## 24 November 2017

### Bought Roy Peter Clark's book, "Writing Tools"

I thought my first copy was lost: I cannot find it in my office shelf. I scanned all my books back and forth, but to no avail. And then I remembered: I gave my copy to my sister years ago. That explains it.

I love Writing Tools. Strunk and White may give you the bare bones for writing well, but Roy Peter Clark gives you the tools to dissect a prose like a corpse, as what da Vinci did to study the anatomy of the human body. Knowing how a prose is designed allows you to think of writing as a design process: how to connect the parts and stitch them together. Well, there's always a danger of making a Frankenstein monster--something you see in this age of Google and Wikipedia: different sentences from diverse voices and tenses lumped together to form a hideous paragraph. The danger is there, but the reward is greater: ars poetica--the perfection of the word made flesh.

I went to FullyBooked, but there is no more copy left in all their branches. So I went to National Bookstore.

"Miss, do you have the book, Writing Tools, by Roy Peter Clark?" I asked

"Please write down the title and author," she said and gave me a piece of post-it paper. Then she typed something in her computer.

"Writing Tools: 50 Strategies for Every Writer? Is this the book?" She asked.

"Yes, that's the book," I said.

She went upstairs through a spiral staircase. After a while, she came down holding a book in spring green cover. It's Writing Tools.

I shall be a writer again. Tonight, I shall write the saddest lines.

## 16 November 2017

### Strike, dip, and rake directions in focal mechanism

Vincent S. Cronin wrote A Primer on Focal Mechanism Solutions for Geologists (2010). My interest in his work is in his descriptions of fault vectors and angles. I need to use these standard names if I wish to write a paper on Focal Mechanism of Earthquakes.

Based on Cronin's diagram in p. 6, the reference strike, which we shall denote by $\mathbf e_{strike}$ appears to be the direction of the fault line as seen from a drone camera flying overhead high above the fault. The dip vector, which we shall denote by $\mathbf e_{dip}$, is a vector perpendicular to the reference strike $\mathbf e_{strike}$ and lies along the fault plane. The direction of $\mathbf e_{dip}$ is downward along the fault in Cronin. In this way, if we define the rake $\mathbf e_{rake}$ as the direction of the movement of the one side of the fault, then $\mathbf e_{rake}$ can be expressed as a rotation of $\mathbf e_{strike}$ about $\mathbf e_{dip}\times\mathbf e_{strike}$ by an angle $\theta_{rake}$, which is positive if the rotation is counterclockwise and negative if clockwise, following the right hand rule. These considerations results to the following expression for the rake direction $\mathbf e_{rake}$:

\mathbf e_{rake} = \mathbf e_{strike}\cos\theta_{rake} - \mathbf e_{dip}\sin\theta_{dip}.

But even then, there is an uncertainty in the definition of the strike direction $\mathbf e_{strike},$ since $-\mathbf e_{strike}$ can also be the initial definition. Perhaps, the strike direction should be defined as that which makes an acute angle with respect to the north direction.

## 15 November 2017

### Trend and plunge angles of faults

In his web page on Data in Structural Geology, W. F. Waldron of University of Alberta defined fault directions in terms of the trend angle $T$ and the plunge angle $P$. Here, we shall use his angular notations, but rewrite his coordinate system in vector form and redraw his diagram.

To define the direction of the trend-plunge unit vector $\mathbf e_{TP}$, we first define a right-handed coordinate system $\mathbf e_1$, $\mathbf e_2$, and $\mathbf e_3$ for East, North, and Up directions. The plunge angle $P$ would then be the angle made by $\mathbf e_{TP}$ with the East-North plane. In other words,

\mathbf e_{TP}\cdot\mathbf e_3 = -\cos(90^\circ-P)=-\sin P\equiv n,

so that the projection onto the East-North Plane would then be $\cos P$. Next, we define the trend angle $T$ as the clockwise angle from North to East that the $\cos P$ projection of $\mathbf e{TP}$ makes with the Northward axis $\mathbf e_2$. This allows us to compute the other direction cosines along $\mathbf e_1$ and $\mathbf e_2$:
\begin{align}
\mathbf e_{TP}\cdot\mathbf e_1 &= \cos P\sin T\equiv \ell,\\
\mathbf e_{TP}\cdot\mathbf e_2 &= \cos P\cos T\equiv m.
\end{align}
Combining these relations, we obtain the expression for the vector $\mathbf e_{TP}$ in Eastward, Northward, and Upward coordinates:
\begin{align}
\mathbf e_{TP} &= \mathbf e_1\cos P\sin T + \mathbf e_2 \cos P\cos T -\mathbf e_3\sin P\nonumber\\
&=\ell\mathbf e_1 + m\mathbf e_2 + n\mathbf e_3.
\end{align}

## 12 November 2017

### Writing three paragraphs per sitting is liberating

With three paragraphs I can already tell a story--a story with a beginning, middle, and end--though not necessarily in that order, as Jean-Luc Godard would say.

There is sheer joy in writing--something like chiseling a Pieta from a marble block with letters, words, and paragraphs. Then something takes shape: the words become the mirror of my mind. "In the beginning was the Word," says the John the Beloved. Christ is the Word of God. Christ is the image of God---perhaps in the same way as our words reveal who we are. And yet in this case our metaphor fail, though they are the closest theologians can think of in describing the relationship of the Father and the Son in the Uni Trinoque or the Holy Trinity.

I haven't blogged for a long, long time. And writing these three paragraph spurts has been cathartic. I just need to get words out of my heart, before I go crazy trying to hold them in. And so with Jeremiah, I pray: "You duped me, O LORD, and I let myself be duped...I say to myself, I will not mention him, I will speak in his name no more. But then it becomes like fire burning in my heart, imprisoned in my bones; I grow weary holding it in, I cannot endure it." (Jer 20:7-9)

### If you have time, read Ecclesiastes 12:1-8

It is a meditation on old age. But what really captivates me is the power of its poetry. It is just one long sentence separated by semicolons, and then one short sentence with vanity repeated thrice:
Remember your Creator in the days of your youth, before the evil days come and the years approach of which you will say, “I have no pleasure in them”; 2 before the sun is darkened and the light and the moon and the stars and the clouds return after the rain; 3 * when the guardians of the house tremble, and the strong men are bent; when the women who grind are idle because they are few, and those who look through the windows grow blind; 4 When the doors to the street are shut, and the sound of the mill is low; when one rises at the call of a bird, and all the daughters of song are quiet; 5 when one is afraid of heights, and perils in the street; when the almond tree blooms, and the locust grows sluggish and the caper berry is without effect, because mortals go to their lasting home, and mourners go about the streets; 6 * before the silver cord is snapped and the golden bowl is broken, and the pitcher is shattered at the spring, and the pulley is broken at the well, 7 and the dust returns to the earth as it once was, and the life breath returns to God who gave it.* a 8 Vanity of vanities, says Qoheleth, all things are vanity! (Eccl 12:1-8)
Someday, perhaps next year, I wish to make a poster illustrating the nouns and verbs described in this passage: the darkening sun, the tranquil night, the old warrior, the idle grindstone, the blossoming almond tree, the tired locust, the caper berry, the street mourners, the snapped silver cord, the broken golden bowl, the shattered pitcher, the broken pulley.

Or perhaps instead of a poster, I shall write a story.

## 11 November 2017

### Today, I deleted all my blog posts

Well, not exactly. I only hid them from view. They are still there in in my blog, buried like a treasure in the field. Perhaps, this is what Virgil felt regarding his Iliad. Or Brahms regarding his musical compositions. Or Gerard Manley Hopkins regarding his poems. Nothing short of perfection should be regarded as art. Carthage must be destroyed.

I need a new leaf in life. I felt stretched and weary, spread out too thinly butter, as Bilbo would say. I felt that my previous posts had defined me as just one of those bloggers for hire, churning out dozens of utilitarian how-to posts and listicles every week to feed the insatiable appetite of social media platforms and search engines. I am tired running after eyeballs. I need the solitude of deep writing. I need a monastery.

I am Jaguar Paw! This is my forest! I am Quirino Sugon Jr. This is my blog.

1. This is my first use of TweetDeck.  I logged in using my Twitter account: @QuirinoSugonJr. I used TweetDeck for five reasons

### On blogging

1. I still can't figure out what to do with this blogPerhaps, I over think too much when it comes to blogging. Talent is both a gift and a burden, as my high school Trigonometry teacher once told me. I know that I have a gift for blogging, but this gift is also a burden. And a blogging fit has seized me again with the following question: Should I consolidate my blogs into one blog or should I make separate blogs for each of my interests? I have been trying to answer this question again and again. And my blogger friend in FB would always laugh at me and say that she also had too many blogs before; now, she just have one blog. And she advises me to do likewise.
2. The things I write here are for Blogger users. But most of the things here also apply for Wordpress users.
3. One of the perennial problems of bloggers is how to categorize their posts.  Sometimes, one category has 100 articles written about it, while another category only has 10, and still another has only 2. Clearly, one needs a balance in the number of articles per category.  If a category gets too many articles compared to the others, that category needs to broken up into sub-categories.

## 06 July 2017

### Cover of Introduction to Physics by Glover and Sugon

 "An Introduction to Physics" by Fr. Francisco Glover, SJ and Dr. Quirino Sugon Jr (C & Publishing, May 2017, 575 pages) is an excellent textbook for senior high schools in both public and private schools. Price is Php 745. To order your copies, contact qsugon@ateneo.edu.

### How to use file folders to organize your documents

I felt stressed. There were assorted documents stashed inside my bag. On my table lie some loose papers I haven't filed: they were sitting on top of notebooks in various stages of disarray. The file folders on the right side of my desk are arranged neatly, but I know at the back end are some documents that I haven't properly filed. And what was my filing system again?

Entropy in Physics is a measure of the state of disorder of a system. According to the 2nd Law of Thermodynamics, the state of disorder of an isolated system can only increase. Hence, the mess.

So I decided to overhaul my folder filing system. I sorted the papers into different folders. Each folder has a two or three level classification system. In some folders, I use the institutional categories. The is usually an institution, such as Ateneo (for Ateneo de Manila University) and MO (Manila Observatory). The succeeding keywords are just modifiers, e.g. "MO history CD" or "Ateneo faculty appointment." The folders are then arranged alphabetically. In other papers, I use topical categories, e.g. "Person," "Medical," and "Magazine." For example, "Person: Sugon, Paul," "Medical: HealthDev," and "Magazine: Space Weather Quarterly."

I have thrown about 500 papers of trash, which I cut into thin strips by ripping a handful of papers by hand--about four to five strips per paper. The folders I keep. I can always relabel them using a self-adhesive continuous label paper--just a simple paper sticker of size 24 mm x 90 mm, with 10 pieces per fold. I did not anymore use my electronic labelers, because printing a plastic label is costly, though the labels last long and won't fade with time. But my priorities are organization efficiency and cheap price, not beauty and elegance. So I stick with paper stickers.

It took me 6 hours to reclassify and file my documents. Hopefully, I should now be able to find any document in less than one minute.

My next job is to overhaul my drawers.

## 24 March 2017

### Notes: "Telluric currents: The Natural Environment and Interactions with Man-Made Systems" by Lanzerotti and Gregori 1986

I am interested in telluric currents, because they are somehow connected with the equatorial electrojet and earthquakes. What I'll do is to extract some passages from the paper by Lanzerotti and Gregori (1986) which are relevant to EEJ and earthquakes, and then write my comments.

A. Sources of Telluric Currents
The term telluric currents can be interpreted to include currents flowing both within the solid Earth and within the seas and oceans.... They are produced either through electromagnetic induction by the time-varying, external-origin geomagnetic field or whenever a conducting body (such as seawater) moves.... across the Earth's permanent magnetic field. Both causes produce telluric currents, which in turn produce magnetic fields of their own---fields that add to the external origin geomagnetic field and produce a feedback on the ionosphere current system... (Lanzerotti and Gregori 1986, p. 232)
How fast the seawater move along the horizontal direction? In Antartica the ocean current 2 miles below the surface travels at the speed of 0.2 m/s (Fox News). In the US, the Gulf Stream reaches 2.5 m/s at its peak and goes down to 0.44 m/s (NOAA). These currents also cause magnetic field variations:
It's well established that ocean currents, such as the Gulf Stream in the Atlantic, form the circulatory system of the seas. These currents bring up nutrient-rich cold water from the ocean depths and carry it to different parts of the Earth. It's also known that dissolved salts in seawater conduct electricity, and as ocean currents move within Earth's main magnetic field, they generate their own secondary magnetic field. Scientists had previously made spot measurements of this "oceanic" magnetic field and concluded that it is too weak to explain secular variation. But based on his new mathematical model, Ryskin says, the total field generated by all the ocean currents in the world is roughly equal to measurements of secular variation. If his calculations are correct, anything that affects the flow of the ocean's currents—from global warming to plate tectonics—can also impact Earth's protective magnetic shield. (National Geographic)
B. Lunar Tidal Harmonic Component
Malin (1970, 1973), in considering the lunar tidal harmonic component $M_s$ (... with a period of half a lunar day), succeeded in separating the effect of direct electromagnetic induction from the ionosphere from the currents produced by oceanic tidal flow. He assumed that the geomagnetic variation associated with the tidal component should always be observed, independent of local time, whereas the ionosphere component should be negligible at midnight.(Lanzerotti and Gregori 1986, p. 232) (
What is a lunar day?
A lunar day is the period of time it takes for the Earth's Moon to complete one full rotation on its axis with respect to the Sun. Equivalently, it is the time it takes the Moon to make one complete orbit around the Earth and come back to the same phase. It is marked from a new moon to the next new moon. With respect to the stars, the Moon takes 27 Earth days, 7 hours and 43 minutes 12 seconds to complete its orbit;[1] but since the Earth-Moon system advances around the Sun in the meantime, the Moon must travel further to get back to the same phase. On average(mean), this synodic period lasts 29 days, 12 hours, 44 minutes and 3 seconds.[1]
The term "lunar day" may also refer to the period between moonrises in a particular location on Earth. This period is typically slightly longer (50 minutes) than a 24-hour Earth day, as the Moon revolves around the Earth in the same direction as the Earth's axial rotation.[2] (Wikipedia: Lunar Day)
There is an ambiguity in the definition of the lunar day. but I think Malin's work uses the 25:10 hour-minute duration. I can check this later. Nevertheless, half a lunar day is still about 12 hours, while an equatorial electrojet varies with a 24 hour period. I would be interesting to observe the contributions of ocean currents due to lunar tides in magnetometer data.

C. Local Earth Conductivity Anomalies
No equivalently sophisticated modeling, even for long-period geomagnetic variations, can usually be found for Earth currents. This situation exists principally because of the frustrating indeterminacies introduced by local Earth conductivity anomalies. (Lanzerotti and Gregori 1986, p. 233)
The local magnetic field due to crustal magnetization were already mapped this year 2017 by Swarm satellites:
Although this ‘lithospheric magnetic field’ is very weak and therefore difficult to detect from space, the Swarm trio is able to map its magnetic signals. After three years of collecting data, the highest resolution map of this field from space to date has been released. “By combining Swarm measurements with historical data from the German CHAMP satellite, and using a new modelling technique, it was possible to extract the tiny magnetic signals of crustal magnetisation,” explained Nils Olsen from the Technical University of Denmark, one of the scientists behind the new map.....“The new map defines magnetic field features down to about 250 km and will help investigate geology and temperatures in Earth’s lithosphere.” (European Space Agency)
Since this is now established, it may soon be possible to map out the Earth currents.

REFERENCES

Lanzerotti, L.J. and Gregori, G.P., 1986. Telluric currents: the natural environment and interactions with man-made systems. The Earth’s electrical environment, National Academy Press, Washington, DC, pp.232-257.

## 23 March 2017

### Square roots of 1, -1, and 0 in Geometric Algebra

Clifford (geometric) algebra is so simple that it can be learned by an undergraduate mathematics, physics, or engineering major. There are only three fundamental rules that distinguish it from other mathematics:
1. If $\mathbf e_1$ is a unit vector, then $\mathbf e_1^2=1$. (Normality Rule)
2. If $\mathbf e_2$ is another unit vector perpendicular to $\mathbf e_1$, then $\mathbf e_1\mathbf e_2=-\mathbf e_2\mathbf e_1$. (Orthogonality Rule)
3. The juxtaposition products of vectors are associative. (Associativity Rule)
What I shall now show is that these three rules would allow us to define the square roots of 1, -1, and 0.  In doing so I shall teach you the fundamentals of Clifford (Geometric) Algebra.  And I assure you that once you learn geometric algebra, you'll never see vectors and imaginary numbers in the same way again.

1. Square Roots of 1

Let us now take our proposed rules as they are and try out some products:
\begin{align} \mathbf e_1\mathbf e_1 &= 1,\\ \mathbf e_2\mathbf e_2 &= 1. \end{align}. This means that there are at least six things that are square roots of $1$:

\sqrt{1} = \{\pm 1, \pm\mathbf e_1, \pm\mathbf e_2 \}.

2. Square Roots of -1

Let us define a new quantity $\hat\imath$ (pronounced as "i hat" or "I am wearing a hat" if you wish to be very literal):
$$\hat\imath = \mathbf e_1\mathbf e_2.$$ What is the product of $\hat i$ with itself? Following our rules, here are the steps: \begin{align} \hat\imath^2 &= (\mathbf e_1\mathbf e_2)(\mathbf e_1\mathbf e_2)\nonumber\\ &= \mathbf e_1\mathbf e_2\mathbf e_1\mathbf e_2\nonumber\\ &= \mathbf e_1(\mathbf e_2\mathbf e_1)\mathbf e_2\nonumber\\ &= \mathbf e_1(-\mathbf e_1\mathbf e_2)\mathbf e_2\nonumber\\ &= -\mathbf e_1(\mathbf e_1\mathbf e_2)\mathbf e_2\nonumber\\ &= -\mathbf e_1\mathbf e_1\mathbf e_2\mathbf e_2\nonumber\\ &= -(\mathbf e_1\mathbf e_1)(\mathbf e_2\mathbf e_2)\nonumber\\ &= -(1)(1)\nonumber\\ &= -1. \end{align}
So $\hat\imath^2=-1$, which means that $\hat\imath$ is an imaginary number. Thus, the imaginary number has become imaginable by expressing it in terms of vectors. Actually, there are now at least two square roots of $-1$:
\sqrt{-1} = \pm \mathbf e_1\mathbf e_2.

3.  Square Roots of 0

Let us define the following quantities:
\begin{align} \hat{\mathbf e}_+ &= \mathbf e_1+\mathbf e_1\mathbf e_2 = \mathbf e_1 + \hat\imath,\\ \hat{\mathbf e}_- &= \mathbf e_1-\mathbf e_1\mathbf e_2 = \mathbf e_1 - \hat\imath,\\ \end{align}
Using our rules, we can show that both $\hat{\mathbf e}_+$ and $\hat{\mathbf e}_-$ square to zero. It suffices to prove only the case for one of them.  But before we do this, let us first note that \begin{align} \mathbf e_1\hat\imath &= \mathbf e_1(\mathbf e_1\mathbf e_2) = \mathbf e_2 = -\hat\imath \mathbf e_1,\\ \mathbf e_2\hat\imath &= \mathbf e_2(\mathbf e_1\mathbf e_2) = -\mathbf e_1 = -\hat\imath\mathbf e_2. \end{align}
That is, the unit vectors $\mathbf e_1$ and $\mathbf e_2$ anticommute with the imaginary number $\hat\imath =\mathbf e_1\mathbf e_2$, and that right-multiplying these vectors with $\hat\imath =\mathbf e_1\mathbf e_2$ rotates the vectors counterclockwise by $90^\circ$.

We can now proceed with our proof: \begin{align} \hat{\mathbf e}_+^2 &= (\mathbf e_1 +\hat\imath)^2\\ &= (\mathbf e_1 +\hat\imath)(\mathbf e_1 +\hat\imath)\\ &= \mathbf e_1\mathbf e_1 + \mathbf e_1\hat\imath + \hat\imath\mathbf e_1 + \hat\imath^2\\ &= 1 +\mathbf e_2 - \mathbf e_2 - 1\\ &= 0. \end{align} The proof for $\hat{\mathbf e}_-^2=0$ is similar.

In the succeeding posts, I shall discuss the geometric interpretations of our vector product rules. I shall also show how to rotate vectors in three dimensions and how to unify the dot and cross products of vectors into a single geometric product.

## 19 March 2017

### How to find the shortest distance between two skew lines

 Fig. 1. Two lines initially at $\mathbf r_{01}$ and $\mathbf r_{02}$ are drawn towards directions $\mathbf n_1$ and $\mathbf n_2$ at distances $s_1'$ and $s_2'$ from their initial positions. Fig. 2. Two unit vectors $\mathbf n_1$ and $\mathbf n_2$ and their parallel and perpendicular projections with respect to each other.

A. PROBLEM

Suppose you have two lines $\mathbf r_1$ and $\mathbf r_2$ passing through points $\mathbf r_{01}$ and $\mathbf r_{02}$ with directions defined by the unit vectors $\mathbf n_1$ and $\mathbf n_2$:
\begin{align}
\mathbf r_1 = \mathbf r_{01} + \mathbf n_1 s_1,\\
\mathbf r_2 = \mathbf r_{02} + \mathbf n_2 s_2,
\end{align}
where $s_1$ and $s_2$ are scalar parameters.  What is the shortest distance between the two lines?

B. SOLUTION

Let $\mathbf r_1=\mathbf r_1'$ and $\mathbf r_2=\mathbf r_2'$ be the endpoints of the line segment that corresponds to the shortest distance between the two lines:
\begin{align}
\mathbf r_1' &= \mathbf r_{01} +\mathbf n_1s_1',\\
\mathbf r_2' &= \mathbf r_{02} +\mathbf n_2s_2'.
\end{align}
The difference between these two equations is

\mathbf b = \mathbf r_2'-\mathbf r_1' = \mathbf a+\mathbf n_2s_2'-\mathbf n_1s_1',

where

\mathbf a = \mathbf r_{02}-\mathbf r_{01}.

To find the shortest distance $b = |\mathbf b|$, we need to express the distances $s_1'$ and $s_2'$ in terms of the given parameters $\mathbf a$,  $\mathbf n_1$, and $\mathbf n_2$.

From geometry, we know that at the shortest distance $b$ between the two lines, the vector $\mathbf b$ must be perpendicular to both directions $\mathbf n_1$ and $\mathbf n_2$, so that
\begin{align}
\mathbf b\cdot\mathbf n_1 &= 0,\\
\mathbf b\cdot\mathbf n_2 &= 0.
\end{align}
Substituting the expressions for $\mathbf b$, we get
\begin{align}
\mathbf a\cdot\mathbf n_1  &=  s_1' - (\mathbf n_2\cdot\mathbf n_1) s_2',\\
\mathbf a\cdot\mathbf n_2 &= (\mathbf n_1\cdot\mathbf n_2) s_1' - s_2' .
\end{align}
Solving for the distances $s_1'$ and $s_2'$ yields our desired expressions:
\begin{align}
s_1' &=\frac{(\mathbf a\cdot\mathbf n_1)-(\mathbf n_1\cdot\mathbf n_2)(\mathbf a\cdot\mathbf n_2)}{1 - (\mathbf n_1\cdot\mathbf n_2)^2},\\
s_2' &= \frac{- (\mathbf a\cdot\mathbf n_2)+(\mathbf n_1\cdot\mathbf n_2)(\mathbf a\cdot\mathbf n_1) }{1-(\mathbf n_1\cdot\mathbf n_2)^2}.
\end{align}

Another way to rewrite the expressions for $s_1'$ and $s_2'$ is to define two vectors $\mathbf c_1$ and $\mathbf c_2$:
\begin{align}
\mathbf c_1 &= \mathbf n_1 -(\mathbf n_1\cdot\mathbf n_2)\mathbf n_2,\\
\mathbf c_2 &= \mathbf n_2 -(\mathbf n_1\cdot\mathbf n_2)\mathbf n_1.
\end{align}
These two vectors have the same magnitude $c$:

c = c_1 = c_2 = \sqrt{1 - (\mathbf n_1\cdot\mathbf n_2)^2}.

Thus, $s_1'$ and $s_2'$ simplify to
\begin{align}
s_1' &= \frac{\mathbf a\cdot\mathbf c_1}{c^2},\\
s_2' &= \frac{-\mathbf a\cdot\mathbf c_2}{c^2}.
\end{align}

Using these expressions for $s_1'$ and $s_2'$, the vector $\mathbf b$ becomes

\mathbf b = \mathbf a - \left(\frac{\mathbf a\cdot\mathbf c_2}{c^2}\right)\mathbf n_2-\left(\frac{\mathbf a\cdot\mathbf c_1}{c^2}\right)\mathbf n_1.

The magnitude $b$ of $\mathbf b$ is the shortest distance between the two lines whose initial points are connected by the vector $\mathbf a$ and whose directions are given by $\mathbf n_1$ and $\mathbf n_2$, with $\mathbf c_1$ being the component of $\mathbf n_1$ perpendicular to $\mathbf n_2$ and $\mathbf c_2$ being the component of $\mathbf n_2$ perpendicular to $\mathbf n_1$.

## 18 March 2017

### Notes: "The Relationship Between Loss, Conductivity, and Dielectric Constant" by Bishop 2001

I found a thorough discussion on the relationship of loss, conductivity, and dielectric constant written by Chris Bishop in 2001. His derivations are based on Maxwell's equations in electrodynamics, using Advanced Engineering Electromagnetics by Balanis as reference. My interests in his paper are only in his scalar relations, which I need for modelling the electrical properties of soil, sand, and rocks.

1. Conductivity and Mobility

The conductivity $\sigma_s$ of a medium is related to its electric mobility $\mu_e$ by

\sigma_s = -q\mu_e,

where $q$ is the magnitude of the electronic charge. This is the first time that I have heard of the term electric mobility $\mu_e$, but it looks like it is a measure of conductivity per electron. The symbol $\mu_e$ is similar to the permeability of free space $\mu_0$, but the two quantities are different.

2. Complex Permittivity

The complex permittivity $\epsilon$ may be decomposed as

\epsilon = \epsilon' - i\epsilon'',

where $\epsilon'$ is the real component and $-i\epsilon''$ is the imaginary component. I used the symbol $i$ for the imaginary number instead of the symbol $j$ because I am a physicist not an engineer. To convert this into the form of Bishop (2001), we write

\epsilon = \epsilon_0\epsilon_r,

where $\epsilon_0$ is the permittivity of free space. Bishop said that the imaginary part of the relative permittivity is related to energy loss.

3. Conductivities for Static and Alternating Fields

If the applied electric field is not stationary but fluctuating with a frequency $\omega$, the effective conductivity $\sigma_e$ is the sum of the conductivities $\sigma_s$ and $\sigma_a$ for the static field and alternating fields:

\sigma_e = \sigma_s + \sigma_a,

where

\sigma_a = \omega\epsilon''.

Notice that if the field is constant, then the angular frequency of the field is $\omega = 0$, so that

\sigma_e = \sigma_s.

4. Loss Tangent

The loss tangent is defined as

\tan \delta_e = \frac{\sigma_e}{\omega\epsilon'}.

Expanding the effective conductivity $\sigma_e$, we get
\begin{align}
\tan \delta_e &= \frac{\sigma_s + \sigma_a}{\omega\epsilon'}
= \frac{\sigma_s + \omega\epsilon''}{\omega\epsilon'}
=\frac{\sigma_s}{\omega\epsilon'} +\frac{\epsilon''}{\epsilon'}.
\end{align}
According to Bishop (2001), the first term $\sigma/\omega\epsilon$ describes loss due to collisions of electrons with other electrons and atoms, while the second term $\epsilon''/\epsilon'$ how much energy supplied by an external electric field is dissipated as motion and heat. In dielectrics, $\epsilon''/\epsilon'>>\sigma/\omega\epsilon$. In metals, the real and imaginary parts of the permittivity are approximated as $\epsilon'=\epsilon_0$ and $\epsilon''=0$. And for semiconductors,$\epsilon''/\epsilon'\approx\sigma/\omega\epsilon$.

REFERENCES

Balanis, C.A., 2012. Advanced engineering electromagnetics. John Wiley & Sons.

## 05 March 2017

### Notes on "Medium effect on the characteristics of the coupled seismic and electromagnetic signals" by Huang et al. 2015

Recently developed numerical simulation technique can simulate the coupled
seismic and electromagnetic signals for a double couple point source or a finite fault planar source.
Besides the source effect, the simulation results showed that both medium structure and medium
property could affect the coupled seismic and electromagnetic signals. The waveform of coupled
signals for a layered structure is more complicated than that for a simple uniform structure.
Different from the seismic signals, the electromagnetic signals are sensitive to the medium properties
such as fluid salinity and fluid viscosity. Therefore, the co-seismic electromagnetic signals may be

REFERENCES

Huang, Q., Hengxin, R.E.N., Zhang, D. and Chen, Y.J., 2015. Medium effect on the characteristics of the coupled seismic and electromagnetic signals. Proceedings of the Japan Academy, Series B, 91(1), pp.17-24.

### Notes on "Anomalous behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9.0)" by Xu et al. 2013

There have been many reports on ultra-low-frequency (ULF) electromagnetic phenomena associated with earthquakes in a very wide frequency range. In this study, unusual behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9.0) have been reported. Ratios of diurnal variation range between the target station Esashi (ESA) which is about 135 km from the epicenter and the remote reference station Kakioka (KAK) about 302 km distant to the epicenter have been computed. The results of 10-day running mean of the ratios showed a clear anomaly exceeding the statistical threshold in the vertical component about 2 months before the mega event. This anomaly is unique over a 3-year background, and the further stochastic test indicates that this anomaly is unlikely a random anomaly, which is highly suggestive of correlation with the mega event. The original records of geomagnetic fields of the ESA station also exhibit continuous anomalous behaviors for about 10 days in the vertical component approximate 2 months prior to the Mw9.0 earthquake.

REFERENCES

Xu, G., Han, P., Huang, Q., Hattori, K., Febriani, F. and Yamaguchi, H., 2013. Anomalous behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9. 0). Journal of Asian Earth Sciences, 77, pp.59-65.

### Notes on "Shifting Correlation Between Earthquakes and Electromagnetic Signals: A Case Study of the 2013 Minxian–Zhangxian ML 6.5 (MW 6.1) Earthquake in Gansu, China" by Jiang et al. 2016

The shifting correlation method (SCM) is proposed for statistical analysis of the correlation between earthquake sequences and electromagnetic signal sequences. In this method, the two different sequences were treated in units of 1 day. With the earthquake sequences fixed, the electromagnetic sequences were continuously shifted on the time axis, and the linear correlation coefficients between the two were calculated. In this way, the frequency and temporal distribution characteristics of potential seismic electromagnetic signals in the pre, co, and post-seismic stages were analyzed. In the work discussed in this paper, we first verified the effectiveness of the SCM and found it could accurately identify indistinct related signals by use of sufficient samples of synthetic data. Then, as a case study, the method was used for analysis of electromagnetic monitoring data from the Minxian–Zhangxian ML 6.5 (MW 6.1) earthquake. The results showed: (1) there seems to be a strong correlation between earthquakes and electromagnetic signals at different frequency in the pre, co, and post-seismic stages, with correlation coefficients in the range 0.4–0.7. The correlation was positive and negative before and after the earthquakes, respectively. (2) The electromagnetic signals related to the earthquakes might appear 23 days before and last for 10 days after the shocks. (3) To some extent, the occurrence time and frequency band of seismic electromagnetic signals are different at different stations. We inferred that the differences were related to resistivity, active tectonics, and seismogenic structure.

REFERENCE

Jiang, F., Chen, X., Zhan, Y., Zhao, G., Yang, H., Zhao, L., Qiao, L. and Wang, L., 2016. Shifting Correlation Between Earthquakes and Electromagnetic Signals: A Case Study of the 2013 Minxian–Zhangxian M L 6.5 (M W 6.1) Earthquake in Gansu, China. Pure and Applied Geophysics, 173(1), pp.269-284.

### Notes on "Characteristics of Seismoelectric Wave Fields Associated with Natural Microcracks" by Fujinawa and Noda 2016

Properties of seismoelectric waves in relation to natural earthquakes have been investigated. The electromagnetic disturbances were analyzed to test the hypothesis that pulse-like electric variations are directly related to microcracks as source. Because variation is very difficult to detect, there have been few quantitative field investigations. We used selected events with clear S and P phases from the data catalog obtained before the Tohoku earthquake in 2011. The electric strength of the fast P wave (Pf), S wave (S), and electromagnetic wave (EM) associated with formation of cracks of tensile mode were estimated. The co-seismic electric signal accompanied by the S wave has the largest strength, well above the noise level, and the EM wave has the lowest strength. Analytical estimation of the ratio of the strengths of the Pf and EM phases to that of the S phase by use of Pride’s equations gave results partially in agreement with observation (the order was Apf > As > Aem). The strength of the observed electromagnetic mode is approximately two orders of magnitude larger than that estimated from the theory. We suggest this greater strength can be attributed to the converted modes at layer contracts or to the effect of the boundary between free atmosphere and crust. Overall agreement between observations and theoretical estimates suggests that electromagnetic anomalies, crustal deformation, and groundwater changes can be investigated on the basis of the unified equations for the coupled electromagnetics, acoustics, and hydrodynamics of porous media.

REFERENCES

Fujinawa, Y. and Noda, Y., 2016. Characteristics of seismoelectric wave fields associated with natural microcracks. Pure and Applied Geophysics, 173(1), pp.255-268.

### Notes on "Electromagnetic attenuation of eight earthquakes registered in Mexico using FFT-based spectrum and t-test statistical analysis for ULF Q-R ratios signals" by Chavez et al. 2015

A method to improve the detection of seismo-magnetic signals is presented herein. Eight events registered for periods of 24 hours with seismic activity were analyzed and compared with non-seismic periods of the same duration. The distance between the earthquakes (EQs) and the ultra-low frequency detector is of ρ = (1.8) 100.45M, where M is the magnitude of the EQ reported by the Seismological National Service of Mexico, in a period of three years. An improved fast Fourier transform analysis in the form of the ratio of the vertical magnetic field component to the horizontal one (Q = Bz/Bx) has been developed. There are important differences between the frequencies obtained during the days of seismic activity compared with those with no seismic activity.

REFERENCES

Chavez, O., Millan-almaraz, J.R., Cruz-abeyro, J.A.L. and Rojas, E., 2016. Electromagnetic attenuation of eight earthquakes registered in Mexico using FFT-based spectrum and t-test statistical analysis for ULF QR ratios signals. Geomatics, Natural Hazards and Risk, 7(4), pp.1207-1218.

## 04 March 2017

### Notes on "Evaluation of seismo-electric anomalies using magnetic data in Taiwan" by Chen et al. 2013

Abstract. The Parkinson vectors derived from 3-component geomagnetic data via the magnetic transfer function are discussed with respect to epicentre locations and hypocentre depths of 16 earthquakes (M ≥ 5.5) in Taiwan during a period of 2002–2005. To find out whether electric conductivity changes would happen particularly in the seismoactive depth ranges, i.e. in the vicinity of the earthquake foci, the frequency dependent penetration depth of the electromagnetic waves (skin effect) is taken into account. The background distributions involving the general conductivity structure and the coast effect at 20 particular depths are constructed using the Parkinson vectors during the entire study period. The background distributions are subtracted from the time varying monitor distributions, which are computed using the Parkinson vectors within the 15-day moving window, to remove responses of the coast effect and underlying conductivity structure. Anomalous depth sections are identified by deviating distributions and agree with the hypocentre depths of 15 thrust and/or strike-slip earthquakes with only one exception of a normal fault event.

REFERENCES

Chen, C.H., Hsu, H.L., Wen, S., Yeh, T.K., Chang, F.Y., Wang, C.H., Liu, J.Y., Sun, Y.Y., Hattori, K., Yen, H.Y. and Han, P., 2013. Evaluation of seismo-electric anomalies using magnetic data in Taiwan. Natural Hazards and Earth System Sciences, 13(3), p.597.

### Notes on "Observation of Magnetic Signals from Earthquake Faulting Using High-resolution HTS-SQUID Magnetometer: Feasibility of Super-early Warning of Earthquake" by Katori et al. 2015

Electromagnetic changes associated with earthquakes have been investigated previously. Our research group has also employed the magnetometers for seismomagnetic observations since March 2004. Our observation site happened to be situated at an epicentral distance of 26 km from the 2008 Iwate-Miyagi Nairiku earthquake ofM7.2, NE Japan. In this earthquake, we have reported successful observation of "co-faulting" Earth's magnetic field changes (Okubo et al., 2011 EPSL). Magnetic fields began to change almost simultaneously with the onset of the earthquake rupture and grew before the first P wave arrival. Such magnetic signals are most probably generated by the changing stress field due to earthquake rupturing, i.e. the piezomagnetic effect. On the other hand, this observation result suggested that the geomagnetic variation signal accompanying fault movement, whose sources are the piezomagnetic effects, is very small. The observed change of geomagnetic field might be approximately less than several hundred pico-tesla. Therefore, to obtain more observation data of "co-faulting" magnetic field change, development of a higher-sensitive magnetometer system is very important. Then, our research group tried to develop the HTS-SQUID (high-temperature-superconductor based superconducting-quantum-interference-device) magnetometer systems for high-resolution observation of Earth's magnetic field. Since March 2012 we have introduced long-term precise geomagnetic observations using the HTS-SQUID magnetometer system Unit No.1 (mark I) at Iwaki observation site (IWK) in Fukushima, Japan. Additionally, since October 2014, we have also introduced the new HTS- SQUID magnetometer system Unit No.2 (mark II). The sampling interval of the magnetometers is 0.02 sec (50Hz). The system clock has been synchronized by use of GPS signals. A high-resolution accelerometer is also installed at observation point. In this study, we show the observation results of geomagnetic field changes associated with the earthquake using our high-resolution HTS-SQUID magnetometer systems. Further efforts in the future would support a feasibility of a new system for a super-early warning of destructive earthquakes with the combined seismic-magnetic measurements.

REFERENCES

Katori, Y., Okubo, K., Hato, T., Tsukamoto, A., Tanabe, K., Onishi, N., Furukawa, H., Isogami, S. and Takeuchi, N., 2015, December. Observation of Magnetic Signals from Earthquake Faulting Using High-resolution HTS-SQUID Magnetometer: Feasibility of Super-early Warning of Earthquakes. In AGU Fall Meeting Abstracts.

### Notes on "The Pollino 2011-2012 seismic swarm (southern Italy): first results of the ML= 3.6 aftershock recorded by co-located electromagnetic and seismic stations" by Balasco et al. 2015

In the framework of S3 project “Short term earthquake forecasting” supported by Department of Civil Protection (DPC) and National Institute of Geophysics and Volcanology (INGV), a magnetotelluric (MT) station was installed in the Pollino area (southern Italy) during September 2012 by the Institute of Methodologies for Environmental Analysis (IMAA-CNR, Italy) in order to investigate possible correlation between electromagnetic signals and seismicity. For the last two years Pollino area has been characterized by swarm-type seismicity, culminating with the earthquake occurred on October 25, 2012 of magnitude MW=5.0. After the mainshock, the INGV installed a seismic station close to the MT station. In this paper, we focus the analysis on the largest event (ML=3.6) recorded during the colocated electromagnetic and seismic experiment. We applied time-frequency misfit criteria based on the continuous Morlet wavelet transform to compare the electric and seismic homologous components: this analysis confirms an overall good waveform similarity between the signals, but also some interesting differences in amplitude for frequencies above 1 Hz in correspondence of the arrival of particular seismic phases that need further investigations.

REFERENCES

Balasco, M., Lapenna, V., Romano, G., Siniscalchi, A., Stabile, T.A. and Telesca, L., 2015. The Pollino 2011-2012 seismic swarm (southern Italy): first results of the ML= 3.6 aftershock recorded by co-located electromagnetic and seismic stations. Boll Geofis Teor Appl, 56(2), pp.203-210.

### Notes on "Electric and Magnetic Field Changes Observed during a Seismic Swarm in Pollino Area (Southern Italy)" by Ballasco et al. 2014

In this study, we present several cases of EM field variations associated with the passage of seismic waves. The maximum amplitude of the electrical signals registered at the two MT sites and the earthquake magnitude are related by an attenuation factor that depends on the distance between the hypocenter and the MT station. Furthermore, at the two MT sites the maximum electrical anomalies seem to be more appreciable predominantly in different directions, indicating a certain directivity in the propagation of the electric field. A deep analysis of EM time series recorded during the mainshock Mw 5.0 was performed. In particular, by applying time–frequency misfit criteria based on the continuous wavelet transform, we compared the electric field with seismic recordings, and we found a good waveform similarity between signals. Moreover, we also found an EM signal that significantly anticipates the theoretical first P‐wave arrival at the Tramutola MT station.

REFERENCES

Balasco, M., Lapenna, V., Romano, G., Siniscalchi, A., Stabile, T.A. and Telesca, L., 2014. Electric and magnetic field changes observed during a seismic swarm in Pollino area (southern Italy). Bulletin of the Seismological Society of America.

### Notes on "Mapping of the Fault Zones on Basis of Geomagnetic Variations Due to Seismic Wave Propagation" by Loktex and Spivak 2015

Tectonic faults differ from the properties of surround rock. The fault properties determine behavior of the fault due to different external influences. Seismic waves propagating through the fault result to local magnetic field variations. Amplitude and intensity of these variations depend on the conditions for transformation energy between mechanical oscillations and magnetic field. Registrations of the seismo-magnetic effect at the Earth’s crust surface allow determining the presence of the fault and estimating its internal properties. We carried out synchronous registration of seismic waves and magnetic variations along the profile crossing the fault zone situated at the central area of the Russian platform. Geomagnetic variations caused by seismic signals resulting from open-cast mine blasts were analyzed. As a result we determined that magnitude of seismo-magnetic effects is maximum in the central fault's zone and decreases appreciably according to exponential law as the distance from the fault increases. It shows that the transformation of mechanical energy of vibrations into the energy of geomagnetic variations occurs more intensively in the fault. It allows determining the fault location firstly and estimating its broken state and present-day activity secondly.

Loktev, D.N. and Spivak, A.A., 2015, September. Mapping of the Fault Zones on Basis of Geomagnetic Variations Due to Seismic Wave Propagation. In Near Surface Geoscience 2015-21st European Meeting of Environmental and Engineering Geophysics.

### Notes on "Seismomagnetic response of a fault zone" by Adushkin et al. 2017

Based on the results of instrumental observations of geomagnetic variations caused by the propagation of seismic waves through a fault zone, the dependences between the amplitudes of the induced seismomagnetic effect and seismic signal as a function of distance r to the midline of the fault are obtained. For the first time, it is shown that the amplitude of the seismomagnetic effect is maximal in the fault damage zone. The phenomenological model describing the generation of magnetic signals by seismic waves propagating through the crushed rock in the tectonic fault zone is suggested. It is assumed that geomagnetic variations are generated by the changes in the electrical conductivity of the fragmented rocks as a result of the deformation of the rock pieces contacts. The amplitudes of the geomagnetic variations calculated from the model agree with the instrumental observations.

### Notes: "Low-frequency magnetic field measurements near the epicenter of the Ms 7.1 Loma Prieta earthquake" by Fraser-Smith et al. 1990

Abstract. We report the results of measurements of low frequency magnetic noise by two independent monitoring systems prior to the occurrence of the MS 7.1 Loma Prieta earthquake of 17 October 1989. Our measurements cover 25 narrow frequency bands in the more than six-decade frequency range 0.01 Hz–32 kHz, with a time resolution varying from a half hour in the ULF range (0.01–10 Hz) to one second in the ELF/VLF range (10 Hz–32 kHz). The ULF system is located near Corralitos, about 7 km from the epicenter. The ELF/VLF system is located on the Stanford campus, about 52 km from the epicenter. Analysis of the ELF/VLF data has revealed no precursor activity that we can identify at this time. However, the ULF data have some distinctive and anomalous features. First, a narrow-band signal appeared in the range 0.05–0.2. Hz around September 12 and persisted until the appearance of the second anomalous feature, which consisted of a substantial increase in the noise background starting on 5 October and covering almost the entire frequency range of the ULF system. Third, there was an anomalous dip in the noise background in the range 0.2–5 Hz, starting one day ahead of the earthquake. Finally, and perhaps most compelling, there was an increase to an exceptionally high level of activity in the range 0.01–0.5 Hz starting approximately three hours before the earthquake. There do not appear to have been any magnetic field fluctuations originating in the upper atmosphere that can account for this increase. Further, while our systems are sensitive to motion, seismic measurements indicate that there were no significant shocks preceding the quake. Thus, the various anomalous features in our data, and in particular the large-amplitude increase in activity starting three hours before the quake, may have been magnetic precursors. (Fraser-Smith et al. 1990)

A. Methodology

What's the meaning of 6-decade frequency range? In the logarithmic scale, a decade is defined as follows:
One decade is a factor of 10 difference between two numbers (an order of magnitude difference) measured on a logarithmic scale. Along with the octave, it is a logarithmic unit used to describe frequency bands or frequency ratios.[1][2] It is especially useful when referring to frequencies and when describing frequency response of electronic systems, such as audio amplifiers and filters. (Wikipedia: Decade(Log Scale))
The frequency range in the article is 0.01 Hz to 32 kHz. In terms of exponents, the range is from $1.0\times 10^{-2}$ Hz to $3.2\times 10^{4}$ Hz. The ratio of the powers of 10 is $10^6$. So this is probably what the authors refers to as a 6-decade frequency range. The Wikipedia definition has a typographical error. Instead of "(an order of magnitude difference) measured on a logarithmic scale," the entry should have been "(an order of magnitude difference measured on a logarithmic scale)." Notice the change in the closing parenthesis.

The time resolution of the article is "half hour in the ULF range (0.01–10 Hz) to one second in the ELF/VLF range (10 Hz–32 kHz)." To understand this, we note that the the period $\tau$ is inversely proportional to the frequency $f$:

\tau = \frac{1}{f}.

Thus, 0.01-10 Hz correspond to 0.1-10 s in the ULF range, while 10-32 kHz correspond to  0.00003125-0.0001 s. But this does not look right. Perhaps, Fraser-Smith et al are referring to the time window for averaging values. Indeed, as written in p. 1466 of their paper:
As described in greater detail by Bernardi et al. [1989], the basic output of each index generation system is a set of logarithms to the base two of the half-hourly averages of the power in nine frequency bands covering the overall range 0.01-10 Hz. These logarithms comprise our magnetic activity (MA) indices.... (Fraser-Smit et al. 1990)
B. Results and Discussion

The authors say that the anomalies are in the ULF (UltraLow Freqency) range of 0.01-10 Hz (or 0.1-100 s). The MAGDAS system can resolve up to 1 s, but there may be noise in some stations with periods below the 30 s period oscillations due to local effects, e.g. generators and trains. So we could not resolve below 30 s period oscillations. The 100 s period oscillations are easily visible, so this is a useful information in finding co-seismic magnetic fluctuations.

Anomaly 1. Appearance narrow-band signal in the range 0.05–0.2. Hz  (5-20 s period) about 35 days before the quake and persisted for 23 days. The range of the signal is within the error range of some Philippine stations.

Anomaly 2. Substantial increase in the noise background starting on 12 days before the quake and covering almost the entire frequency range of the ULF system. Background noise may be in the ELF, so why are there no ELF anomalies?

Anomaly 3. Anomalous dip in the noise background in the range 0.2–5 Hz (or 0.2-5 s periods), a day before the earthquake. These are too small for me. But if the noise in one station is regular, it may be filtered out.

Anomaly 4.Exceptional increase in high level of activity in the range 0.01–0.5 Hz starting approximately 3 hours before the earthquake. So 3 hours is a good time frame to study quakes. I shall use this in my work.

REFERENCES

Fraser-Smith, A.C., Bernardi, A., McGill, P.R., Ladd, M.E., Helliwell, R.A. and Villard Jr, O.G., 1990. Low-frequency magnetic field measurements near the epicenter of the Ms 7.1 Loma Prieta earthquake. Geophys. Res. Lett, 17(9), pp.1465-1468.

Bernardi, A., Fraser-Smith, A.C. and Villard, O.G., 1989. Measurements of BART magnetic fields with an automatic geomagnetic pulsation index generator. IEEE Transactions on Electromagnetic Compatibility, 31(4), pp.413-417.

## 02 March 2017

### An Introduction to Physics by Francisco Glover, SJ and Quirino Sugon Jr

C & E Publishing has sent us a flyer of our upcoming book: An Introduction to Physics by Fr. Franciso Glover, SJ and Quirino Sugon Jr, PhD. I rearranged the flyer to fit the blog post format of 2:1 length to height ratio to maximize the information viewability of the image snippet in social media platforms like Facebook, Google+, LinkedIn and Twitter. I shall post the paper layout of the flyer in Pinterest where vertical layouts are more dominant.

Hopefully, the book will be out this April 2017 or at most before June 2017.

BOOK DESCRIPTION

This introductory Physics Textbook is a step-by-step guide designed to provide Senior High School students in the STEM track with solid understanding of the fundamental principles of physics so that they can deeply appreciate how and why the physical world works.

Written by Physics professors with more than 50 years of combined teaching experience, this book is an essential reference for Senior High School students and teachers.

AUTHORS' BIOGRAPHY

Fr. Fracisco Glover, SJ holds a Doctor of Philosophy in Thoeretical Physics degree from saint Louis University, St. Louis, Missouri. A naturalized Filipino citizen born in the U.S., his first stint in teaching nphysics was at Ateneo de Manila University in 1950. Since then, he has taught Physics, Math, and Computer Engineering at Ateneo de Manila University, Ateneo de Davao University, and Notre Dame schools in South Cotabato. He has a special interest in the design and fabrication of student laboratory equipment for Physics and Electronic Engineering.

Dr. Quirino Sugon Jr. is an Assistant Professor of the Department of Physics of Ateneo de Manila University and Program Manager of Upper Atmosphere Dynamics at Manila Observatory. He graduated with degrees of Bachelor of Science in Physics (1997), Master of Science in Physics (1999), and Doctor of Philosophy in Physics (2010) from Ateneo de Manila University. He has taught Physics for 15 years, starting at the University of St. La Salle from 1999 to 2002, before moving to Ateneo de Manila University. He has written several peer-reviewed book chapters and journal articles on the applications of Geometric Algebra in Mechanics, Electromagnetics, and Optics. At Manila Observatory, he works on space weather research using MAGDAS magnetometers, FMCW radars, and GPS satellites.

PUBLISHER'S CONTACT INFORMATION

• Address: 839 EDSA, South Triangle, Quezon City, Philippines.
• Tel. No.: (632) 929-5088.
• Fax: (632) 929-5713
• Customer Service Hotline: (632) 352-3458
• Email: customerservice@cebookshop.com
• Website: www.cebookshop.com

## 28 February 2017

### Notes: "Co-seismic geomagnetic variations observed at the 1995 Hyogoken-Nanbu earthquake" by Iyemori et al. 1996

Let us study the paper by Iyemori et al. (1996), Co-seismic geomagnetic variations observed at the 1995 Hyogoken-Nanbu earthquake, published in Journal of geomagnetism and geoelectricity, 48(8), pp.1059-1070:
"Abstract. Impulsive co-seismic geomagnetic variations were observed at two stations nearly 100 km apart from the source region of the 1995 Hyogoken-Nanbu earthquake (M= 7.2). The maximum amplitude at the main shock was 0.6-1.0 nT and the duration was 20-30 seconds. These variations seem to have commenced at the origin time and before the arrival of the seismic waves to the observation site of 17 seconds later. A superposed epoch analysis for the aftershocks also reveals similar geomagnetic variations though the amplitude of them is one order of magnitude smaller than that of the main shock. A crustal dynamo mechanism is discussed as a possible cause of such co-seismic geomagnetic variations." (Iyemori et al. 1996)

A. Introduction

The 1995 Hyogoken-Nanbu is the 1995 Kobe earthquake:
The Great Hanshin earthquake (阪神・淡路大震災 Hanshin Awaji daishinsai?), or Kobe earthquake, occurred on January 17, 1995 at 05:46:53 JST (January 16 at 20:46:53 UTC) in the southern part of Hyōgo Prefecture, Japan, known as Hanshin. It measured 6.9 on the moment magnitude scale and 7 on the JMA Shindo intensity scale.[4] The tremors lasted for approximately 20 seconds. The focus of the earthquake was located 17 km beneath its epicenter, on the northern end of Awaji Island, 20 km away from the city of Kobe. Up to 6,434 people lost their lives; about 4,600 of them were from Kobe.[5] Among major cities, Kobe, with its population of 1.5 million, was the closest to the epicenter and hit by the strongest tremors. This was Japan's worst earthquake in the 20th century after the Great Kantō earthquake in 1923, which claimed more than 105,000 lives. (Wikipedia: The Great Hanshin Earthquake)
It is important to study this quake because it occurred in Kobe, a highly urbanized city like Manila. And the destruction of Manila due to the movement of a fault can cause comparable damage to infrastructure and death to thousands of people. According to the Earthquake Impact Reduction Study for Metropolitan Manila:

Analyzing past historically recorded earthquakes and instrumentally recorded earthquakes, a total 18 earthquakes were selected as scenario earthquakes, which have potential damaging effect to Metropolitan Manila; also earthquake ground motion, liquefaction potential, slope stability and tsunami height are estimated. Finally three models (namely, model 08 (West Valley Faults M.7.2), Model 13 (Manila Trench M.7.9), Model 18 (1863 Manila Bay M.6.5)), were selected for detail damage analysis because these scenario earthquakes show typical and severe damages to Metropolitan Manila. Model 08, as the worst case, 170,000 residential houses will collapse, 340,000 residential houses will be partly damaged, 34,000 persons will die, 114,000 persons will be injured.
Fire will breakout and burnt approximately 1,710 hectares and totally 18,000 additional persons will be killed by this secondary disaster. Moreover, infrastructures and lifelines will also be heavily damaged.
B. Results and Discussion

In the work of Iyemori et al. (1996) on the 1995 Hyogoken-Nanbu earthquake, magnetic stations Mineyama and Shigaraki are about 100 km from the quake epicenter. The quake's hypocenter itself is about 17.5 km deep. The quake is fairly shallow with respect to its distance from the stations. If we check out Fig. 3 of the paper, we see that both $H$ and $Z$ components (northward and downward) show strong dominant peaks with amplitudes 17s seconds after the the quake event. Most likely these are due to Love waves or $Q$ waves (Guglielmi et al 2006). They may also be due to surface waves with amplitudes of several centimeters. The speed of the waves are 100 km / 17 s or about 5.9 km/s. If we check speed vs depth plot for seismic waves, such shallow waves would be $P$ waves (primary), which are compressional. What is interesting is that the rise in amplitude of the geomagnetic field variation commences with the quake event.

The duration of the waves is 20-30 seconds. The filter used by the Ivemori et al. 1996 is a low-pass filter. This type of filter "passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency." Since frequency is inversely proportional to period, then the filter passes signals with periods higher than a certain cutoff period and attenuates signals with periods lower than the cutoff period. If the cutoff period is 30 s, this corresponds to a frequency of 1/30 Hz = 0.033 Hz = 33 mHz. High frequency oscillations corresponds to oscillations with small periods of much less than the cutoff frequency of 30 s.

Within the 2-min interval (120 s), the peak amplitude is more than 3 times the standard deviation. The authors noted that the disturbance in the H-component is positive in Shigaraki and negative in Mineyama. To visualize this, we note that Mineyama is directly north of the quake focus, while Shiragaki is to the east, though slightly north. If the seismic waves radiate spherically from the focus, then, we should expect the H-components at Shigaraki and Mineyama to have the same sign. But since the signs are opposite, maybe there's a fault line between the two stations, as suggested by the elongated red and yellow areas in the USGS plot. Indeed, a check on the fault line map of Japan shows that the 1995 Kobe quake occurred at a fault along the Nojima Fault of the Japan Median Tectonic Line:
 Nojima Fault in relation to 1995 Kobe Quake (CC BY-SA 3.0) (The author is not clearly written. See Wikipedia.)
The Great Hanshin earthquake of 1995 occurred on the Nojima Fault, a branch of the MTL. Approximately 6,434 people lost their lives; about 4,600 of them were from Kobe.[7] It caused approximately ten trillion yen ($100 billion) in damage, 2.5% of Japan's GDP at the time. (Wikipedia: Japan Median Tectonic Line) Nojima Fault (野島断層 Nojima Dansō?) is a fault that is responsible for the Great Hanshin earthquake. It cuts across Awaji Island. It is a branch of the Japan Median Tectonic Line which runs the length of the southern half of Honshu island. (Wikipedia: Nojima Fault) C. Theoretical Framework In their model, Iyemori et al (1996), explained the change in signs of the geomagnetic variation across the fault using the following model: We assume an electrically conducting slab immersed in geomagnetic field$B$as shown in Fig. 9. The slab corresponds to the area of many faults where the conductivity is generally higher than the surrounding region. If the slab moves with a velocity$\mathbf V$, the$\mathbf V \times \mathbf B$electric field drives a current across the slab. The current generates the charge separation which tends to cancel the primary (i.e.,$V\times \mathbf B$) electric field. Such charge separation would be observed as an electric double layer and it would cause the horizontal earth.At the same time, the current across the slab would be short-circuited vertically below the source region and forms a vertical current loop (see Fig. 9(b)). Such current loop would be observed at distant stations as a horizontal magnetic dipole located at the source region. Both currents would cause the geomagnetic variation at Mineyama and Shigaraki with observed sense of direction if the slab moves to the north-east direction. Here we assume a steady state to ignore the induction current by the temporal magnetic variation and the coupling between two current system for simplicity. (Iyemori et al. 1996) In the Philippines, the magnetic field$\mathbf B$is nearly horizontal pointing northward, while in Japan, the magnetic field$\mathbf B$points nearly downward, which is what the the$\otimes$symbol means (or more precisely, the direction is into the paper or your computer screen). The authors' claim that faults are where the conductivity is higher than the surrounding region is supported by the paper of Glover and Adam (2008), "Correlation between crustal high conductivity zones and seismic activity and the role of carbon during shear deformation." If a conductor slab moves perpendicular to the magnetic field, why will electrical currents be induced in the slab as claimed by Iyemori et al. (1996)? If the slab is stationary and current passes through the slab through an electrical potential difference between the ends of the slab, just like connecting a piece of iron nail on two ends of a battery, then there will be a force on the slab given by \mathbf F = L\mathbf I\times\mathbf B, where$L$is the length of the wire or the conducting slab (see Hyperphysics). If the current$\mathbf I$is pointing northeast and the magnetic field$\mathbf B$pointing downward, then the force$\mathbf F$on the slab would be along northwest. But in the work of Iyemori et al. (1996), the conducting slab is not stationary, but is moving with a velocity$\mathbf V$. The authors are using the expression for the following expression for the electromagnetic force$\mathbf F$: \mathbf F = q\mathbf E + q\mathbf V\times \mathbf B. In order to derive the expression for the electric field, the authors set$\mathbf F=0$, so that \mathbf E = -\mathbf V \times\mathbf B. But it is not yet clear to me why the force$\mathbf F=0$. Upon reading Bostrom (1971), Electrodynamics of the Ionosphere, I realized that the trick is to express the force$\mathbf F$in terms of the velocity$\mathbf V$, so that \mathbf F = m\frac{d\mathbf V}{dt} = q\mathbf E + q\mathbf V\times \mathbf B. If we use the first order approximation that the velocity$\mathbf V$is constant, then its derivative is zero, \frac{d\mathbf V}{dt} = 0, so that we can express the electric field$\mathbf E$as negative of the cross product of the velocity$\mathbf V$of the slab and the magnetic field$\mathbf B$of the earth. In this way, if$\mathbf V$is pointing northeast and the magnetic field$\mathbf B$is pointing downward, then Because of the electric field$\mathbf E$generated from$-\mathbf V\times B$, the positive charges will experience a force$\mathbf F_+ = +|q|\mathbf E$, while the negative charges will experience a force$\mathbf F = -|q|\mathbf E$. Since the electric field$\mathbf E$is pointing northwest, then the positive charges will migrate northeast, while the negative charges will migrate. By Coulomb's Law, the new electric field$\mathbf E'$generated would be pointing from the positive charge$+|q|$to the negative charge$-|q|$, so that$\mathbf E'$points southeast, which would tend to cancel the original electric field$\mathbf E$, as the authors claimed. This charge separation would also generate an electric field surrounding the slab similar to a dipole. Positive charges in the surroundings would migrate to the negative layer of the conducting slab, while negative charges in the surroundings would migrate to the positive layer of the conducting slab. The direction of motion of the positive charges correspond to the direction of the current density vector$\mathbf j$in Iyemori et al. (1996). The migration follows the dipole-like electric field lines generated by the charge double layer. Note that this charge double layer is different from the surface double layer in chemistry, because the latter has no conductor between them. Near Mineyama station, the current density$\mathbf j$points northeast. By Ampere's law, the magnetic field generated by the current would be boreal to current's direction (put your right thumb in the direction of the current and the curl of your fingers is the direction of the magnetic field). If this current flows along a wire as drawn in the diagram, Mineyama would be on the left side of this current, so that the magnetic field at Mineyama would be pointing up if the conducting slab is at the surface of the earth. If the conducting slab is below the ground, the magnetic field at Mineyama would be pointing southeast as drawn in the diagram. On the other hand, Shigaraki is on the right side of the current wire model. The current near Shigaraki would be pointing southeast, so that the magnetic field at Shigaraki would be pointing up if the conducting slab is on the surface of the earth. If the conducting slab is below the ground, the magnetic field at Shigaraki would be pointing southwest, as shown in the diagram. In general, the electrical currents do not flow through the imaginary wire, but in all the surroundings of the conducting slab of the quake fault. But since the magnetic field becomes stronger the closer the point is to the charge double layer of the conducting slab, then we can always draw an effective circular wire model, so that the two stations are outside this wire. We can make more circular wires near the poles of the charge double layer with the current intensity increasing as we near the poles. Thus, the conclusions in the previous paragraph regarding the directions of the magnetic field measured by the two stations would still be valid. REFERENCES Iyemori, T., Kamei, T., Tanaka, Y., Takeda, M., Hashimoto, T., Araki, T., Okamoto, T., Watanabe, K., Sumitomo, N. and Oshiman, N., 1996. Co-seismic geomagnetic variations observed at the 1995 Hyogoken-Nanbu earthquake. Journal of geomagnetism and geoelectricity, 48(8), pp.1059-1070. Glover, P.W. and Adám, A., 2008. Correlation between crustal high conductivity zones and seismic activity and the role of carbon during shear deformation. Journal of Geophysical Research: Solid Earth, 113(B12). Boström, R., 1970. Electrodynamics of the ionosphere. ## 26 February 2017 ### Notes: Co-seismic circularly polarized magnetic fields and Love waves by Guglielmi et al. 2006 Abstract. "A method for detecting seismomagnetic signals is considered. These signals are generated during the course of the propagation of surface seismic Love wave from far earthquakes. Magnetic field vector of the seismomagnetic signal rotates counterclockwise and has a circular polarization, which allows us to extract the signal against the background noise. By using the described method of polarization filter the seismomagnetic signals from the earthquake on 4 June 2000 have been detected at two remote magnetic observatories. In the other case, the two signals from the disastrous tsunami 2004 earthquake were detected both for the first arrival of Love wave coming directly from the epicenter along the minor great circle arc, and for the second wave propagating along the major great circle arc." (Guglielmi et al. 2006) Comments If the hypocenter of the quake is beneath the station, then the proposed method in the abstract can be done by extracting the oscillations in the H and D (which corresponds to Northward and Eastward in MAGDAS notation) which have the same amplitude. But if the position of the station with respect to the quake epicenter makes an large angle (about$60^\circ$) with respect to the vertical, then the projection of the circularly polarized magnetic fields on the$H$and$D$axis would result to elliptical orbits. The ellipticity of the orbits may be deduced if we know how the propagation direction of the rotating magnetic field. Perhaps my understanding of the authors' techniques is wrong. The reference position used by the authors is not be the quake hypocenter below the earth's surface, but rather the vertical projection of the hypocenter onto the surface of the earth, which is the epicenter. As the authors wrote in their Section 3: "For subsequent analysis, we transformed the initial dataset of geomagnetic field to a coordinate system rotated about the vertical axis z in such a way as to bring the x-axis into coincidence with the tangent to the arc of the great circle passing through the epicenter and to direct it away from the epicenter." (Guglielmi et al. 2006) In this way, the propagation of the Love waves would be along the$H$and$D$axis, so that the magnetic field fluctuations would be along the plane defined by$\sqrt{H^2 + D^2}$and$Z$. The$(H,D)$data points can then be projected onto the axis of$\sqrt{H^2 + D^2}$. Then the plot of$\sqrt{H_\rho^2 + D_\rho^2}$vs.$Z\$ can be made. The orbits that are circular would be the tell-tale signs of the quake-induced magnetic field fluctuations.

Before the method can be applied, the data needs to be filtered. Otherwise, the original magnetic data set would be dominated by the diurnal equatorial electrojet signals and there would be no co-seismic magnetic signals to observe. In their work, the authors used "broadband filtering with a pass band from 5 to 200 mHz in order to eliminate high-frequency noise and long-period trend." The corresponding time periods of these frequencies are 5 s to 200 s.

It is interesting that the signals the authors measure come not only from the minor great circle arc (shortest distance between the latitude-lontitude position of the quake and the station), but also from the great circle arc as well.

REFERENCES

Guglielmi, A., Hayakawa, M., Potapov, A. and Tsegmed, B., 2006. Polarization method to detect the co-seismic magnetic oscillations. Physics and Chemistry of the Earth, Parts A/B/C, 31(4), pp.299-304.