Our choice of the Nepal

Himalaya velocity model for this first step inversion of hypocenters was guided by the

consideration that it was apparently the best constrained model available which was likely to be

fair representative of the Himalayan arc generally and of the adjoining central Himalaya in

particular. For initial locations the average error in latitude, longitude is 4 km and for depth 5 km

(Fig. 3.2). These events are well distributed all over the region covered by the network and

scanned epicenter distances with in 450 km. All of these events have their local magnitude

between 1 and 5.3. The distribution of located epicenters is shown in Figure 3.3.

Table 3.1: Initial 1-D Velocity model used for location

Depth (km

VP (km/s) Vs (km/s)

0.0

5.50 3.20

3.0

5.70 3.20

23.0

6.30 3.7

>55

8.0 4.5

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Figure 3.1: Wadati diagram. Linear fit of S-P time versus P- time. The root mean square error

(RMS) is 0.09 and the computed VP/VS ratio is 1.73.

Figure 3.2: Histograms showing error statistics for hypocenter (km) (a, b) and time residuals

(c).

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Figure 3.3: Epicenter distribution of initially located earthquakes from 2005-2008. Moderate

size earthquakes in the region are shown with different stars (Blue star: 2005 Chamoli, M 5.3;

Red star: 2007 Kharsali, M 5.0).

Whereas the seismicity of the recording period is widely dispersed in the Kumaon–

Garhwal Himalaya, we observed a well defined band of seismicity following the surface trace of

the MCT zone. However, we also find another parallel band of earthquakes; about 70 km to its

southwest in the Lesser Himalaya, and a significant number both in the Tethys Himalaya and

Ganga basin. We have also located 100 earthquakes in the NCR region.

As shown in Figure 3.3, during the observation period, 6 earthquakes of magnitude range

4<M<5 and two moderate earthquakes of M≥5 occurred in the Kumaon-Garhwal Himalaya

region. The two moderate M≥5 earthquakes are: The chamoli earthquake (2005 December 14,

30.48ºN 79.25ºE, ML= 5.3, blue star) and The Kharsali earthquake (2007 July 23, 30.91ºN

78.31ºE, ML=4.9 and MW=5.0, red star). The histogram in Figure 3.4 shows the depth

distribution of earthquakes. The concentration of the seismicity in the upper part of the crust will

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influence the model parameterization that will be discussed in the next section. In addition, the

depth distribution provides important information about the rheological behavior of the crust.

Figure 3.4: Depth distribution of earthquakes

3.3 Significance of S-arrival time

Theoretically, P- and S- arrival time are interchangeable with given VP/VS ratio. However,

S-wave phases provide important additional constraints on hypocenter locations. Also, the

additions of S- wave data in earthquake locations have several advantages: increase in the

number of observations, better constrain on the hypocenter depth and determination of

independent S-wave velocity structure that provides important information about the rheology of

the earth’s crust. Though widely believed that P and S travel times are inter- related, Frank

(Ph.D, thesis ) showed that the path used by both the rays are quiet different and hence the

information provided by S- wave is complimentary to the P- wave. Also, the depth and lateral

resolvability are different. Figure 3.5 show the path of P- and S- wave for a velocity model.

Gomberg et al. (1990) demonstrated that partial derivatives of S-wave travel times are always

larger than those of P- waves by a factor equivalent to VP/Vs and that they act as a unique

constraint within an epicentral distance of 1.4 focal depths. Therefore, the use of S- wave will in

general result in a more accurate hypocenter location, especially in determination of the focal

depth. On the other hand, error in S- arrival-time at a station close to the epicenter can result in a

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stable solution with a small Root Mean Square (RMS), but actually denoting a significantly miss

located hypocenter even for cases with excellent azimuthal station coverage (Maurer, 1992).

Since the onset of S- phases are often masked or distorted by P- wave coda, error in arrival time

is expected and hence quality control is needed.

Figure 3.5: Ray paths for P and S waves through the one dimensional velocity model for the

ANZA network (After Frank L. Vernon). Seismic sources were placed at 2.5, 5, 10, and 20 km

depth in the model. At each depth the same take-off angles from the source were used for P and

S waves.

3.4 Minimum 1-D velocity model using VELEST

We used the program “VELEST” (Kissling et al., 1994) for simultaneous determination

of hypocenters, 1-D P, S velocity structures and station corrections. The model geometry (layer

thicknesses) is held fixed during inversion. The travel times are calculated by ray tracing using

the shooting method (Thurber, 1981), and directly solves the normal equation with Cholesky

decomposition (Press et al., 1988).

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3.4.1 Data Selection

To estimate a minimum 1-D model we used a set of well located earthquakes because

uncertainties in hypocenter locations will introduce instabilities in the inversion process due to

hypocenter-velocity coupling. Apart from the velocity model, there are three main factors that

control the quality of a location:

Number of readings used: The over-determinacy of the inverse problem depends on the

number of recording stations used and the magnitude of an event. We selected only 385 events

for inversion with minimum of 7 P- and 5 S- readings (Fig. 3.6 and Table 3.2). Thus, a total of

5327 P- phases and 4927 S- phases were used for inversion. Final solution has 1598 variables

(1540 hypocenters, 8 P- and S- velocities and 50 station corrections), against 10254 data

elements, the inverse problem with a fixed velocity was over-determined by a factor of 6.4, when

using P- and S- observations and by a factor 3.3, when only P readings are used.

Geometry of the station distribution: To obtain a well-constrained solution, the

epicenter should be surrounded by recording stations. Thus, well locatable events must occur

within a network. The relative position of an epicenter to network is described by the GAP. This

is the largest azimuthal angle (seen from epicenter), within which no readings are available.

Events that occurred inside a network always have a GAP <180°. We have 385 events with at

least 7 P- and 5 S- readings and with GAP <180°. Figure 3.7 shows the GAP distribution of

earthquakes used for inversion. Assuming small and Gaussian reading errors, the GAP and the

number of observations roughly describe the expected quality of an epicenter location.

Phase reading errors: It is always better to filter out mis-picked arrival times. However, the

use of an in correct velocity model introduces systematic errors that can hide miss-picked

readings. Therefore, the detection of gross errors requires an advanced knowledge of the velocity

structure. To filter out mis-picked arrival times, we have chosen the earthquakes with RMS

residual <1.0 sec. (Table 3.2).

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Figure 3.6: Constraints on the data used for inversion. Histograms show the number of events

with (a) P- readings and (b) S- readings.

Figure 3.7: Distribution of the GAP parameter.

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Table 3.2: Data selection thresholds for the combined P- and S- inversion

Number of Observations per event

≥ 12

Number of P arrivals per event

≥ 7

Number of S arrivals per event

≥ 5

GAP < 180

degrees

Root Mean Square (RMS)

< 1 seconds

Based on the above restrictions, data selection for our data set has been adopted. Then, a

combined inversion for both a P- and S-wave velocity model is done, using the proposed

selection scheme.

3.4.2 P- and S-wave Velocity Inversion

We used three different existing velocity models (Figs. 3.8 a, b) corresponding to the

Nepal Himalaya (Monsalve et al., 2006), Western Himalaya (Rai et al., 2006), and the Delhi

region (Julià et al., 2009), to jointly invert for the earthquake hypocenter and 1-D velocity

model. The initial S-wave velocity models are constructed from P- wave velocity using VP/VS

ratio 1.73. The velocity of the first layer strongly depends on the calculation of the station

corrections. In order to calculate these corrections a boundary condition must be applied. A

possible constraint is the average of all station corrections must be zero. However, because of

heterogeneities of the near surface lithology below the different stations for the inversion, this

constraint leads to a first layer velocity, which is only a mathematical average without any

relation to the actual geology.

Therefore, an alternative approach is chosen: the station correction of one reference

station is fixed to zero. So, the first layer velocity reflects the velocity beneath this reference

station. The station GTH was chosen as reference station, due to following criteria: (a) located

close to the center of the network, (b) not located at the boundary of two units with strongly

different geology, (c) had long recording period comprising of at least 50% of the total possible

readings, and (d) had data of high S/N ratio.

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Figure 3.8: Initial and final velocity models for (a) P- wave, and (b) S- wave

The three input velocity models were initially parameterized as stack of 2 km thick

layers. The optimum model calculation requires number of iterations to select and test control

parameters, which are suitable to data set and problem. The damping parameter provides the

balance between the solution and the initial model. We started with damping coefficient of 0.01,

0.1 and 1.0 for the hypocentral parameters, the station corrections and velocity parameters,

respectively. In subsequent runs we changed the damping parameters of velocity parameters and

station corrections, in order to get data misfit reduction and the good parameter resolution.

The inverted velocity models were then iteratively simplified by fusing layers with

similar velocities to form the next initial model (Kissling, 1994). The RMS residual obtained for

the three velocity models are shown in Table 3.3. The resolving power of the data is defined by

the ray distribution in the modeling volume. The inverted models (Figs. 3.8 a, b) are seen to

resolve layers only up to a depth of ~20 km, this is caused due to inadequate data and criss-cross

incidence at deeper levels. The ray hit count is shown in Figure 3.9. Therefore the velocity of the

layers below this depth is fixed. We kept changing the starting model in subsequent runs as we

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get solutions with smaller misfits. Random variations of this starting model can also be used as

starting model in order to get better solutions. The following criterion is made to judge the

quality of different solutions.

• There should not be large oscillations of model parameter during the inversion.

• Convergence of the solution should be fast and stable.

• The model should adjust the shifted hypocenters properly.

• The station corrections of the neighboring stations should be similar.

Figure 3.9: Ray Distribution in depth.

Table 3.3: Initial and final RMS residual for different models

Model Name

Initial RMS (s) Final RMS (s)

NCR

0.5371 0.4771

Western Himalaya

0.7144 0.4993

Nepal Himalaya

0.5975 0.4582

Optimum 1D (This study) 0.5980 0.4010

The final P and S velocities obtained from combined inversion along with depth

distribution of earthquakes shown in Figure 3.10. The final velocity model resulting from travel

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time inversion is well resolved only down to a depth of 20 km, because of very few hypocenters

(Fig. 3.10) and rays below 20 km (Fig. 3.9). The resolution of different velocity layers obtained

from inversion is shown in Table 3.4. The optimum 1-D velocity model obtained from

simultaneous inversion of arrival times of P- and S- phases is shown in Table 3.5. This shows

that the upper crust to a depth of 20 km into a three-layer structure. At a depth of 4 km first

discontinuity appears and the P- wave velocity becomes 5.90 km/s and S- wave velocity is 3.40

km/s. Below 4 km the velocity is constant and it reaches 6.0 km/s, 3.51 km/s for P- and S- waves

at a depth of 16 km. Another discontinuity is mapped at a depth of 20 km where the velocity

increases to 6.40 km/s, 3.72 km/s for P- and S- waves respectively. The total RMS residual

reduced from 0.598 s before inversion to 0.401 s after inversion (Table 3.3). The epicenter and

depth distribution of 385 earthquakes, used for joint hypocenter location and optimum 1- D

velocity model estimation is shown in Figure 3.11.

Figure 3.10: Final 1-D velocity models from combined inversion for P- and S- wave velocities

and hypocentral parameters.

0

10

20

30

40

50

60

70

De

pth

(k

m)

4 5 6 7 8

Velocity (km/s)

Notresolved

VpVs

NEQ = 2168

191

83

10

79

Figure 3.11: (a) Distribution of 385 earthquakes used in joint inversion for hypocenter and

velocity parameters using VELEST. (b) Earthquake depth distribution is projected along the BB'

cross-section. Topography along the cross-section is also plotted.

Table 3.4: Resolution parameters of various velocity layers

obtained from Travel-Time inversion of P- and S- phases

Depth (km) P Resolution S Resolution

0.0

0.8955 0.8840

4.0

0.9966 0.9839

16.0

0.9742 0.9971

20.0

0.9975 0.9881

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Table 3.5: 1-D Velocity model obtained from Travel-Time

Inversion and Corresponding VP /VS ratio

Depth (km)

VP (km/s) VS (km/s) VP/VS

0.0

5.60 3.20 1.75

4.0

5.90 3.40 1.73

16.0

6.00 3.51 1.70

20.0

6.40 3.72 1.72

In order to obtain stable results, no low-velocity layers have been allowed in the

inversion. However, Kumar et al. (2009) reported existence of low velocity layer at a depth of 15

to 18 km to the north western part of our network. Based on this, combined inversion for P- and

S-wave velocity models is attempted which allows layers with low velocities. In order to resolve

the low velocity layer, it is necessary to resolve at least one layer below the low velocity layer.

Accordingly the stack of layer is subdivided. Even though we have good number of earthquakes

in the depth range of 15 to 18 km and the layer is well resolved, we could not find the low

velocity.

3.4.3 Stability Tests For Velocity model

To test the stability of our optimum 1-D velocity model we carried out the following

tests.

(i) Joint inversion of the phase data was repeated using a relaxed average initial velocity model

with bounds as shown in Figure 3.12. All solutions were found to converge to the optimum 1-D

model obtained earlier, up to a depth of 20 km.

(ii) To test if the earthquake locations were well constrained and not conditioned by the initial

hypocentral parameters, we repeated the inversions using a perturbed model of hypocentral

locations: the latitude, longitude and depth parameters of alternate individual earthquakes being

randomly shifted by ± 12 km (Figs. 3.13 a, b, c). Again, the results show excellent convergence

to the earlier solutions with horizontal and vertical locations suffering a maximum divergence of

700 and 1087 m, respectively.

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(iii) Figure 3.14 compares the RMS travel time residuals, epicenter and focal depth error for

earthquakes located using the Nepal Himalaya velocity model (Monsalve et al., 2006), used for

initial locations, and the 1-D optimum velocity model obtained from our joint inversion. Most of

the earthquakes (more than 80%) located using our optimum 1-D model show RMS value of 0.1-

0.6 s as compared to 0.2- 1.0 s using the Nepal Himalaya model. This is also reflected in error in

epicenter and focal depth skewed to lower values.

Figure 3.12: Stability test for the optimum 1-D velocity model. Thin lines show the upper and

lower bounds of the optimum 1-D velocity model, used as input. Output velocity models and

Optimum 1-D are shown as dashed and thick solid lines, respectively.

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Figure 3.13: Hypocenter stability test with respect to latitude (a), longitude (b), and depth (c).

Black closed circles: coordinate difference between randomized input and minimum 1-D

locations. Grey open circles: difference after inverting with the randomized input data. The

average remaining shifts between the minimum 1-D locations and the output of this test and the

variance is given on the right.

Figure 3.14: Histograms showing error statistics for time residual (s) and hypocenter (km) for

(a) the initial (Monsalve et al., 2006), and (b) optimum 1-D velocity model (this study).

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3.4.4 Station Corrections

Station corrections represents deviations of the 1-D velocity model and depends strongly

upon the topography and lateral velocity variations associated with heterogeneous near-surface

structure which is otherwise not resolved in 1-D model (Kissling, 1995). In the study region the

topography varies from 800 meters in south to 3000 meters in the north. Station corrections for

individual seismograph locations, excluding MNA and DBN having inadequate phase data, were

calculated with respect to the reference station GTH. The station corrections for individual

seismograph locations show variations between -0.4 to 1.0 s for P- wave and -1.26 to 1.5 s for S-

wave (Table 3.6 and Figs. 3.15 a, b). The positive and negative distributions of station

corrections reflect to some part of the overall three dimensionality of the velocity field. Negative

station correction means where the true velocities are higher than the predicted fields at the

recording station with respect to the reference station GTH and positive correction means where

the true velocities are lower than the predicted fields.

As expected, stations in the same geological unit have similar corrections. Relative

positive station corrections of both P- and S- waves are observed for the stations to the south of

MBT, which overlay by the low-velocity Siwalik formation and the sediment filled Indo-

Gangetic plain. The stations to the north of the MBT, in the Higher Himalayan crystalline shows

relatively negative station corrections of both P- and S- waves (Fig. 3.15). The stations near to

the reference station are showing almost zero corrections.

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Table 3.6: P- and S- wave corrections obtained from

travel time inversion

Station Code P-wave

Correction (s) S-wave

Correction (s) LTA -0.24 -0.94

HLG -0.24 -0.63

NAL -0.05 -0.32

SRP 0.05 -0.20

KSL 0.01 -0.27

BNK -0.04 -0.50

MRG -0.15 -0.45

DKL 0.13 -0.14

PKH -0.31 -0.74

JLM -0.15 -1.02

GHT -0.09 -0.41

OKM 0.01 -0.44

ALM 0.12 -0.46

NTI -0.07 -0.87

KSP -0.14 -0.95

TMN -0.14 -1.11

BGR -0.10 -0.49

BHT -0.07 -0.78

NND 0.05 -0.66

DRS 0.11 -0.41

NTL 0.27 0.14

MNY -0.41 -0.60

PTG -0.17 -0.49

DCL -0.08 -0.20

DDR 0.15 -0.37

NTR 0.29 -0.38

HSL -0.01 -1.26

SYT 0.04 -0.11

PPL -0.12 -0.55

KTD 0.36 0.15

LGS -0.29 -0.64

TNP 0.16 -0.75

ALI -0.12 -0.52

ABI -0.08 0.25

CKA -0.22 0.48

DDN 1.00 1.50

GKD -0.10 -0.11

GTU 0.16 0.45

KSI -0.12 0.37

KHI -0.18 -0.12

NHN -0.24 0.44

TPN -0.02 -0.05

GTH 0.00 0.00

85

Figure 3.15: Station corrections (in seconds) for (a) P- waves and (b) S- waves with respect to

reference station GTH (marked as star). Variations in sizes of triangle and circle correspond to

magnitude of positive and negative station correction values, respectively.