Real-Time Earthquake Tracking and Localisation: A Formulation for Elements in Earthquake Early Warning Systems (Eews)

By George R. Daglish and Iurii P. Sizov

After the great tsunami of 2004 and the earthquake in Sichuan, China, in 2008, two big thinkers knew they must try to prevent the damage inflicted by surprise earthquakes.
George R. Daglish and Iurii P. Sizov teamed up to create an experimental seismic software system that contains application areas for inclusion in an earthquake early warning software structure.
In this book, they highlight the work they’ve done thus far.
The algorithms can be grouped into several main types: planar earth calculations to determine epicentres; calculations over a spherical earth model to determine epicentres; rapid tabular scans to determine epicentres and hypocentres concurrently, using either a spherical or a spheroidal earth geometry directly; and hypocentre scans using spheroidal earth geometry.
The authors also describe the testing of all members of the grouping, using real earthquake data. They assess the timing and accuracy of each against received and current results taken from the Incorporated Research Institutions for Seismology archive.
If the world doesn’t take concerted action to predict and track earthquakes, the consequences will be unthinkable, which is why we must work toward Real-Time Earthquake Tracking and Localisation.

• Language: English
• Publisher: AuthorHouse UK
• Release date: Sep 30, 2018
• ISBN: 9781546296812

George R. Daglish

George R. Daglish earned a bachelor of arts degree from Open University in England and a doctorate in applied mathematics from Birkbeck College in London. He retired from industry and academia. He’s seeking to create real-time algorithms for earthquake localisation algorithms for tsunami prediction. Iurii P. Sizov, a professor and Russian scientist, graduated from the physics department at Kazan State University before pursuing a Ph.D. at the Russian Academy of Sciences. He worked with the Pushkov Institute of Terrestrial Magnetism on the ionosphere and on radio wave propagation as well as the Russian Academy of Sciences. He is an inventor of geomagnetic equipment with several patents.

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© 2018 George R. Daglish and Iurii P. Sizov. All rights reserved.

No part of this book may be reproduced, stored in a retrieval system, or transmitted by any means without the written permission of the author.

Published by AuthorHouse 10/14/2019

ISBN: 978-1-5462-9682-9 (sc)

ISBN: 978-1-5462-9681-2 (e)

Library of Congress Control Number: 2018909612

Any people depicted in stock imagery provided by Getty Images are models,

and such images are being used for illustrative purposes only.

Certain stock imagery © Getty Images.

Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them.

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Contents

Chapter 1 Introduction

Chapter 2 Guidelines for Prototype Seismic System (EEW)

Chapter 3 Mathematical Discussion

Chapter 4 Hypocentre Location Using Tabular Data with Preliminary Illustrative Results

Chapter 5 The Ray Tracers Used

Chapter 6 Rapid and Concurrent Localisation of Epicentre and Hypocentre Pairs

Chapter 7 Reduced Simulation of Real-Time Earthquake Localisation – I

Chapter 8 Reduced Simulation of Real-Time Earthquake Localisation – II

Chapter 9 Concurrent Epicentre and Hypocentre Localisation using a Spheroidal Earth Model

Chapter 10 Earthquake Localisation and the Elliptic Correction

Acknowledgements

Annex A Description of System Entities

Annex B Basic System Diagrams

Annex C The Programs UETST 00.cpp and UETST 01.cpp

Annex D Wave Structure by Frequency Band Splitting

Annex E Levels of Integration: Verification of FFT against IDFT

Annex F Examples of the Basic Tabular Data

Annex G Some Preliminary Results of Hypocentre Determination

Annex H Results of Second Trial of Tabular Scanning

Annex I Derivation of the Calculation for the Surface Geodesic Curve Constant

Annex J Grid Scan for Global Minimum Using a Spider

Chapter 1

Introduction

The existence of powerful seismic events causing disaster, devastation, and severe dislocation is manifest.¹

This problem, which can deeply affect human society, is confronted from at least four vantage points:

• The epicentral/hypocentral location of earthquakes²³ – enabled by a global multiplicity of seismic station networks, international cooperation, and an understanding of the inner structure of the earth.

• The development of our understanding of the mechanisms that result in earthquakes and the direct observation of these.

• Direct observation at the confluence of tectonic plates by sea-going drilling platforms.

• Attempts to identify earthquake precursors.

It would appear vital for the future well-being of those who live in zones of high seismicity and potential high seismicity, for Advanced seismological processing networks (ASPNs) of some kind to be set up. Such networks could, in real, or near real time:

• Perform automatic epicentral/hypocentral localisations (with display and dissemimation of this information), by employing automatic detection of P and S arrivals, as well as surface wave onsets,

• Analyse and process incoming seismic signals to shed light on various models of earthquake mechanisms,

• Where the opportunity arises, correlate this signal analysis with knowledge gleaned from drilling activity—drilling though conjoined tectonic plates, as mentioned above.⁴

For long-range monitoring and possible prediction of minor and major earthquakes by such ASPN networks, several ranks, or levels, of data would appear to be required:

• The accurate extraction of the onset times for P, S, and various surface waves at seismic stations from seismic traces deconvolved from those output by receiving seismometers⁵⁶

• The nature of those physical structures found within the scope of active zones and regions thought to contain mechanisms for earthquake generation

• The nature of those physical structures through which the various wave species emitted by the seismic events are to travel, together with their state.

• Those parameters fundamental to models of earthquake mechanisms.⁷

• The state of such parameters

• And finally, the ongoing correlation of the above information with the time sequences of past earthquakes, within given zones of significant seismicity.⁸⁹

Prompted, particularly, by the great tsunami of 2004 and the 2008 Sichuan earthquake in China, we decided we should attempt to join these efforts by generating an experimental seismic software system, which should contain facilities, or application areas, that we could work up for inclusion as components in an earthquake early warning (EEW) software structure.

The body of Real-Time Earthquake Tracking and Localisation represents the state this experimental system has so far reached.

We first drew up a high-level project specification to give some direction and backbone to our research.

Specification

Those considerations set out initially call for research and development aimed at providing the consolidated theoretical background that should ultimately enable the implementation of such large intelligent seismic array systems with wide aperture.

The range of earthquakes that such systems would have to perceive, analyse and, locate should range from micro- and ultra-micro earthquakes ( 7388.png < 3) to small and moderate earthquakes 7377.png and to major earthquakes 7369.png Here 7360.png represents local magnitude in the Richter/Gutenberg sense. Further measures for magnitude include:

1. Surface wave magnitude (Gutenburg): 7352.png

2. Body wave magnitude (Gutenburg): 7341.png

3. Generalised magnitude (Bath): 7333.png

4. Duration magnitude (Suteau and Whitcomb): 7324.png

The dynamic range of seismic recording can be such that different families of stations should be provided to sense earthquakes at the aforementioned and correspondingly different bands of magnitude.

As stated at the outset, the need for such seismic arrays is manifest. They are required to monitor seismicity in regions where serious earthquakes occur on a regular basis. Further, they should provide a monitoring capability on a global scale both for natural and man-made seismic events.

Such a network should be available to study patterns of seismic activity, foreshock activity, P-wave velocity, velocity anomalies, and more. Statistics can then be gathered and built up to evaluate, for instance, any predictive/descriptive formulae derived from the Ishimoto–Iida relation. For example,

7315.png

The original Ishimoto–Iida relation was discovered as

7307.png

Here, N is the frequency of occurrence, and A is the maximum trace amplitude for earthquakes at approximately similar focal distances. m is found empirically to be 1.74. The number 7297.png of earthquakes is seen to increase tenfold with unit decrease in magnitude. Therefore, the greater number of smaller magnitude events one can collect, the greater knowledge of the occurring seismicity patterns one may obtain.

Precursor concepts include the LASA (Large Aperture Seismic Array) in Montana, United States of America; the NORSAR in Norway, Scandinavia; the World-Wide Standardized Seismic Network (WWSSN), along with the Global Seismic Network (GSN), established by Incorporated Research Institutes for Seismology (IRIS) and the USGS Central Californian Microearthquake Network.

The projected research program, as envisaged, could be split into two phases:

1. Exploration of the basic concepts and their validation in small- and large-scale simulation

2. Validation of the basic concepts by constructing simulated prototype seismological systems that emulate real-time working

Phase 1: Exploration of the Basic Concepts and their Validation in Small- and Large-Scale Simulation

This initial body of research is seen as having at least the following five components:

1. Development of the simple spherical shell or lamina and then the solid sphere, with regard to the solution of these simplified equation systems, in particular

7284.png       (1741,1)

Image11979v2%20NEW.psd    (1,2)

where

7265.png

and

7257.png

Then the solution vector for both (1.1) and (1.2) is:

7249.png

The Cartesians referred to here are coordinates within a space frame whose origin coincides with that of the centre of the object sphere. Thus, in (1.1),

7239.png

This fact allows the following derivation:

An arc length is given by an expression such as Rθ where R is the radius of the sphere or circle in question. Therefore, considering the sphere on whose surface emissions are being transmitted and removing the coordinate system origin to the centre of this sphere, we get

7230.png

Transposing functions gives

7222.png

as above. This system is then solved for 7213.png

To fix x use this system, 7205.png . It is notable that the above system is in the form of a set of planes the lengths of whose normals to the origin are time dependent and oscillate as cosine functions. We can write therefore for one such plane

7192.png

Here, a is now a vector of direction cosines for the ith normal. And x is the Cartesian point of emission in the space frame within which the sphere is embedded and whose origin coincides with the centre of the sphere.

These direction cosines will be given by

7180.png

A wave front corresponding to a specific velocity, 7170.png (in some sense a mean value for an isotropic medium) is defined by the intersection of the oscillating plane and a sphere of radius R.

It is also of note that the period of oscillation for the entire set of planes is given by

7162.png

The restitution of x can be considered to represent the point where all n planes mutually intersect and where, indeed, the point of intersection lies on the spherical surface of radius R.

The first of these equation systems (1.1) represents transmission over the surface of a spherical lamina. The second system represents a simple expression for transmission through the body of a solid and, ultimately, an arbitrarily layered sphere (Geiger’s method).

The Geiger concepts may be invoked so that either the earthquake focus (hypocentre) is found or estimated using a simple radial velocity structure or a simultaneous inversion problem can be solved, establishing the hypocentre parameters, using a complex three-dimensional velocity structure.

2. Investigation of the properties of (micro) seismic events in terms of the wave trains emitted as acoustic emissions – Investigation will include the following wave types:

P and S waves

Rayleigh waves

Love waves

Lamb waves

The use of initial system, above, allows for the analysis of three questions. First, can surface wave types (Rayleigh and Love waves), which are prevalent in certain earthquakes, be transmitted in such a way that this system may be deployed to determine epicentres (or mesocentres) from very long range to close up? Second, is there a mechanism that converts P and S waves to surface waves of this type when they impinge on the surface of the crust? Third, what is the occurrence and range of the approximation of the ducting of P and S waves by the lithosphere and is this a truly viable means of finding the epicentre using this system ?

These questions can be summed up as follows: What are the interrelationships between this group of waveforms and which forms can be processed by this system to establish seismic event parameters? Also how does directed body wave energy manifest itself to a surface or interface?

3. Projected properties of the acoustic emissions (AE) on and within spherical lamina in terms of

a) total internal reflection and

b) interference patterns

Both will be governed by the refractive properties, the radius of curvature, and the laminar thickness of the body. With regard to the velocity calculations, then, with ducting, the slowest path is that which progresses with reflections made at the critical angle.

The attenuation and bandpass effects of the earth system (surface, stratification, interfaces, and so on) on the body and surface waves generated by seismic events should also be investigated with a view to establishing an optimal spatial distribution for any projected layout of a system.

4. A study of the means whereby automatic (in other words, hands off) arrival time detection and cut-off time definition is to be achieved, given the characteristics of the wave patterns so formed – There are many suggestions to be taken from successful monitoring systems for this component.

One basic observation is that, given an onset of any of these wave types, in particular the potential arrival of P energy, then we might say

7154.png

This is onset detection by energy considerations, and the following definitions apply:

7146.png

We note that 7140.png and that τα < τβ.

If, then, the ratio γ exceeds a prescribed threshold 7135.png , an onset is deemed to have occurred.

However, we must also take into account new work instigated and developed by Pang Sze Kim et al. (13), which detects events in energy profiles using particle filters.

A further question is, Could we elevate the concept of motion intensity to the status of a pure onset indicator?

5. A study of the optimal manner in which to process all arrival times to (a) produce locations of hypocentres, epicentres, and mesocentres, together with their parameters, and (b) establish velocity structures for the region.

This will also involve the processing of event swarms. These aspects will include:

a. Arrival time buffering

b. Combinatorial scans in real time using cross-correlation, semblance functions and the like to ease the computational load

c. Estimation of error and