tag:blogger.com,1999:blog-25802866069799865082018-03-09T23:51:58.824+08:00Quirino Sugon Jr, PhDPhysicistQuirino Sugon Jr.noreply@blogger.comBlogger96125tag:blogger.com,1999:blog-2580286606979986508.post-50137507662595301722017-11-24T00:51:00.000+08:002017-11-24T00:55:59.863+08:00Bought Roy Peter Clark's book, "Writing Tools"<a href="https://www.amazon.com/gp/product/0316014990/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0316014990&linkCode=as2&tag=quirinosugonjr-20&linkId=878782e9b69c9fba53aed133a5a3ba4e" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0316014990&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=quirinosugonjr-20" /></a><img alt="" border="0" height="1" src="//ir-na.amazon-adsystem.com/e/ir?t=quirinosugonjr-20&l=am2&o=1&a=0316014990" style="border: none !important; margin: 0px !important;" width="1" />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.<br /><br />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: <a href="https://www.poetryfoundation.org/poetrymagazine/poems/17168/ars-poetica">ars poetica</a>--the perfection of the word made flesh.<br /><br />I went to FullyBooked, but there is no more copy left in all their branches. So I went to National Bookstore.<br /><br />"Miss, do you have the book, Writing Tools, by Roy Peter Clark?" I asked<br /><br />"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.<br /><br />"Writing Tools: 50 Strategies for Every Writer? Is this the book?" She asked.<br /><br />"Yes, that's the book," I said.<br /><br />She went upstairs through a spiral staircase. After a while, she came down holding a book in spring green cover. It's Writing Tools.<br /><br />I shall be a writer again. <a href="https://genius.com/Pablo-neruda-tonight-i-can-write-the-saddest-lines-annotated">Tonight, I shall write the saddest lines</a>.<br /><br /><script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "55f2fe11188a3886d501c91fa787bc43"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; amzn_assoc_asins = "0316014990,0811854299,0473334461,1440509573"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script> <meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="Bought Roy Peter Clark's book, "Writing Tools"" /><meta name="twitter:description" content="I thought my first copy was lost." /><meta name="twitter:image" content="https://images-na.ssl-images-amazon.com/images/I/41AnHoBJ8iL._SX331_BO1,204,203,200_.jpg" />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0Katipunan Ave, Quezon City, Metro Manila, Philippines14.6300245 121.0741000000000414.568569 120.99341900000005 14.691479999999999 121.15478100000004tag:blogger.com,1999:blog-2580286606979986508.post-5654247816556056062017-11-16T11:47:00.001+08:002017-11-16T11:56:44.626+08:00Strike, dip, and rake directions in focal mechanism<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-x9Ff6dD-plg/Wg0EirVYJfI/AAAAAAAAZTM/OAAfSrGrpD8n2t0HBpGnprEKWR0R5prcACLcBGAs/s1600/quirinosugonjr_strike_dip_rake_focal_mechanism_20171116.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="500" data-original-width="798" height="200" src="https://2.bp.blogspot.com/-x9Ff6dD-plg/Wg0EirVYJfI/AAAAAAAAZTM/OAAfSrGrpD8n2t0HBpGnprEKWR0R5prcACLcBGAs/s320/quirinosugonjr_strike_dip_rake_focal_mechanism_20171116.png" width="320" /></a></div>Vincent S. Cronin wrote <a href="http://croninprojects.org/Vince/Course/IntroStructGeol/Focal_mechanism_primer_v4.pdf">A Primer on Focal Mechanism Solutions for Geologists (2010)</a>. 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.<br /><br />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 $\mathbf e_{rake}$:<br />\begin{equation}<br />\mathbf e_{rake} = \mathbf e_{strike}\cos\theta_{rake} - \mathbf e_{dip}\sin\theta_{dip}.<br />\end{equation}<br />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.<br /><br /><script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "8102a46bc4714985fc0a9c4ec60b38ed"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; amzn_assoc_asins = "0521708427,0198717415,B0030ZRPBO,147360155X"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script> <meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="Strike, dip, and rake directions in focal mechanism" /><meta name="twitter:description" content="Based on Vincent S. Cronin's Primer on Focal Mechanism Solutions for Geologists (2010)" /><meta name="twitter:image" content="https://2.bp.blogspot.com/-x9Ff6dD-plg/Wg0EirVYJfI/AAAAAAAAZTM/OAAfSrGrpD8n2t0HBpGnprEKWR0R5prcACLcBGAs/s320/quirinosugonjr_strike_dip_rake_focal_mechanism_20171116.png" />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-58499205810752496222017-11-15T21:18:00.002+08:002017-11-15T22:05:47.549+08:00Trend and plunge angles of faults<a href="https://3.bp.blogspot.com/-GiihYeNHk8Q/Wgw9yVxV08I/AAAAAAAAZRg/bh9zfjdMdgo_XW0MkWVZPjkicDNOge7ugCLcBGAs/s1600/quirinosugonjr_trend_plunge_fault_vector_20171114%2B%25283%2529.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="609" data-original-width="754" height="258" src="https://3.bp.blogspot.com/-GiihYeNHk8Q/Wgw9yVxV08I/AAAAAAAAZRg/bh9zfjdMdgo_XW0MkWVZPjkicDNOge7ugCLcBGAs/s320/quirinosugonjr_trend_plunge_fault_vector_20171114%2B%25283%2529.png" width="320" /></a>In his web page on <a href="https://courses.eas.ualberta.ca/eas421/lecturepages/orientation.html">Data in Structural Geology</a>, 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. <br /><br />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,<br />\begin{equation}<br />\mathbf e_{TP}\cdot\mathbf e_3 = -\cos(90^\circ-P)=-\sin P\equiv n,<br />\end{equation}<br />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 $\mathbf e_2$:<br />\begin{align}<br />\mathbf e_{TP}\cdot\mathbf e_1 &= \cos P\sin T\equiv \ell,\\<br />\mathbf e_{TP}\cdot\mathbf e_2 &= \cos P\cos T\equiv m.<br />\end{align}<br />Combining these relations, we obtain the expression for the vector $\mathbf e_{TP}$ in Eastward, Northward, and Upward coordinates:<br />\begin{align}<br />\mathbf e_{TP} &= \mathbf e_1\cos P\sin T + \mathbf e_2 \cos P\cos T -\mathbf e_3\sin P\nonumber\\<br />&=\ell\mathbf e_1 + m\mathbf e_2 + n\mathbf e_3.<br />\end{align} <script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "099f7d7ce1033b3e5ddd5edc6393a2eb"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; amzn_assoc_asins = "0521708427,1891389637,012732870X,0071615458"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script><meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="Trend and plunge angles of faults" /><meta name="twitter:description" content="Fault directions are defined in terms of the trend angle T and plunge angle P." /><meta name="twitter:image" content="https://3.bp.blogspot.com/-GiihYeNHk8Q/Wgw9yVxV08I/AAAAAAAAZRg/bh9zfjdMdgo_XW0MkWVZPjkicDNOge7ugCLcBGAs/s1600/quirinosugonjr_trend_plunge_fault_vector_20171114%2B%25283%2529.png" />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-22437059207041021132017-11-12T11:21:00.000+08:002017-11-12T11:21:32.302+08:00Writing three paragraphs per sitting is liberating<a href="https://www.amazon.com/gp/product/1578060818/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1578060818&linkCode=as2&tag=quirinosugonjr-20&linkId=6c3465d573537674ea51a336c5545046" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=1578060818&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=quirinosugonjr-20" /></a><img alt="" border="0" height="1" src="//ir-na.amazon-adsystem.com/e/ir?t=quirinosugonjr-20&l=am2&o=1&a=1578060818" style="border: none !important; margin: 0px !important;" width="1" />With three paragraphs I can already tell a story--a story with a beginning, middle, and end--though not necessarily in that order, as <a href="https://www.goodreads.com/quotes/160501-a-story-should-have-a-beginning-a-middle-and-an">Jean-Luc Godard</a> would say.<br /><br />There is sheer joy in writing--something like chiseling a <a href="https://en.wikipedia.org/wiki/Piet%C3%A0_(Michelangelo)">Pieta</a> 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 <a href="https://en.wikipedia.org/wiki/O_Salutaris_Hostia">Uni Trinoque</a> or the <a href="https://en.wikipedia.org/wiki/Trinity">Holy Trinity</a>.<br /><br /> 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." (<a href="http://www.usccb.org/bible/jeremiah/20">Jer 20:7-9</a>)<br /><br /><script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "06bec31c9418f06d13359d062f426a57"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; amzn_assoc_asins = "1578060818,1439156816,024129942X,0895553341"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script> <meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="Writing three paragraphs per sitting is liberating" /><meta name="twitter:description" content="With three paragraphs I can already tell a story" /><meta name="twitter:image" content="https://images-na.ssl-images-amazon.com/images/I/41QRYiXRWdL.jpg" /> Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-26916200995223871622017-11-12T01:37:00.001+08:002017-11-12T01:42:09.429+08:00If you have time, read Ecclesiastes 12:1-8It 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 <i>vanity</i> repeated thrice:<br /><blockquote class="tr_bq"><a href="https://www.amazon.com/gp/product/B00Z6JBXYM/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B00Z6JBXYM&linkCode=as2&tag=quirinosugonjr-20&linkId=11972939f511125ac60615ba94790922" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=B00Z6JBXYM&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=quirinosugonjr-20" /></a><img alt="" border="0" height="1" src="//ir-na.amazon-adsystem.com/e/ir?t=quirinosugonjr-20&l=am2&o=1&a=B00Z6JBXYM" style="border: none !important; margin: 0px !important;" width="1" />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! (<a href="http://www.usccb.org/bible/ecclesiastes/12">Eccl 12:1-8</a>)</blockquote> 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.<br /><br />Or perhaps instead of a poster, I shall write a story.<br /><br /><script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "fdc9bc69fe2d919757c9376c911976e2"; amzn_assoc_asins = "1607748894,1682780422,0805440887,B0718Z9G5W"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script> <meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="If you have time, read Ecclesiastes 12:1-8" /><meta name="twitter:description" content="It is a meditation on old age." /><meta name="twitter:image" content="https://images-na.ssl-images-amazon.com/images/I/71cepAuwxNL._SL1000_.jpg" /> Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-40262597595682662092017-11-11T18:46:00.000+08:002017-11-11T23:08:28.905+08:00Today, I deleted all my blog posts<a href="https://www.amazon.com/gp/product/B000NOKFHQ/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B000NOKFHQ&linkCode=as2&tag=quirinosugonjr-20&linkId=f3b208842add1df29c5f164e12bad166" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=B000NOKFHQ&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=quirinosugonjr-20" /></a><img alt="" border="0" height="1" src="//ir-na.amazon-adsystem.com/e/ir?t=quirinosugonjr-20&l=am2&o=1&a=B000NOKFHQ" style="border: none !important; margin: 0px !important;" width="1" />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.<br /><br />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.<br /><br />I am Jaguar Paw! This is my forest! I am Quirino Sugon Jr. This is my blog.<br /><br /><script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "manual"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "My Amazon Picks"; amzn_assoc_linkid = "62cf2c8ab8dd324be4b95eff34e79569"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; amzn_assoc_asins = "0143105132,B00BR0LWCW,0199538859,B000NOKFHQ"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script><br /><br /> <meta name="twitter:card" content="summary" /><meta name="twitter:site" content="@QuirinoSugonJr" /><meta name="twitter:title" content="Today, I deleted all my blog posts" /><meta name="twitter:description" content="Well, not exactly." /><meta name="twitter:image" content="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=B000NOKFHQ&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=quirinosugonjr-20" />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-40870636874234152302017-11-11T17:07:00.000+08:002018-02-18T16:04:27.176+08:00On Twitter<br /><ol><li>This is my first use of TweetDeck. I logged in using my Twitter account: @QuirinoSugonJr. I used TweetDeck for five reasons</li><li><br /></li></ol>Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-5065922941908264512017-11-11T16:16:00.000+08:002018-02-18T16:04:28.621+08:00On blogging<div class="separator" style="clear: both; text-align: center;"></div><br /><ol><li><b><a href="https://quirinosugonjr.blogspot.com/2015/01/figure-out-blog.html">I still can't figure out what to do with this blog</a>. </b>Perhaps, 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.</li><li><a href="https://quirinosugonjr.blogspot.com/2015/01/things-write-blogger-users.html">The things I write here are for Blogger users</a>. But most of the things here also apply for Wordpress users.</li><li><a href="https://quirinosugonjr.blogspot.com/2015/01/problem-bloggers-categorize-posts.html">One of the perennial problems of bloggers is how to categorize their posts</a>. 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.</li><li><br /></li></ol>Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-2755604425293226952017-07-12T19:10:00.000+08:002018-02-18T16:04:25.999+08:00How to write an interviewQuirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-4871627561940200812017-07-10T22:42:00.001+08:002018-02-18T16:04:28.098+08:00How book publishers can benefit from a blogQuirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-45646339871679213662017-07-06T18:56:00.000+08:002018-02-18T16:04:27.968+08:00Cover of Introduction to Physics by Glover and Sugon<table style="width: 100%;"> <tbody><tr> <td><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-vi7p6rT7XH4/WV4WUdiT3WI/AAAAAAAAW9g/AzMD8YKguZYZz345uAnQjqomHJBsbQJsQCLcBGAs/s1600/glover_sugon_introduction_physics_book_cover_20170612.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="428" data-original-width="335" height="200" src="https://1.bp.blogspot.com/-vi7p6rT7XH4/WV4WUdiT3WI/AAAAAAAAW9g/AzMD8YKguZYZz345uAnQjqomHJBsbQJsQCLcBGAs/s200/glover_sugon_introduction_physics_book_cover_20170612.PNG" width="156" /></a></div><br /></td> <td>"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. </td> </tr></tbody></table>Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-27756172702470253662017-07-06T13:04:00.000+08:002018-02-18T16:04:26.129+08:00How to use file folders to organize your documents<div style="text-align: left;"><a href="https://4.bp.blogspot.com/-YLNHBJtDpAY/WV3AcPvTMPI/AAAAAAAAW8k/VEkPlXEEQcA4eeUP4ik7hhsHjMSHNn3IwCLcBGAs/s1600/quirinosugonjr_file_folders_20170607.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="960" height="240" src="https://4.bp.blogspot.com/-YLNHBJtDpAY/WV3AcPvTMPI/AAAAAAAAW8k/VEkPlXEEQcA4eeUP4ik7hhsHjMSHNn3IwCLcBGAs/s320/quirinosugonjr_file_folders_20170607.png" width="320" /></a></div>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?<br /><br />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.<br /><br />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."<br /><br />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.<br /><br />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.<br /><br />My next job is to overhaul my drawers. <script type="text/javascript">amzn_assoc_placement = "adunit0"; amzn_assoc_tracking_id = "quirinosugonjr-20"; amzn_assoc_ad_mode = "search"; amzn_assoc_ad_type = "smart"; amzn_assoc_marketplace = "amazon"; amzn_assoc_region = "US"; amzn_assoc_title = "Shop Related Products"; amzn_assoc_default_search_phrase = "labeler"; amzn_assoc_default_category = "All"; amzn_assoc_linkid = "4c7a974b5439c1cb7a5a421799c71e49"; amzn_assoc_rows = "4"; amzn_assoc_design = "text_links"; </script><script src="//z-na.amazon-adsystem.com/widgets/onejs?MarketPlace=US"></script> <meta name="twitter:card" content="summary_large_image"><meta name="twitter:site" content="@QuirinoSugonJr"><meta name="twitter:creator" content="@QuirinoSugonJr"><meta name="twitter:title" content="How to use file folders to organize your documents"><meta name="twitter:description" content="You need a labeler and a tagging system."><meta name="twitter:image" content="https://4.bp.blogspot.com/-YLNHBJtDpAY/WV3AcPvTMPI/AAAAAAAAW8k/VEkPlXEEQcA4eeUP4ik7hhsHjMSHNn3IwCLcBGAs/s320/quirinosugonjr_file_folders_20170607.png"> Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-8713411630045696952017-03-24T21:10:00.001+08:002018-02-18T16:04:30.731+08:00Notes: "Telluric currents: The Natural Environment and Interactions with Man-Made Systems" by Lanzerotti and Gregori 1986I 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 <a href="https://www.nap.edu/read/898/chapter/18">Lanzerotti and Gregori (1986)</a> which are relevant to EEJ and earthquakes, and then write my comments.<br /><br /><b>A. Sources of Telluric Currents</b><br /><blockquote class="tr_bq">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)</blockquote>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 (<a href="http://www.foxnews.com/tech/2010/04/26/fastest-ocean-current-flows-beneath-antarctica.html">Fox News</a>). In the US, the Gulf Stream reaches 2.5 m/s at its peak and goes down to 0.44 m/s (<a href="http://oceanservice.noaa.gov/facts/gulfstreamspeed.html">NOAA</a>). These currents also cause magnetic field variations:<br /><blockquote class="tr_bq">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. (<a href="http://news.nationalgeographic.com/news/2009/06/090622-earths-core-dynamo_2.html">National Geographic</a>)</blockquote><b>B. Lunar Tidal Harmonic Component</b><br /><blockquote class="tr_bq">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) (</blockquote>What is a lunar day?<br /><blockquote class="tr_bq">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]<br />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] (<a href="http://a%20lunar%20day%20is%20the%20period%20of%20time%20it%20takes%20for%20the%20earth%27s%20moon%20to%20complete%20one%20full%20rotation%20on%20its%20axis%20with%20respect%20to%20the%20sun.%20equivalently%2C%20it%20is%20the%20time%20it%20takes%20the%20moon%20to%20make%20one%20complete%20orbit%20around%20the%20earth%20and%20come%20back%20to%20the%20same%20phase.%20it%20is%20marked%20from%20a%20new%20moon%20to%20the%20next%20new%20moon.%20%20with%20respect%20to%20the%20stars%2C%20the%20moon%20takes%2027%20earth%20days%2C%207%20hours%20and%2043%20minutes%2012%20seconds%20to%20complete%20its%20orbit%3B[1]%20but%20since%20the%20earth-moon%20system%20advances%20around%20the%20sun%20in%20the%20meantime%2C%20the%20moon%20must%20travel%20further%20to%20get%20back%20to%20the%20same%20phase.%20on%20average%28mean%29%2C%20this%20synodic%20period%20lasts%2029%20days%2C%2012%20hours%2C%2044%20minutes%20and%203%20seconds.[1]%20%20%20the%20term%20%22lunar%20day%22%20may%20also%20refer%20to%20the%20period%20between%20moonrises%20in%20a%20particular%20location%20on%20earth.%20this%20period%20is%20typically%20slightly%20longer%20%2850%20minutes%29%20than%20a%2024-hour%20earth%20day%2C%20as%20the%20moon%20revolves%20around%20the%20earth%20in%20the%20same%20direction%20as%20the%20earth%27s%20axial%20rotation.[2]/">Wikipedia: Lunar Day</a>)</blockquote>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.<br /><br /><b>C. Local Earth Conductivity Anomalies</b><br /><blockquote class="tr_bq">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)</blockquote>The local magnetic field due to crustal magnetization were already mapped this year 2017 by Swarm satellites:<br /><blockquote class="tr_bq">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.” (<a href="http://www.esa.int/Our_Activities/Observing_the_Earth/Swarm/Unravelling_Earth_s_magnetic_field">European Space Agency</a>)</blockquote>Since this is now established, it may soon be possible to map out the Earth currents.<br /><br /><br /><br /><br /><b>REFERENCES</b><br /><b><br /></b>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.Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-16606430116887150042017-03-23T20:48:00.000+08:002018-02-18T16:04:24.817+08:00Square roots of 1, -1, and 0 in Geometric AlgebraClifford (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: <br /><ol><li>If $\mathbf e_1$ is a unit vector, then $\mathbf e_1^2=1$. (Normality Rule) </li><li>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)</li><li>The juxtaposition products of vectors are associative. (Associativity Rule)</li></ol><div>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.</div><div class="separator" style="clear: both; text-align: center;"></div><br /> <b>1. Square Roots of 1</b><br /><br />Let us now take our proposed rules as they are and try out some products:<br />\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 $1$:<br />\begin{equation}<br />\sqrt{1} = \{\pm 1, \pm\mathbf e_1, \pm\mathbf e_2 \}.<br />\end{equation}<br /><br /> <b>2. Square Roots of -1</b><br /><br />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):<br />\begin{equation} \hat\imath = \mathbf e_1\mathbf e_2. \end{equation} 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}<br />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 $-1$:<br />\begin{equation} \sqrt{-1} = \pm \mathbf e_1\mathbf e_2.<br />\end{equation} <br /><br /> <b>3. Square Roots of 0</b><br /><br />Let us define the following quantities:<br />\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}<br />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}<br />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 $90^\circ$.<br /><br />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.<br /><br />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. Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-60418225329140674622017-03-19T10:59:00.000+08:002018-02-18T16:04:29.213+08:00How to find the shortest distance between two skew lines<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-vIAL2UwDcxU/WM3yypXA6ZI/AAAAAAAAT3g/-jzi50R01YQWGu17IJj0NOk9OyAvUyMWwCLcB/s1600/quirinosugonjr_skew_lines_20170319.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://3.bp.blogspot.com/-vIAL2UwDcxU/WM3yypXA6ZI/AAAAAAAAT3g/-jzi50R01YQWGu17IJj0NOk9OyAvUyMWwCLcB/s640/quirinosugonjr_skew_lines_20170319.png" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Fig. 1. </b>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. <b style="font-size: 12.8px;">Fig. 2</b><span style="font-size: 12.8px;">. Two unit vectors $\mathbf n_1$ and $\mathbf n_2$ and their parallel and perpendicular projections with respect to each other.</span></td></tr></tbody></table><br /><br /><b>A. PROBLEM</b><br /><b><br /></b>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 $\mathbf n_2$:<br />\begin{align}<br />\mathbf r_1 = \mathbf r_{01} + \mathbf n_1 s_1,\\<br />\mathbf r_2 = \mathbf r_{02} + \mathbf n_2 s_2,<br />\end{align}<br />where $s_1$ and $s_2$ are scalar parameters. What is the shortest distance between the two lines? <br /><br /><b>B. SOLUTION</b><br /><b><br /></b>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:<br />\begin{align}<br />\mathbf r_1' &= \mathbf r_{01} +\mathbf n_1s_1',\\<br />\mathbf r_2' &= \mathbf r_{02} +\mathbf n_2s_2'.<br />\end{align}<br />The difference between these two equations is<br />\begin{equation}<br />\mathbf b = \mathbf r_2'-\mathbf r_1' = \mathbf a+\mathbf n_2s_2'-\mathbf n_1s_1',<br />\end{equation}<br />where<br />\begin{equation}<br />\mathbf a = \mathbf r_{02}-\mathbf r_{01}.<br />\end{equation}<br />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 $\mathbf n_2$.<br /><br />From geometry, we know that at the shortest distance $b$ between the two lines, the vector $<br />\mathbf b$ must be perpendicular to both directions $\mathbf n_1$ and $\mathbf n_2$, so that<br />\begin{align}<br />\mathbf b\cdot\mathbf n_1 &= 0,\\<br />\mathbf b\cdot\mathbf n_2 &= 0.<br />\end{align}<br />Substituting the expressions for $\mathbf b$, we get<br />\begin{align}<br />\mathbf a\cdot\mathbf n_1 &= s_1' - (\mathbf n_2\cdot\mathbf n_1) s_2',\\<br />\mathbf a\cdot\mathbf n_2 &= (\mathbf n_1\cdot\mathbf n_2) s_1' - s_2' .<br />\end{align}<br />Solving for the distances $s_1'$ and $s_2'$ yields our desired expressions:<br />\begin{align}<br />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},\\<br />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}.<br />\end{align}<br /><br />Another way to rewrite the expressions for $s_1'$ and $s_2'$ is to define two vectors $\mathbf c_1$ and $\mathbf c_2$:<br />\begin{align}<br />\mathbf c_1 &= \mathbf n_1 -(\mathbf n_1\cdot\mathbf n_2)\mathbf n_2,\\<br />\mathbf c_2 &= \mathbf n_2 -(\mathbf n_1\cdot\mathbf n_2)\mathbf n_1.<br />\end{align}<br />These two vectors have the same magnitude $c$:<br />\begin{equation}<br />c = c_1 = c_2 = \sqrt{1 - (\mathbf n_1\cdot\mathbf n_2)^2}.<br />\end{equation}<br />Thus, $s_1'$ and $s_2'$ simplify to<br />\begin{align}<br />s_1' &= \frac{\mathbf a\cdot\mathbf c_1}{c^2},\\<br />s_2' &= \frac{-\mathbf a\cdot\mathbf c_2}{c^2}.<br />\end{align}<br /><br />Using these expressions for $s_1'$ and $s_2'$, the vector $\mathbf b$ becomes<br />\begin{equation}<br />\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.<br />\end{equation}<br />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 $\mathbf n_1$. Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-85508872918074205602017-03-18T20:17:00.000+08:002018-02-18T16:04:30.399+08:00Notes: "The Relationship Between Loss, Conductivity, and Dielectric Constant" by Bishop 2001<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-wcFzOoyxGZk/WM0jSqOtJXI/AAAAAAAAT04/07vC4EzJGAgQi6UTGfJN7jCaP1HFfCzDQCLcB/s1600/quirinosugonjr_loss_conductivity_dielectric_20170318.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-wcFzOoyxGZk/WM0jSqOtJXI/AAAAAAAAT04/07vC4EzJGAgQi6UTGfJN7jCaP1HFfCzDQCLcB/s400/quirinosugonjr_loss_conductivity_dielectric_20170318.png" width="400" /></a></div><br />I found a thorough discussion on the relationship of <a href="http://www.electromagnetics.biz/the%20relationship%20between%20loss.pdf">loss, conductivity, and dielectric constant written by Chris Bishop in 2001</a>. 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.<br /><b><br /></b><b>1. Conductivity and Mobility</b><br /><br />The conductivity $\sigma_s$ of a medium is related to its electric mobility $\mu_e$ by<br />\begin{equation}<br />\sigma_s = -q\mu_e,<br />\end{equation}<br />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.<br /><br /> <b>2. Complex Permittivity</b><br /><br />The complex <a href="https://en.wikipedia.org/wiki/Permittivity">permittivity</a> $\epsilon$ may be decomposed as<br />\begin{equation}<br />\epsilon = \epsilon' - i\epsilon'',<br />\end{equation}<br />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<br />\begin{equation}<br />\epsilon = \epsilon_0\epsilon_r,<br />\end{equation}<br />where $\epsilon_0$ is the permittivity of free space. Bishop said that the imaginary part of the relative permittivity is related to energy loss.<br /><br /><b>3. Conductivities for Static and Alternating Fields</b><br /><br />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:<br />\begin{equation}<br />\sigma_e = \sigma_s + \sigma_a,<br />\end{equation}<br />where<br />\begin{equation}<br />\sigma_a = \omega\epsilon''.<br />\end{equation}<br />Notice that if the field is constant, then the angular frequency of the field is $\omega = 0$, so that<br />\begin{equation}<br />\sigma_e = \sigma_s.<br />\end{equation}<br /><br /><b>4. Loss Tangent</b><br /><b><br /></b>The loss tangent is defined as<br />\begin{equation}<br />\tan \delta_e = \frac{\sigma_e}{\omega\epsilon'}.<br />\end{equation}<br />Expanding the effective conductivity $\sigma_e$, we get<br />\begin{align}<br />\tan \delta_e &= \frac{\sigma_s + \sigma_a}{\omega\epsilon'}<br />= \frac{\sigma_s + \omega\epsilon''}{\omega\epsilon'}<br />=\frac{\sigma_s}{\omega\epsilon'} +\frac{\epsilon''}{\epsilon'}.<br />\end{align}<br />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,$\epsilon''/\epsilon'\approx\sigma/\omega\epsilon$.<br /><br /><b>REFERENCES</b><br /><b><br /></b>Balanis, C.A., 2012. Advanced engineering electromagnetics. John Wiley & Sons. Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-87168969550535258372017-03-05T13:07:00.002+08:002018-02-18T16:04:30.861+08:00Notes on "Medium effect on the characteristics of the coupled seismic and electromagnetic signals" by Huang et al. 2015Recently developed numerical simulation technique can simulate the coupled<br />seismic and electromagnetic signals for a double couple point source or a finite fault planar source.<br />Besides the source effect, the simulation results showed that both medium structure and medium<br />property could affect the coupled seismic and electromagnetic signals. The waveform of coupled<br />signals for a layered structure is more complicated than that for a simple uniform structure.<br />Different from the seismic signals, the electromagnetic signals are sensitive to the medium properties<br />such as fluid salinity and fluid viscosity. Therefore, the co-seismic electromagnetic signals may be<br />more informative than seismic signals.<br /><br /><b>REFERENCES</b><br /><b><br /></b>Huang, Q., Hengxin, R.E.N., Zhang, D. and Chen, Y.J., 2015. <a href="https://www.jstage.jst.go.jp/article/pjab/91/1/91_PJA9101B-02/_pdf">Medium effect on the characteristics of the coupled seismic and electromagnetic signals</a>. Proceedings of the Japan Academy, Series B, 91(1), pp.17-24.<br /><br />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-17063627328668521362017-03-05T12:29:00.000+08:002018-02-18T16:04:24.947+08:00Notes on "Anomalous behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9.0)" by Xu et al. 2013There 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.<br /><br /><b>REFERENCES</b><br /><b><br /></b>Xu, G., Han, P., Huang, Q., Hattori, K., Febriani, F. and Yamaguchi, H., 2013. <a href="http://www.sciencedirect.com/science/article/pii/S1367912013004197">Anomalous behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9. 0)</a>. Journal of Asian Earth Sciences, 77, pp.59-65.Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-3852064506946260932017-03-05T11:06:00.001+08:002018-02-18T16:04:26.981+08:00Notes 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. 2016The 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.<br /><br /><b>REFERENCE</b><br /> <b><br /></b>Jiang, F., Chen, X., Zhan, Y., Zhao, G., Yang, H., Zhao, L., Qiao, L. and Wang, L., 2016. <a href="https://link.springer.com/article/10.1007/s00024-015-1055-4">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</a>. Pure and Applied Geophysics, 173(1), pp.269-284.<br /><br />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-41598991142306932362017-03-05T11:02:00.000+08:002018-02-18T16:04:27.307+08:00Notes on "Characteristics of Seismoelectric Wave Fields Associated with Natural Microcracks" by Fujinawa and Noda 2016Properties 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. <br /><br /><b>REFERENCES</b><br /><br />Fujinawa, Y. and Noda, Y., 2016. <a href="https://link.springer.com/article/10.1007/s00024-015-1043-8">Characteristics of seismoelectric wave fields associated with natural microcracks</a>. Pure and Applied Geophysics, 173(1), pp.255-268.Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-50046457651010043282017-03-05T10:51:00.000+08:002018-02-18T16:04:28.425+08:00Notes 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. 2015A 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.<br /><br /><b>REFERENCES</b><br /> <b><br /></b>Chavez, O., Millan-almaraz, J.R., Cruz-abeyro, J.A.L. and Rojas, E., 2016. <a href="http://www.tandfonline.com/doi/abs/10.1080/19475705.2015.1047903">Electromagnetic attenuation of eight earthquakes registered in Mexico using FFT-based spectrum and t-test statistical analysis for ULF QR ratios signals</a>. Geomatics, Natural Hazards and Risk, 7(4), pp.1207-1218.Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-79134869246923979232017-03-04T23:16:00.001+08:002018-02-18T16:04:29.864+08:00Notes on "Evaluation of seismo-electric anomalies using magnetic data in Taiwan" by Chen et al. 2013Abstract. 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.<br /><br /><b>REFERENCES</b><br /><br />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. <a href="http://search.proquest.com/openview/83ea364468b15c0af103231131cf320d/1?pq-origsite=gscholar&cbl=105722">Evaluation of seismo-electric anomalies using magnetic data in Taiwan. Natural Hazards and Earth System Sciences</a>, 13(3), p.597.<br /><br /><br />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0Taiwan23.69781 120.9605149999999916.258457 110.6333665 31.137163 131.28766349999998tag:blogger.com,1999:blog-2580286606979986508.post-24327642080325447892017-03-04T23:07:00.000+08:002018-02-18T16:04:25.404+08:00Notes 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. 2015Electromagnetic 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.<br /><br /><b>REFERENCES</b><br /><b><br /></b>Katori, Y., Okubo, K., Hato, T., Tsukamoto, A., Tanabe, K., Onishi, N., Furukawa, H., Isogami, S. and Takeuchi, N., 2015, December. <a href="http://adsabs.harvard.edu/abs/2015AGUFM.S33B2770K">Observation of Magnetic Signals from Earthquake Faulting Using High-resolution HTS-SQUID Magnetometer: Feasibility of Super-early Warning of Earthquakes. </a>In AGU Fall Meeting Abstracts.<br /><br /><br />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0tag:blogger.com,1999:blog-2580286606979986508.post-23353796251900579522017-03-04T22:30:00.000+08:002018-02-18T16:04:25.273+08:00Notes 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. 2015In 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.<br /><br />REFERENCES<br /><br />Balasco, M., Lapenna, V., Romano, G., Siniscalchi, A., Stabile, T.A. and Telesca, L., 2015. <a href="https://www.researchgate.net/profile/Tony_Alfredo_Stabile/publication/281115745_The_Pollino_2011-2012_seismic_swarm_southern_Italy_First_results_of_the_ML36_aftershock_recorded_by_co-located_electromagnetic_and_seismic_stations/links/55d6f2ac08aed6a199a50453.pdf">The Pollino 2011-2012 seismic swarm (southern Italy): first results of the ML= 3.6 aftershock recorded by co-located electromagnetic and seismic stations</a>. Boll Geofis Teor Appl, 56(2), pp.203-210.Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0Pollino, 87012 Castrovillari, Province of Cosenza, Italy39.9070026 16.18886380000003613.406491099999997 -25.119730199999964 66.4075141 57.497457800000035tag:blogger.com,1999:blog-2580286606979986508.post-10678504673726231142017-03-04T22:12:00.000+08:002018-02-18T16:04:24.227+08:00Notes on "Electric and Magnetic Field Changes Observed during a Seismic Swarm in Pollino Area (Southern Italy)" by Ballasco et al. 2014In 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. <br /><br /><b>REFERENCES </b><br /><br /> Balasco, M., Lapenna, V., Romano, G., Siniscalchi, A., Stabile, T.A. and Telesca, L., 2014. <a href="http://www.bssaonline.org/content/early/2014/05/20/0120130183.abstract">Electric and magnetic field changes observed during a seismic swarm in Pollino area (southern Italy)</a>. Bulletin of the Seismological Society of America.<br /><br /><br />Quirino Sugon Jr.https://plus.google.com/104887715369634785296noreply@blogger.com0