A statistical approach for controlling the probability of false alarm and missed detection in smartphone-based earthquake early warning systems

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A statistical approach for controlling the probability of false

alarm and missed detection in smartphone-based earthquake

early warning systems

Frank Yannick Massoda Tchoussi1and Francesco Finazzi2

1Department of Economics, University of Bergamo, via dei Caniana, 2, Bergamo,

24127, Italy

October 28, 2022

Abstract

Smartphone-based earthquake early warning systems (EEWS) are emerging as a complemen-

tary solution to classic EEWS based on expensive scientiﬁc-grade instruments. Smartphone-

based systems, however, are characterized by a highly dynamic network geometry and by noisy

measurements. Thus the need to control the probability of false alarm and the probability of

missed detection.

This paper proposes a statistical approach based on the maximum likelihood method to

address this challenge and to jointly estimate in near real-time earthquake parameters like

epicentre and depth.

The approach is tested using data coming from the Earthquake Network citizen science

initiative which implements a global smartphone-based EEWS.

Keywords: Maximum likelihood, Monte Carlo simulation, hypothesis testing.

1 Introduction

Earthquake early warning systems (EEWSs) [1, 2] are deployed in seismic areas to detect earthquakes

in real-time, in order to send a forewarning to citizens and to stop critical processes before the ground

shaking begins. Classic EEWSs are based on a dense network of scientiﬁc-grade instruments with

construction and operational costs in the order of millions of euros [3].

As a result of the accessibility of smartphones, and the advancement of technologies for mobile

apps development, low-cost EEWSs can be implemented. This path has been explored by the

Earthquake Network (EQN) citizen science initiative [4, 5, 6], which, since 2013, implements the

ﬁrst smartphone-based EEWS.

Smartphones are used to detect the ground shaking induced by the earthquake and a warning is

issued as soon as the earthquake is detected. People living at a further distance from the epicentre

may be alerted before they are reached by the damaging seismic waves.

The primary challenge faced by the EQN is to control the probability of false alarm and the prob-

ability to miss an earthquake. Since the earthquake detection is based on smartphone accelerometer

readings, alerts may be triggered by events unrelated with earthquakes. Also, it is possible that the

network misses a (possibly strong) earthquake, especially if the number of monitoring smartphones

is small. Both false alarms and missed detections undermine people trustiness on the EEWS.

arXiv:2210.15466v1 [stat.AP] 27 Oct 2022

This paper proposes a statistical approach based on maximum likelihood and hypothesis testing

methods to address the above mentioned problems and to jointly estimated earthquake epicentre

and depth in near real-time (i.e., in less than one or two seconds).

The statistical approach is developed and tested using Monte Carlo simulations which rely on the

EQN smartphone network, and it is then applied to some true and false EQN earthquake detections.

2 Detection algorithm

Before describing the statistical methodology developed in this work, we detail the output of the

earthquake detection algorithm currently implemented by EQN [7]. For any given area of radius

30 km, the algorithm compares the number of triggering smartphones in the last 10 seconds with

the number of active smartphones. A triggering smartphone is a smartphone that detected an

acceleration above a threshold, while an active smartphone is a smartphone known to be monitoring

for earthquakes. If the ratio between triggering smartphones and active smartphones exceeds a

threshold, an earthquake is claimed to be detected. The output of the detection algorithm consist

of the detection location and of the list of the triggering smartphones (triggers for short), which are

identiﬁed by their spatial coordinates (latitude and longitude) and by the triggering time.

3 Statistical modelling

The generic observed triggering time for a smartphone sensing an earthquake is modelled as

ti=t∗

i+i,(1)

where t∗

iis the expected triggering time while i∼N(0, σ2

) is a random component. More in detail

t∗

i=Di,H

v+tO,(2)

with

Di,H =sd2

E+ 4R(R−dE)sin Di,E

2R2

,(3)

the distance between the hypocentre and the smartphone location, vthe seismic wave speed and

tOthe earthquake origin time. In (3), Di,E is the distance between the epicentre (latE, lonE) and

the smartphone location, dEis the earthquake depth and Rthe earth radius (6371 km). Here, it

is assumed that all smartphones either detect the primary seismic wave (v= 7.8 km/s) or they

all detect the secondary wave (v= 4.5 km/s). This assumption is justiﬁed by the fact that the

earthquake detection is based on smartphones within a radius of 30 km, which is a relatively small

area.

The role of the random component iis to model the diﬀerence between the expected and the

observed triggering time. This diﬀerence is mainly due to the smartphone detection delay and to a

seismic wave speed that may diﬀer from the expected values.

Let us deﬁne ∆ti=ti−t∗

i, then ∆ti∼N(0, σ2

). The model parameter vector is θ=

(latE, lonE, dE, tO, σ2

).

To classify an earthquake detection between true and false, we implement a statistical hypothesis

test on the variance of ∆ti. The system of hypothesis is given by

H0:σ2

=δ

H1:σ2

> δ. (4)

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摘要：

Astatisticalapproachforcontrollingtheprobabilityoffalsealarmandmisseddetectioninsmartphone-basedearthquakeearlywarningsystemsFrankYannickMassodaTchoussi1andFrancescoFinazzi21DepartmentofEconomics,UniversityofBergamo,viadeiCaniana,2,Bergamo,24127,ItalyOctober28,2022AbstractSmartphone-basedearthquakee...

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A statistical approach for controlling the probability of false alarm and missed detection in smartphone-based earthquake early warning systems

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