Article,
Seismic traveltime inversion for 2-D crustal velocity structure
Geophysical Journal International, 108 (1): 16--34 (January 1992)
DOI: 10.1111/j.1365-246X.1992.tb00836.x
Abstract
A method of seismic traveltime inversion for simultaneous determination
of 2-D velocity and interface structure is presented that is applicable
to any type of body-wave seismic data. The advantage of inversion,
as opposed to trial-and-error forward modelling, is that it provides
estimates of model parameter resolution, uncertainty and non-uniqueness,
and an assurance that the data have been fit according to a specified
norm. In addition, the time required to interpret data is significantly
reduced. The inversion scheme is iterative and is based on a model
parametrization and a method of ray tracing suited to the forward
step of an inverse approach. The number and position of velocity
and boundary nodes can be adapted to the shot-receiver geometry and
subsurface ray coverage, and to the complexity of the near-surface.
The model parametrization also allows ancillary amplitude information
to be used to constrain model features not adequately resolved by
the traveltime data alone. The method of ray tracing uses an efficient
numerical solution of the ray tracing equations, an automatic determination
of take-off angles, and a simulation of smooth layer boundaries that
yields more stable inversion results. The partial derivatives of
traveltime with respect to velocity and the depth of boundary nodes
are calculated analytically during ray tracing and a damped least-squares
technique is used to determine the updated parameter values, both
velocities and boundary depths simultaneously. The stopping criteria
and optimum number of velocity and boundary nodes are based on the
trade-off between RMS traveltime residual and parameter resolution,
as well as the ability to trace rays to all observations. Methods
for estimating spatial resolution and absolute parameter uncertainty
are presented. An example using synthetic data demonstrates the algorithm's
accuracy, rapid convergence and sensitivity to realistic noise levels.
An inversion of refraction and wide-angle reflection traveltimes
from the 1986 IRIS-PASSCAL Nevada, USA (Basin and Range province)
seismic experiment illustrates the methodology and practical considerations
necessary for handling real data. A comparison of our final 2-D velocity
model with results from studies using other 1-D and 2-D forward and
inverse methods serves as a check on the validity of the inversion
scheme and provides estimates of parameter uncertainties that account
for the bias introduced by the modelling approach and the interpreter.
