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Multi arrival tomography

Juerg Hauser, Malcolm Sambridge and Nicholas Rawlinson

Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

Figure 1. a) Layered velocity model and associated first arrival paths used in the inversion test. Point sources are denoted by stars and receivers by triangles. Note that paths also emanate from two impinging plane waves. b) Relative error in percent between the true model and the inversion result. Contour lines are plotted at 1.5% intervals.

 

In seismic imaging the focus has largely been on first arrivals, with a wide variety of schemes developed for their calculation. However, later arrivals often contribute to the length and shape of a recorded wave train, particularly in regions of complex geology. They are likely to contain additional information about seismic structure as their two point paths, differs from that of the first arrival. If they can be used in seismic tomography, improved images should result. Here we use the wavefront construction principle as the basis of a new scheme for computing travel times for first and later arrivals that arise from smooth variations in both velocity structure and interface geometry.

To investigate the possibility of using later arrivals to improve seismic imaging a numerical test is performed. We compare the results of first and multi arrival tomography, when recovering a two layered crustal scale structure characterised by two low velocity anomalies and a u-shaped valley in the interface. The inversion is performed simultaneously for interface and velocity structure. There are sources above and below the interface and two incoming plane waves are also simulated. Figures 1.a and 2.a show the ray path coverage of the structure, which we will try to recover using travel times. Clearly the later arrivals not only contain additional information about the two low velocity anomalies but also about the shape of the valley in the interface. Figure 1.b shows the difference between the inversion result and the true structure when only first arrivals are used in the inversion. The trade off between interface geometry and velocity anomaly is clearly not as well resolved compared to when both first and later arrivals are used (figure 2.b).

This example demonstrates that multi arrival tomography has the potential to lead to an improved recovery of structure. An important difference between first and later arrivals is that the existence of a later arrival is a function of the structure. This means that during the iterative inversion procedure, the number of ray paths and hence data is not constant. Using later arrival therefore makes the inverse problem much more non-linear, which means that care must be taken to avoid instabilities in an iterative non-linear approach.

Potential applications of multi arrival tomography include surface wave tomography, where observations of multipathing has been a long recognised phenomenon, with measurements and analysis using earthquake sources dating back many decades.

Figure 2. a) Layered velocity model and associated first and later arrival paths used in the inversion test. Point sources are denoted by stars and receivers by triangles. Note that paths also emanate from two impinging plane waves. b) Relative error in percent between the true model and the inversion result. Contour lines are plotted at 1.5% intervals.