Solution (source code)

= Solution

Assume an Earth-like reversing planetary <magnetic field> and magnetizable crust that acquires <thermoremanent magnetization> on cooling. Alternating polarity intervals then produce <marine magnetic stripes> parallel to each <spreading ridge>, with matching age/polarity sequences on its two sides. AB has <half-spreading rate> 10 mm/year, whereas AC has <half-spreading rate> 24 mm/year. Thus the same polarity interval $\Delta t$ produces widths $10\Delta t$ and $24\Delta t$ mm when time is in years: the AC stripes are 2.4 times wider. Age increases away from each ridge. The transform produces no new crust; bands end or are displaced at it, rather than forming a third symmetric stripe sequence centred on BC. This is the remanent-magnetization/spreading mechanism developed from marine magnetic observations.<Magnetic Anomalies Over Oceanic Ridges by F. J. Vine and D. H. Matthews>[pp. 947–949, alternating remanent magnetization and the spreading interpretation]{ref}

A more precise local sketch can be made in the northern junction frame. Let $x,y$ be distances in kilometres along the fixed tangent axes and $t$ the crustal age in Myr; numerically, mm/year equals km/Myr. Relative to the moving junction, the <velocities> are $\mathbf w_A=(24,10)$, $\mathbf w_B=(24,-10)$ and $\mathbf w_C=(-24,10)$. In A the steady age field is $t_A=\min(x/24,y/10)$, since backwards advection first reaches either the AC or AB ridge. Equal-age bands therefore join as right-angle corners within A, with the corners migrating along the ray $(24,10)$. In the B wedge, $t_B=-y/10$ and the stripes meet the transform. On the C flank directly supplied from AC, $t_C=-x/24$; other parts of C carry older crust whose inherited pattern requires earlier boundary history.

\Image[/past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2016/paper-1-magnetic-stripes.png]
{title=Original conditional remanent-polarity sketch in the north-junction frame; reversal intervals are illustrative and unsupplied older crust is left unassigned}

The sketch displays <magnetization> polarity, not a computed total-field anomaly amplitude. Actual anomalies depend on the planetary field direction, source depth, <magnetization> strength and observation geometry. The paper supplies no field history, so a numerical reversal chronology or an absolute positive/negative anomaly sequence cannot be inferred. Without field reversals, ridge accretion alone does not imply alternating polarity stripes.