3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

Abstract

In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised 'irregular' approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised 'irregular' over the 'regular' approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the 'regular' approach) and less number of total nodes. The introduction of 'soft' and 'hard' bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.

2-D/3-D multiply transmitted, converted and reflected arrivals in complex layered media with the modified shortest path method

“…(2) Easy handling of media containing large velocity contrasts (Bai & Greenhalgh 2005a). This is due to velocity values being bilinearly or trilinearly linked to secondary nodes or source and receiver positions.…”

2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications

“…Based on the previous algorithm for traveltime tomography (Bai & Greenhalgh 2005), in which the MSPM algorithm was used as ray tracer and the DMNCLS‐CG (damped minimum norm and constrained least‐squares problem, solved by the conjugate gradient approach) as non‐linear inversion solver, we incorporate our multiple event location algorithm (Bai & Greenhalgh 2006) to form a simultaneous inversion routine to update both the velocity field and the source parameters (Bai et al 2008). Now we incorporate our newly developed multistage ISPM (or MSPM) algorithm as ray tracer and the DMNCLS‐CG as non‐linear inversion solver to update both velocity model and reflection interface (or subsurface) geometry (2‐D case, Huang & Bai 2010; 3‐D case, Bai & Huang 2010).…”

What Controls Sill Formation: An Overview From Analogue Models

“…Sills, or sub-horizontal intrusions, are common means to emplace shallow magma, as shown by geologic (i.e., Famin & Michon, 2010), geodetic (e.g., Sigmundsson et al, 2010;Di Vito et al, 2016), and geophysical data (e.g., Auger et al, 2001;Bai & Greenhalgh, 2005). Sill emplacement is fundamental to growing laccoliths and lopoliths, or more in general the thick tabular intrusions that commonly constitute the eroded plutons (Cruden, 1998;Brown, 2013;De Saint-Blanquat et al, 2006;Leuthold et al, 2012;Pasquarè & Tibaldi, 2007;Petford et al, 2000).…”