Journal of Natural Disaster Science, Volume 40，Number 2，2020，pp14-25

Visualizing Data Saturation Process in Mapping Site Amplification of Earthquake
Ground Motions

Anirban CHAKRABORTY* and Hiroyuki GOTO***Department of Urban Management, Graduate School of Engineering, Kyoto University**Disaster Prevention Research Institute, Kyoto University(Received: Sep. 10, 2019 Accepted: Jan. 21, 2020)

Abstract
Seismic hazard maps play an important role in earthquake disaster risk reduction. The availability of spatial datais crucial to generate these maps that plot the spatial distribution of hazard potentials to emphasize spatialdifferences. The past few decades have seen an exponential increase in the availability of geospatial data.
However, we cannot ascertain whether the amount of available data is sufficient, and we have no guidelines todraw the maps based on the available data consistent with the data accumulation. In this study, we address theseissues in terms of data visualization techniques. Using information theory, we propose a parameter that measures
the incremental information gain as maps are updated with new data over time. Data saturation occurs as the
proposed parameter approaches zero. The concept is applied to a case study area in the Furukawa district ofJapan where earthquake data has been collected over 7 years from 31 seismometers in a dense seismic array.
Convergence in site amplification maps generated over different observation periods conclude that the mappingin Furukawa district is approaching data saturation and from the viewpoint of information theory, the current
operation may be terminated.
Keywords: data visualization; disaster risk reduction; seismic hazard map; site amplification; uncertainty

1. INTRODUCTION
Earthquake disasters are significant events causing large-scale destruction to human society. In order to reduce
the extent of earthquake damage, possible scenarios should be assessed taking into account the spatial variationof the seismic risk. Earthquake ground motion amplifications are the main cause of these spatial differences (e.g.,Kawase, 1996) and have recently been summarized in seismic hazard maps.
In order to generate seismic hazard maps that plot the spatial distribution of earthquake ground motion
amplifications or other hazard potentials, the availability of spatial data is important. In the past few decades,
advancement in data collection, e.g., high-resolution remote sensing, monitoring sensor networks, etc., has
increased the availability of spatial data considerably (Lee and Kang, 2015).
However, it is usually not clear if the amount of available data is sufficient to extract the desired
information for the physical process. More data collection has been attempted if the amount of data isdetermined to be insufficient. This concept is based on the idea that the goal of the hazard maps is to plot
accurate information using sufficient data, which can contribute to disaster reduction.
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On the other hand, in practice, we need to plot the maps based on only the available data. In such asituation, there are two essential questions: (1) how do we determine whether the amount of available data issufficient, and (2) how do we draw the maps consistent with the data accumulation?
In this study, we address these issues in terms of data visualization techniques. Visualization is an
important aspect to help the user directly understand the data saturation. The objective of this study is tovisualize data saturation in mapping. We introduce KL divergence increments, based on information theory(Kullback and Leibler, 1951), that measures the incremental information gain as we update a map. Data
saturation or sufficiency is reached when no more incremental information gain is observed even after adding
new data to a map. In the literature, papers addressing the issue of data saturation in spatial mapping are rare.
Some papers have addressed the issue of optimal sampling, however, the focus is on assessing the grid layout
rather than the optimal amount of data (Hughes and Lettenmaier, 1981; Wang et al., 2012; James and Gorelick,1994). Past research in other fields has seen some papers addressing the issue of data saturation (Chaudhuri et al.,
1998; Guest et al., 2006; Fusch and Ness, 2015). However, many of them are qualitative in nature and none ofthem considers data uncertainty in their formulations and hence the question on reliability remains unanswered.
In this study, we consider Uncertainty Projected Mapping (UPM) (Chakraborty and Goto, 2018) as the
mapping tool. Unlike conventional mapping (e.g., ordinary kriging), which does not consider the record torecord variability and uses only a single averaged value for each site, UPM projects the data uncertainty on the
map resolutions and adds statistical significance to the estimated values at the sites. Also, as we shall see in thispaper, UPM has an interesting characteristic of being dependent on the number of observations. This
characteristic is crucial to enable use of our proposed parameter in measuring the information gain as more andmore data is added to a map. The novelty of the idea lies in involving data saturation with the spatial resolution.
In this study, we examine a methodology to visualize and quantify the excess or deficiency of data inmapping earthquake ground motion amplifications. In the next section, we discuss the UPM model andintroduce the incremental KL divergence parameter to quantify data saturation. In Section 3, we introduce a
numerical experiment to discuss how the parameter can help in quantifying and visualizing data saturation in
spatial maps. In Section 4, we apply our methodology to a real earthquake site amplification dataset from a casestudy area in Japan and discuss how the results can help us decide when to stop collecting more data.

2. METHODOLOGY
2.1 Uncertainty Projected Mapping (UPM)
Mapping is a popular visualization tool applied to understand a spatial process. Kriging (Matheron, 1963) is avery useful tool to spatially interpolate data based on spatial variations. However, most of the conventional
visualization techniques assume that the data is free of uncertainty and uses only the mean (𝜇𝜇𝑗𝑗 ) at site j (Brodlie
et al., 2012). Many researchers believe that displaying uncertainty on maps could lead to better decisions(Harrower, 2003). Our motivation is to put more information (uncertainty) into the map resolutions and hence, inthis study, we use UPM as the mapping tool.
UPM considers two uncertainties in a spatial process: record to record variability at a site j ( σ𝑗𝑗 ) and site
to site variability in the neighborhood of j ( 𝑠𝑠𝑗𝑗 ). The record to record variability is the same as the standard
deviation at site j. There are two goals of UPM: (1) to project the information of 𝜎𝜎𝑗𝑗 into posterior estimates of𝜇𝜇𝑗𝑗 at site j, and (2) to decrease the map resolution in zones of high 𝜎𝜎𝑗𝑗 . Using (1), it adds statistical significanceto the estimated mean (𝜇𝜇𝑗𝑗 ) and hence, it can statistically explain the difference in values at the two sites. To
achieve (2), a constraint relation is introduced such that (Chakraborty and Goto, 2018)15

Journal of Natural Disaster Science, Volume 40，Number 2，2020，pp14-25

𝑐𝑐 = 𝑠𝑠𝑗𝑗 𝜎𝜎𝑗𝑗

(1)where c is a constant. Equation (1) relates the smoothness or roughness of map resolutions to 𝜎𝜎𝑗𝑗 , i.e., therecord to record variability at site j. Generally, 𝑠𝑠𝑗𝑗 , i.e., the site to site variability in the neighborhood of j,
determines the form of the map resolutions. A low 𝑠𝑠𝑗𝑗 value means low variability around j and hence, a smooth
resolution. However, a high 𝑠𝑠𝑗𝑗 means a rough variability around j and thus, a rough resolution. In UPM, wewant the map resolutions to be smooth in zones of high 𝜎𝜎𝑗𝑗 . Equation (1) achieves this by constraining an inverse
relation between 𝜎𝜎𝑗𝑗 and 𝑠𝑠𝑗𝑗 . In zones of high 𝜎𝜎𝑗𝑗 we impose a low 𝑠𝑠𝑗𝑗 and make the resolutions smooth. In
zones of low 𝜎𝜎𝑗𝑗 , we impose a high 𝑠𝑠𝑗𝑗 and make the resolutions rough. The constant c is unique to the model
setting and the optimum value of the constant c is based on model evaluation as discussed later.
Thus, in UPM, the mapping follows conventional mapping (e.g., ordinary kriging) in areas with low
record to record variability. However, as the record to record variability increases, the mapping becomes smoothand similar to the neighboring sites. This is the uniqueness of UPM. It can project the information of theuncertainty in the map resolutions.
Neighborhood is an important component in modelling UPM. In many cases, the spatial sites may not be
uniformly spaced or there may be some missing sites where the values need to be estimated. So, in general, we
create uniformly distributed sites (by adding missing sites, if necessary) so that ideally every site has the same
number of neighbors.
UPM is based on a Bayesian hierarchical model (Banerjee et al., 2014). The unknown parameters 𝜇𝜇,σand s are assigned a prior distribution and estimated based on a posterior probability distribution using MCMC
(Gilks and Spiegelhalter, 1995) algorithms. The plot of the 𝜇𝜇 thus obtained is called the UPM of the spatial
variable. However, based on different c values, many different UPMs can be generated. In Chakraborty and
Goto (2018) model evaluation was conducted using a k-fold cross-validation (Stone, 1974). However, it iscomputationally very expensive as the model data needs to be split into many parts. To avoid that splitting of thedataset into subsequent parts, in this study, we replace cross-validation with computationally faster
Watanabe-Akaike information criterion (WAIC) (Watanabe, 2010; Gelman et al., 2014). The c model with theminimum WAIC is considered as the best model. In this paper, all the UPM results come from the optimal c
model.

2.2 ∆𝐃𝐃𝐊𝐊𝐊𝐊 : Proposed parameter to quantify data saturation

The estimated mean (𝜇𝜇𝑗𝑗 ) and estimated record to record variability (𝜎𝜎𝑗𝑗 ) improve as more and more data isadded to the mapping. In other words, maps evolve with the addition of data in time. In this study, we visualize
and quantify this property of maps and decide the point of data saturation, which means that a further increase indata adds no more information to the map.
As we will see in Sections 3 and 4, UPM has a property of converging with conventional mapping(ordinary Kriging) as the number of data increases. To quantify this convergence in UPM, we use a parameterbased on Kullback-Leibler (KL) divergence (Kullback and Leibler, 1951). KL divergence measures the degreeof difference between two probabilistic distributions. It is usually defined as∞

𝑝𝑝(𝑥𝑥)
� 𝑑𝑑𝑑𝑑𝑞𝑞(𝑥𝑥)𝐷𝐷𝐾𝐾𝐾𝐾 (𝑃𝑃||𝑄𝑄) = ∫−∞ 𝑝𝑝(𝑥𝑥) log �

where 𝑃𝑃 and 𝑄𝑄 are continuous random variables and 𝑝𝑝 and 𝑞𝑞 are the associated probability densities.
In this study, we define a quantity called incremental KL divergence (∆𝐷𝐷𝐾𝐾𝐾𝐾 ) given by
16(2)

A.CHAKRABORTY, H.GOTO∆𝐷𝐷𝐾𝐾𝐾𝐾[𝑁𝑁+∆𝑁𝑁] = ∑𝑗𝑗 𝐷𝐷𝐾𝐾𝐾𝐾 �𝑃𝑃[𝑁𝑁],𝑗𝑗 ||𝑃𝑃[𝑁𝑁+∆𝑁𝑁],𝑗𝑗 �(3)where ∆𝐷𝐷𝐾𝐾𝐾𝐾[𝑁𝑁+∆𝑁𝑁] is the DKL between the probability distribution P[N] at the 𝑁𝑁 observation data case and theprobability distribution 𝑃𝑃[𝑁𝑁+∆𝑁𝑁] at the 𝑁𝑁 + ∆𝑁𝑁 observation data case summed over the 𝑗𝑗 sites. In theliterature, such convergence measure has been proposed to evaluate the performance of numerical analysis (Gotoand Bielak, 2008).
The parameter ∆𝐷𝐷𝐾𝐾𝐾𝐾 measures the information gain as the maps are updated with more and more datain time. Data saturation occurs when ∆𝐷𝐷𝐾𝐾𝐾𝐾 approaches zero, which means that no more spatial information isadded even upon adding more data to the map. The uniqueness of the parameter ∆𝐷𝐷𝐾𝐾𝐾𝐾 is that unlike
conventional measures of data saturation, it also considers the data uncertainty in its formulation and hence adds
a sense of reliability to the measurement.
It is difficult to define a ∆𝐷𝐷𝐾𝐾𝐾𝐾 like parameter to measure data saturation in conventional mapping(ordinary Kriging). The reason can be explained based on the differences between the mapping characteristics of
UPM and ordinary Kriging, which can be listed as follows: (1) Unlike UPM, ordinary Kriging needs to estimate
the distribution of both mean (𝜇𝜇𝑗𝑗 ) and record to record variability (𝜎𝜎𝑗𝑗 ), separately. (2) Unlike UPM, no
statistical dependences between the mean and record to record variability are incorporated in ordinary Kriging.
(3) Unlike ordinary Kriging, the UPM maps vary with the amount of observation data. When there is lessobservation data, UPM maps are smooth. The ordinary Kriging maps, on the other hand, are rough even when
there is less observation data. However, as the observation data increase, the UPM maps change and approachthe conventional mapping. This change in UPM map characteristics with the amount of observation data helps
quantify the convergence process.

3. NUMERICAL EXPERIMENT
3.1. Data
In engineering seismology, it is well established that alluvial deposits can significantly affect the amplitudes of
the incident seismic waves (Trifunac, 1971). Past studies indicate with high confidence (low uncertainty) that thewaves become highly amplified at around the center of an alluvial valley. However, there is a low confidence(high uncertainty) concerning the amplification characteristics at the boundary between the rock site and alluvial
valley. This is because the incident angle and frequency contents are well affected.
For the numerical experiment, we create a hypothetical model of the wave amplification in and aroundan alluvial valley as a spatial process (Fig. 1). Sixty-three sites are considered in one dimension. The sites are all
equally spaced except at the boundary between the rock site and alluvial valley where the sites are more densely
spaced. The reason behind this is to properly model the change in uncertainty as one moves away from highuncertainty at the boundary to the low uncertainty regions.
Random wave amplification samples (mean values shown as black dots in Fig. 1) are artificiallygenerated as observations at all these sites. Each observation sample refers to the wave amplification observedfor incident seismic waves during one earthquake event. The random samples at each site follow a lognormal
distribution. The known arithmetic means (µ) increase as a parabolic curve from the rock site to the center of thevalley representing high wave amplification. The record to record variability (σ ) is treated as the uncertainty,
which is high in the boundary zone of the rock site and the alluvial valley and low otherwise. The extreme
amplitude changes at the basin boundary occur as the incident angle and frequency contents are well affected at
the basin boundary (Trifunac, 1971).
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Fig. 1. Numerical experiment: A hypothetical model of wave amplification in andaround an alluvial valley

3.2 Results
Figure 2a shows eight different cases with 8, 16, 32, 64, 128, 256, 512 and 1024 artificial random samples persite. Each succeeding dataset with higher earthquake events includes the preceding dataset with lower
earthquake events. In all these cases, the gray circular dots show random samples, the blue line shows the
Kriging mapping, and the red line shows the UPM.
For cases with a low number of observations (N), the UPM shows a smooth transition in the highly
uncertain boundary zone between the rock site and alluvial valley, unlike the conventional mapping which isvery rough and fluctuating. This smoothness is introduced by Equation (1). The boundary zone has a high 𝜎𝜎𝑗𝑗 .
So, UPM makes the transition smooth by imposing a low sj in the boundary zone. A low sj means the 𝜇𝜇𝑗𝑗
values around site j do not vary much which makes the UPM smooth. However, in the low uncertainty areas
including the center of the valley, UPM behaves like Kriging. UPM maintains the Kriging shape in areas of low
𝜎𝜎𝑗𝑗 by imposing a high sj around j. A high sj means the 𝜇𝜇𝑗𝑗 values around site j vary considerably and hence nosmoothness is introduced in UPM in areas other than the boundary zone.
As the number of observations (N) increases, UPM starts to converge with Kriging. This change in thecharacteristics of UPM with the increase in the number of observations (N) is significant to gain anunderstanding of the population.
When the number of observations is low, there is less information for modelling and so the estimatedmodel parameters are quite unstable. The conventional mapping for the low observation dataset when comparedwith the known mean values is erroneous in the high uncertainty zone. In such a situation, the smoothness
introduced in the UPM in the highly uncertain boundary zone between the rock site and alluvial valley is a better
representative of the physical process than the erroneous conventional mapping.
However, when the number of observations (N) is high, there is more information for modelling and so
the estimated model parameters are stable. The conventional mapping for the 1024-observation dataset when18

A.CHAKRABORTY, H.GOTO

compared with the known mean values is almost the same. Due to increased data, error is also reduced in thehigh uncertainty region. It is very interesting to observe that the UPM now converges with the conventional
mapping. This finding shows that UPM yields reliable results as compared to conventional mapping when lessinformation is available and can be used to hint at data saturation as the number of observations increases.
Figure 2b shows the incremental KL divergence (∆𝐷𝐷𝐾𝐾𝐾𝐾 ) with respect to the number of observations,calculated using Equation (3). Sites located at the edges are not included in the calculation of ∆𝐷𝐷𝐾𝐾𝐾𝐾 because wewant to discuss the results as an interpolation problem. At the edge, the values are estimated as an extrapolation
problem. It is observed that ∆𝐷𝐷𝐾𝐾𝐾𝐾 starts to converge as the number of observations increases. This indicates thatthe mapping on UPM reaches convergence and the data set is sufficient to extract the population statistics.
Among them, we can set up the observation strategy to refer to the evolution of ∆𝐷𝐷𝐾𝐾𝐾𝐾 through the UPM.
It is difficult to take a similar approach using conventional mapping (ordinary Kriging). In Fig. 2a, UPM
gives a smoother transition under poor data information, which is very reasonable in the sense of appearance.
However, the ordinary Kriging has an unreasonably rough transition under poor data information. When data
information is richer, the UPM maps and the ordinary Kriging maps approach the hypothetical model of wave
amplification in Fig. 1. This transition of UPM maps from reasonably smooth to rough mapping with the change
in information quantity, allows the quantification of the convergence process.

Fig. 2. (a) Evolution of UPM and Kriging maps for numerical experiment(b) Plot of ∆𝐷𝐷𝐾𝐾𝐾𝐾 vs N for the UPM maps

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4. APPLICATION: REAL DATA
4.1 Data
The 2011 off the Pacific coast of Tohoku Earthquake caused heavy damage to life and property due to thetsunami and the strong ground motion. Severe damage occurred not only close to the shoreline, but also in areas
further into the mainland. Furukawa district in Osaki City, Miyagi prefecture of Japan experienced severe
damage in downtown residential areas (Goto and Morikawa, 2012). Significant spatial differences caused
mainly due to ground motion amplification (site amplification) were observed even on the sub-kilometer scale.
In the aftermath of the earthquake, a very dense seismic network for strong ground motions has been operated in
Osaki city (Goto et al., 2012). Figure 3 shows the layout of the seismic array consisting of 31 seismometers inthe significantly damaged area in Osaki city. The seismic array observation was jointly organized by Kyoto
University, Tokyo Institute of Technology, Osaki city office and aLab Co., Ltd.

Fig. 3. Spatial distribution of seismometers (▲) in Furukawa district, Japan
In this case study, earthquake data collected over 7 years from 31 sites in the seismic array is used togenerate a site amplification map of the area. A total of 176 earthquake events recorded between October 29,
2011 and September 19, 2018, were used for the analysis. These earthquake events are mostly aftershocks fromthe 2011 off the Pacific coast of Tohoku Earthquake and include all recorded events in the above-mentioned
period without any restriction on the amplitude threshold or source location condition. The average peak groundacceleration (PGA) of the recorded events ranges from 6 gal to 119 gal. The availability of observation data
varies with the sites. To study the convergence process, 6 datasets were created using groups of 8, 16, 32, 64, 128
and 176 earthquake events. Each succeeding dataset with higher earthquake events includes the preceding
dataset with lower earthquake events.
The mapping parameter in this case study is a factor of site amplification observed at site j during anearthquake event. It is defined as the logarithmic ratio of observed peak ground acceleration (PGA) or peakground velocity (PGV) at site j to the spatial average calculated over all the available sites during one earthquake
event. The PGA and PGV are calculated from the vector sum of the EW component and NS component of theearthquake record. To generate a UPM map of the site amplification, the dataset was comprised of 431 sites with
31 measurement sites from the seismic network and 400 missing sites, all distributed in a rectangular grid.
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4.2 Results
Figures 4a and 4b show the site amplification maps calculated using PGAs. For all the datasets, UPM has been
compared with Kriging maps. When the number of observations (N) is low, the UPM has a smooth characterwith gradual transitions between the site amplification values as compared to the Kriging map. However, as thenumber of observations increases, the two maps start to become increasingly similar. If we focus on how the
UPM changes with the increase in the number of observations, we observe that spatial variation starts appearing
on the map and starts to converge as the number of observations (earthquake events) increases. To discuss thisconvergence quantitatively, Fig. 4c shows a plot of ∆𝐷𝐷𝐾𝐾𝐾𝐾 with the N, the number of observations. The ∆𝐷𝐷𝐾𝐾𝐾𝐾 is
calculated only for the available sites common to all the events. It is shown that as the number of observations
increases, the ∆𝐷𝐷𝐾𝐾𝐾𝐾 decreases and starts to approach the minimum zero value. From the viewpoint of
information theory, it can be concluded that the data is approaching saturation. We can then manage the seismic
network, e.g., the observation period, and rearrange the layout to resolve the map in an unclear area, based on
UPM.

Fig. 4. (a) Evolution of Kriging maps of PGA amplifications in Furukawa district, Japan(b) Evolution of UPM maps of PGA amplifications in Furukawa district, Japan(c) Plot of ∆DKL vs N for the UPM maps of PGA amplifications
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Figures 5a and 5b show the site amplification maps calculated using PGVs. As before, both the UPM andKriging maps have been prepared for the datasets. The first glance shows the PGV plots are smoother incomparison to the PGA plots. As observed in the case of the PGA plots, in this case too the UPM plots start toconverge with the increasing number of observations. Figure 5c confirms that the data is approaching
convergence from the viewpoint of information theory.
Thus, both the site amplification plots conclude that the mapping in Furukawa is approaching data
saturation and based on the viewpoint of information theory, the current operation may be terminated. The
seismometers may be rearranged to resolve the unclear areas.

Fig. 5. (a) Evolution of Kriging maps of PGV amplifications in Furukawa district, Japan(b) Evolution of UPM maps of PGV amplifications in Furukawa district, Japan(c) Plot of ∆𝐷𝐷𝐾𝐾𝐾𝐾 vs N for the UPM maps of PGV amplifications

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5. DISCUSSION
It is evident from the cases discussed in Sections 3 and 4, that the optimum number of data which is deemedsufficient to extract useful information depends on the available dataset. In the case of numerical experiments,
data saturation is attained after 512 observations have been collected. However, in the case of the seismic arrayin Furukawa, Japan, 176 observations seem to be sufficient to understand the population statistics.
The reason for this difference might be explained based on the record to record variability present at thesites. In the numerical experiment, the peak of true record to record variability was high (𝜎𝜎𝑗𝑗 =3) in the boundary
zone. Thus, more data is necessary to accurately estimate the mean and the record to record variability (standard
deviation) in the boundary zone. However, although we will never know the true value of the population
statistics for the case study area in Furukawa, Japan, the maximum estimated record to record variability
recorded at any site was much lower and hence, lesser data was required to extract the desired information. Thus,
the optimum number of data will vary from case to case and is most likely to be affected by the presence of highuncertainty zones.
For the case study area in Furukawa, Japan, we used 400 missing sites to create the PGA and PGV site
amplification maps from 31 measurement sites, and the convergence process was quantified based on the maps
obtained. However, the convergence process would not change if the grid size was any different. This is because
the convergence is quantified considering the measurement sites only. Increase or decrease of grids using only
missing sites will have no effect on the quantification of the convergence process.
Also, the convergence processes for PGA and PGV site amplification maps are not identical. One reason
could be that the PGA and PGV processes are not the same. The spatial distribution patterns in Fig. 4 and Fig. 5
are clearly different. This means that the spatial datasets of PGA and PGV are different. Another reason could be
the difference in the information gain process for the two processes. Unless two processes have the same
incremental information gain and the same record to record variabilities at all locations, it will be rare for them tohave the same convergence process based on information theory.

6. CONCLUSION
The availability of data has increased over the recent decades. However, we cannot ascertain whether the amountof available data is sufficient, and we have no guidelines to plot the maps based on the available data consistent
with the data accumulation. In this study, we addressed these issues in terms of data visualization techniques.
We adopted UPM, which is a recently introduced mapping model that projects data uncertainties onto the map
resolutions and hence, is more reliable statistically. As a measure of data saturation, we define a parameter ∆𝐷𝐷𝐾𝐾𝐾𝐾 ,based on information theory, which quantifies information gain as maps are updated with new data over time.
Data saturation occurs when ∆𝐷𝐷𝐾𝐾𝐾𝐾 approaches zero, which means that no more spatial information is being
added to the maps and we can stop updating them.
The concept of visualizing data saturation was introduced as a numerical experiment using a simple
model of wave amplification in and around an alluvial valley. The boundaries between the rock site and alluvial
valley are high uncertainty zones. The results show that as we increase the number of observations, UPM starts
converging with the Kriging map. This is a significant finding as it shows that UPM yields reliable results ascompared to conventional mapping when less information is available and can be used to hint at data saturation
as the number of observations increases. Measuring the change in ∆𝐷𝐷𝐾𝐾𝐾𝐾 with the increasing number ofobservations, we found data saturation occurs after 512 observations have been collected.
The concept was then applied to a case study area in the Furukawa district of Japan where earthquake
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Journal of Natural Disaster Science, Volume 40，Number 2，2020，pp14-25

data has been collected for over 7 years from 31 seismometers in a dense seismic array. Convergence in site
amplification maps generated over different observation periods conclude that the mapping in Furukawa district
is approaching data saturation and from the viewpoint of information theory, the current operation may beterminated and the seismometers may be rearranged to resolve mapping in the unclear areas.

Acknowledgement
We are grateful to Prof. Sumio Sawada from the Disaster Prevention and Research Institute, Kyoto University,
Japan for his valuable comments and insights on the manuscript. We would also like to thank the twoanonymous reviewers whose comments helped improve and clarify the manuscript. This work was supported by
KAKENHI, Japan Society for the Promotion of Science (19H02224).

Computer Code Availability
Software Required: R, WinBUGS
Code Access: https://github.com/anirban1990/Visualising_DataSaturation_inUPM

Data availability
The seismic array data from Furukawa, Japan used in the application (Section 4) can be downloaded from:http://sn.catfish.dpri.kyoto-u.ac.jp/event_list/index.html. In total, there are 37 seismometers installed in the area.
However, in this study, 31 seismometers that are in the significantly damaged area were utilized. The
seismometers not considered in this study are F15, F21, F30, F32, F36 and F37.

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