= Solution
\b[<Earthquake> location.] The <hypocentre> is rupture initiation; its surface projection is the <epicentre>. Record calibrated arrival times at stations of known coordinates, identify <P wave> and <S wave> phases, and predict their <travel times> through a stated <velocity> model. <Earthquake location by arrival times> fits
$$
t_i=t_0+T_i(\mathbf x),
$$
for the three source coordinates and origin time $t_0$. <Linearization> supplies residual equations $\delta t_i=\delta t_0+\nabla T_i\cdot\delta\mathbf x$. A grid search or iterative <weighted least squares> inversion can use pick uncertainties, while station geometry controls whether those parameters are well constrained. Four independent arrival constraints are the minimum for four unknowns, not a guarantee of a reliable solution.
In a homogeneous medium, an arrival-time difference between an <S wave> and a <P wave> cancels origin time and estimates source-to-station distance,
$$
r=\frac{t_S-t_P}{1/v_S-1/v_P}.
$$
Several distances intersect to locate the event; real layered or three-dimensional <Earth> structure requires curved-ray <travel times>. Nearby stations and diverse takeoff angles help resolve depth. Clock errors, phase misidentification, poor azimuthal coverage and incorrect <velocities> introduce uncertainty or systematic bias. Closely spaced <earthquakes> can be relocated precisely relative to each other because common-path errors partly cancel, even when their absolute locations remain uncertain. \b[Report a location uncertainty and model assumptions, not merely a best-fit point.]
\b[<H. F. Reid>'s earthquake-cycle model.] A <fault> can remain locked while long-term tectonic motion slowly deforms the surrounding rocks. Elastic <strain> <energy> and <shear stress> accumulate. When resistance is overcome, rapid <fault slip> releases part of that stored <energy> as seismic waves, frictional <heat> and other irreversible <work>. The adjoining rocks partly recover their elastic distortion while retaining a permanent displacement discontinuity across the <fault>: this is <elastic rebound>. Surface markers initially crossing the <fault> become bent during loading and offset after slip.<Reid's Elastic Rebound Theory by United States Geological Survey>[Explanation of gradual strain accumulation, sudden release and the displaced fence; cites Reid's 1910 report, especially pp. 16–28]{ref}
A simple sketch is a slow rise of <stress> followed by a rapid <stress> drop, then renewed loading; the plate displacement continues throughout. Geodetic deformation, observed <fault> offsets and <earthquake> <stress> changes can test the picture. Actual cycles need not repeat with identical slips or times: creep, afterslip, <stress> transfer and heterogeneous <friction> complicate the idealization. The release need not remove all pre-existing <stress>. \b[<Elastic rebound> explains storage and release; it is not a deterministic <earthquake> clock.]
\Image[/past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2013/paper-1-pep-notes.png]
{title=Schematic magnetic stripes, convection rolls, arrival-distance constraints and elastic loading–release cycle; no measured data}
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