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 $\mathbf e_{rake}$:
\begin{equation}
\mathbf e_{rake} = \mathbf e_{strike}\cos\theta_{rake} - \mathbf e_{dip}\sin\theta_{dip}.
\end{equation}
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,
\begin{equation}
\mathbf e_{TP}\cdot\mathbf e_3 = -\cos(90^\circ-P)=-\sin P\equiv n,
\end{equation}
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}