Recent work suggests that slab dip may be controlled by differences in dynamic pressure above and below the slab at mid‐asthenospheric depth, motivating exploration of how plate and slab motion are linked to dynamic pressure in the asthenosphere. This paper, the first of two companion papers, presents an analytical method for determining dynamic pressure and velocity in a thin asthenospheric channel, with linear viscosity, consistent with prescribed plate and slab kinematics. Slabs are explicitly incorporated as vertical barriers to asthenospheric flow. Dynamic pressure is expressed as sums of functions with two functional forms, P _edge and P _wall; the former generates discontinuities in velocity (but not pressure) at non‐slab boundaries, and the latter generates discontinuities in pressure (but not velocity) at boundaries with slabs. Application to simple rectangular plate systems demonstrates that asthenospheric velocities within about one trench length of slabs are insensitive to processes on the opposing side of the slab, that dynamic pressure scales linearly with trench length for a given plate aspect ratio and scales approximately linearly with the shortest plate dimension. Although dynamic pressure is quasisymmetrical across convergent plate boundaries that lack slabs, the presence of slabs creates discontinuity and asymmetry in dynamic pressure across subduction zones. When flux of asthenosphere into the lower mantle occurs adjacent to subducting slabs, dynamic pressure is decreased on the side of the slab where down‐flux occurs. This analytical method, applied to systems with multiple arbitrarily shaped plate boundaries, yields excellent results as benchmarked against 3‐D numerical solutions.

中文翻译：

---

俯冲动力学和地幔压力：1.一个与俯冲几何，板块运动和软流层压力有关的分析框架

最近的工作表明，板坯的倾角可能受软流圈中深度处板坯上方和下方的动压力差的控制，这激发了人们探索板坯和板坯运动如何与软流圈中动压相关的问题。本文是两篇附带论文中的第一篇，提出了一种分析方法，该方法可确定具有线性粘度，符合规定的平板和平板运动学的薄弱的软流圈通道中的动压力和速度。平板被明确地纳入为软流圈流动的垂直屏障。动态压力表示为具有两种功能形式的函数之和，即P _edge和P _wall; 前者在非板边界处产生速度不连续性（但不产生压力），而后者在板的边界处产生不连续的压力（但不产生速度）。在简单的矩形板系统上的应用表明，在大约一个板块沟槽长度内的软气圈速度对板块相对侧的过程不敏感，对于给定的板长宽比，动态压力与沟槽长度成线性比例关系，而在最短的情况下，动压近似呈线性比例变化板尺寸。尽管动压在缺少板片的会聚板块边界上是准对称的，但板片的存在会在俯冲带上的动压中产生不连续性和不对称性。当软流圈流向俯冲板块附近进入下地幔时，平板上发生向下通量的一侧的动压力会降低。这种分析方法适用于具有多个任意形状的板边界的系统，以3D数值解为基准，可产生出色的结果。