Abstract
Abstract. The finite physical source problem is usually studied with the concept of volume and time integrals over Green's functions (GFs), representing delta-impulse solutions to the governing partial differential field equations. In seismology, the use of realistic Earth models requires the calculation of numerical or synthetic GFs, as analytical solutions are rarely available. The computation of such synthetic GFs is computationally and operationally demanding. As a consequence, the on-the-fly recalculation of synthetic GFs in each iteration of an optimisation is time-consuming and impractical. Therefore, the pre-calculation and efficient storage of synthetic GFs on a dense grid of source to receiver combinations enables the efficient lookup and utilisation of GFs in time-critical scenarios. We present a Python-based framework and toolkit – Pyrocko-GF – that enables the pre-calculation of synthetic GF stores, which are independent of their numerical calculation method and GF transfer function. The framework aids in the creation of such GF stores by interfacing a suite of established numerical forward modelling codes in seismology (computational back ends). So far, interfaces to back ends for layered Earth model cases have been provided; however, the architecture of Pyrocko-GF is designed to cover back ends for other geometries (e.g. full 3-D heterogeneous media) and other physical quantities (e.g. gravity, pressure, tilt). Therefore, Pyrocko-GF defines an extensible GF storage format suitable for a wide range of GF types, especially handling elasticity and wave propagation problems. The framework assists with visualisations, quality control, and the exchange of GF stores, which is supported through an online platform that provides many pre-calculated GF stores for local, regional, and global studies. The Pyrocko-GF toolkit comes with a well-documented application programming interface (API) for the Python programming language to efficiently facilitate forward modelling of geophysical processes, e.g. synthetic waveforms or static displacements for a wide range of source models.
Highlights
Green’s functions (GFs) are used abundantly to represent force excitations of many different processes inside the Earth
The given matrix formulation is convenient for an efficient numerical implementation in the GF store and it allows for a generalisation of mixed problems
To constrain the finite duration of moment release at a source point, we extend the delta-force excitation to force excitations in time, which is known as the source–time function (STF)
Summary
Green’s functions (GFs) are used abundantly to represent force excitations of many different processes inside the Earth. Solving the non-linear inverse problem of determining the parameters of sources with a finite duration and finite extent is a computational costly effort It involves the repeated numerical calculation of a large number of GFs for combinations of force excitations in the context of an optimisation algorithm. Pre-calculated GFs have long been used for operational routine seismological source inversion (Dahm and Krüger, 2014, Table 3). Often, these are in-house-developed database solutions or other structured storage linked to specific forward modelling and inversion codes.
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