Chapter 3 Minimum 1-D Velocity Model: Using joint...
Transcript of Chapter 3 Minimum 1-D Velocity Model: Using joint...
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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
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10
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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
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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.