By Richard D. Miller, John H. Bradford, Klaus Holliger
Published via the yankee Geophysical Union as a part of the Geophysical improvement sequence, quantity 15.
Advances in Near-surface Seismology and Ground-penetrating Radar (SEG Geophysical advancements sequence No. 15) is a set of unique papers through well known and revered authors from worldwide. applied sciences utilized in the appliance of near-surface seismology and ground-penetrating radar have noticeable major advances within the final numerous years. either equipment have benefited from new processing instruments, elevated laptop speeds, and an elevated number of applications.
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Extra resources for Advances in Near-surface Seismology and Ground-penetrating Radar, Volume 15
Li ! Liþ1 ! . ! Ln21 ! Ln ! 0; d ¼ LDb; and I is the identity matrix. A solution to this constrained (weighted) least-squares problem (equation 3) with minimum modiﬁcation to model parameters is sought so that the convergence procedure will remain stable for each iteration. This does not necessarily mean that the ﬁnal model will be closer to the initial model than with other optimization techniques, such as the Newton method. The modiﬁcation determined at each iteration (equation 4) is added to the previous model, thereby producing an updated model (x kþ1 ¼ x k þ Dx).
Saunders, 1982, LSQR: An algorithm for sparse linear equations and sparse least squares: Transactions of Mathematical Software, 8, 43–71. , and I. Lecomte, 1991, Finite difference computation of traveltimes in very contrasted velocity models: A massively parallel approach and its associated tools: Geophysical Journal International, 105, 271–284. Pratt, R. , 1999, Seismic waveform inversion in the frequency domain, Part 1: Theory and veriﬁcation in a physical scale model: Geophysics, 64, 888–901.
2006b) gave the partial derivatives with respect to these parameters, so the accurate Jacobian matrix for the same inversion algorithm discussed in the previous section can be calculated. 5) is critical to ensure convergence of the inversion. A minimum of three data points is required in the inversion. , 1999) discussed in the previous section was used to invert Rayleigh waves to estimate three parameters that determine the S-wave velocities. The same real-world data (Figure 2a) used for the layered-earth model were employed again to demonstrate 23 the use of the continuously layered-earth model.
Advances in Near-surface Seismology and Ground-penetrating Radar, Volume 15 by Richard D. Miller, John H. Bradford, Klaus Holliger