Seismic Refraction Layer
Modelling in 2D
Background to RayINVR
RAYINVR (Zelt and Smith, 1992; Zelt, 1999)
Model parameterization:
• 2D velocity model is composed of a sequence of
layers; Each layer boundary is defined by
boundary nodes connected by straight-line
segments of arbitrary dip; Vertical boundaries
separate each layer into trapezoidal blocks;
Velocity varies linearly between velocity points
located on layer boundaries;
Velocity discontinuities resulting in reflections are defined by upper and lower layer
velocity points at selected boundary nodes
Forward problem:
• Traveltimes through velocity model computed using zero-order asymptotic ray
theory by solving the ray tracing equations numerically
Inverse problem:
• Damped least-squares inversion; Can be limited to a set of model parameters
Goal:
•
Develop a detailed velocity model of the subsurface by applying a top-down layerstripping approach; Fit various seismic phases to first constrain shallow structure
and then progressively construct the deeper layers
Strategies for modelling seismic refraction/wide-angle reflection travel-times to obtain
2-D velocity and interface structure
Given the unique characteristics of each data set and the local earth structure,
there is no single approach to modelling wide-angle data that is best.
The Zelt (1999) paper describes the best modelling strategies according to (1)
the model parametrization, (2) the inclusion of prior information, (3) the
complexity of the earth structure, (4) the characteristics of the data, and (5)
the utilization of coincident seismic reflection data.
The most important advantages of an inverse method are the ability to derive
simpler models for the appropriate level of fit to the data, and the ability to
assess the final model in terms of resolution, parameter bounds and nonuniqueness. [However,] if there is strong lateral heterogeneity in the nearsurface only, layer stripping works well. Direct model assessment techniques
that derive alternative models that satisfactorily fit the real data are the best
means of establishing the absolute bounds on model parameters and whether
a particular model feature is required by the data.
With good-quality reflection data, the final section can often be presented in uninterpreted form so that the reader can assess the interpretation provided and
objectively establish their own interpretation.
With wide-angle data, the primary goal is to produce a velocity model that
predicts the observed travel-times. Thus, the final result of the modelling
approach, the model, is fundamentally different from the result of the processing
approach, since it looks nothing like the data. It is left to the modeller to establish
the credibility of the model, usually through ray diagrams, overlaying the data
with predicted times, comparing the observed and predicted times directly, or
presenting the diagonal values of the resolution matrix.
These methods are insufficient because of the non-uniqueness of the problem;
that is, none of these displays address whether particular model structure is
required by the data and what range of models fit the data.
A model developed by the analysis of wide-angle travel-time is only as good as
the picks.
Arrivals should only be included in the modelling once they can be confidently
identified. Assigning layers to refracted arrivals may unnecessarily bias the
modelling process. In obvious cases it may be worthwhile to identify the
refracting layer since it may help to stabilize an inversion or supply more
confidence when forward modelling.
The use of fully automated picking routines is uncommon, particularly for later
arrivals. An efficient approach is a semi-automated scheme whereby a few picks
are made interactively, and the intervening picks are determined automatically
using a cross-correlation scheme. Picks should not be interpolated to provide a
uniform spatial coverage, especially when there are significant data gaps, since
this will provide an incorrect sense of model resolution.
Assigning uncertainties to the arrival picks is necessary, to avoid over- or underfitting the data. Data fitting is strongly linked with the data uncertainties. Ideally,
an overall normalized χ2 travel-time misfit of 1 should be achieved [NB: but may
require dense node spacings that result in poor resolution].
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
NB: For marine case, s=receiver is fixed along line and r=shot
position varies to give correct ranges for each receiver. Best fit line
= great circle path. Flat earth valid for ranges < 500 km.
Refraction/reflection traveltime modeling/inversion using RAYINVR
Starting Model
Inversion Strategies
uniform/fine grid
tomography
minimum
structure
Full inversion
Model testing
non-uniform/
coarse grid
Ray Invr
non-minimum
(prior) structure
Partial (top-down/
layer stripping)
inversion
Node spacing ≈ receiver spacing (0.5 near surface)
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Cratonic continent
oceanic
margin
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Refraction/reflection traveltime modeling/inversion using RAYINVR
Some Examples from Dalhousie
Refraction/reflection traveltime modeling/inversion using RAYINVR
Gerlings et al., 2011
Refraction/reflection traveltime modeling/inversion using RAYINVR
Gerlings et al., 2011
Refraction/reflection traveltime modeling/inversion using RAYINVR
Lau et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Lau et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Funck et al., 2004
Refraction/reflection traveltime modeling/inversion using RAYINVR
Lau et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Lau et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
OBS 14
OBS
Lau et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Wu et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Wu et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Wu et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Wu et al., 2006
Refraction/reflection traveltime modeling/inversion using RAYINVR
Summary for RAYINVR Modeling
• Forces model into a limited number of discrete layers which may or may
not correspond to geological boundaries – e.g. changes in velocity
gradient require separate layers not necessarily related to structure.
• Modeler needs to define arrivals by layer number and type of arrival (i.e.
reflection or refraction). Proceed with forward models from top to bottom
using as few layers as possible.
• Inversion rarely works for entire model unless highly simplified – e.g. for
continental crust with simple boundaries and only a few layers. Generally
need to limit inversion to one layer at a time.
• Uncertainties in crustal velocities and boundaries are typically ± 0.1 km/s
and ± 1-2 km with good control and ± 0.2-0.3 km/s and ± 5 km for poorer
control.
• For marine data, works best with coincident reflection data to define
upper layer geometry (i.e. sediment and basement) and compare deeper
structure between reflections and velocity model.
References
Funck, T., Jackson, H.R., Louden, K.E., Dehler, S.A.& Wu,Y., 2004. Crustal structure of the northern Nova Scotia
rifted continental margin (Eastern Canada), J. geophys. Res., 109, B09102, doi:10.1019/2004JB003008.
Gerlings, J., Louden, K.E., & Jackson, J.R., 2011, Crustal structure of the Flemish Cap Continental Margin
(Eastern Canada): An analysis of a seismic refraction profile, Geophys. J. Int., 185, 30-48.
Lau K.W.H., Louden, K.E., Funck, T., Tucholke, B.E., Holbrook, W.S., Hopper, J.R. & Larsen, H.C., 2006. Crustal
structure across the Grand Banks–Newfoundland Basin Continental Margin–I. Results from a seismic
refraction profile, Geophys. J. Int., 167, 127–156.
Wu, Y., Louden, K.E., Funck, T., Jackson, H.R., & Dehler, S.A., 2006. Crustal structure of the central Nova Scotia
margin off Eastern Canada, Geophy. J. Int., 166, 878–906.
Zelt, C.A., 1999. Modeling strategies and model assessment for wide-angle seismic traveltime data, Geophys.
J. Int., 139, 183–204.
Zelt, A.C.& Smith, R.B., 1992. Seismic travel time inversion for 2-D crustal velocity structure, Geophys. J. Int.,
108, 16–34.