GEOCHEMICAL EFFECTS OF MAGMATIC SOLITARY WAVES .2. SOME ANALYSIS

As a complement to the numerical solutions of Watson & Spiegelman (199 4; hereafter known as Paper I), we present some analytic solutions and proofs to illustrate more generally how a single magmatic solitary wa ve affects the transport of trace elements. In the absence of any diff usion or dispersion, the equations for trace element transport can be solved by the method of characteristics. This analysis shows that with out diffusion, a solitary wave can transport chemical signals but cann ot permanently change the shape of an initial trace element distributi on. The solitary waves, however, can locally steepen trace element gra dients by a distortion factor S which depends only on the ratio of ini tial and local transport velocities. These results are quite general a nd are expected for any solitary wave of permanent form and constant v elocity because these waves always provide a frame of reference where the melt and solid velocities are steady state.