![]() ![]() For the first model, these anomalies are described with a curvilinear boundary F(x) as Figure 2a. Both models have two shallow velocity anomalies. In this example, we use the two descriptions of the shallow velocity anomalies. To illustrate this, let’s consider two models with shallow velocity anomalies, as shown in Figure 2. It means that if we describe a shallow velocity anomaly using either a laterally changing interval velocity or a curvilinear boundary, we will come very close to the same result. After differentiating this equation twice, we come to the connection between the second-order derivatives of the two forms:Ĭomparing formulas (1) and (2) from the paper (Blias, 2006a) and taking into account the last formula, we see that both shallow velocity anomaly descriptions give close to NMO velocities. Where s(x) is slowness in the layer: s(x)= 1/u(x). It means that we have a connection between the boundary F(x) and velocity u(x) (Fig. Let’s assume that the interval velocity in the second model gives the same vertical time in the first layer as in the first model within the layer between 0 and the depth h. We may also use a laterally inhomogeneous layer with the velocity u(x), fig. We can use a curvilinear boundary z = F(x), which separates two layers with constant velocities, fig. There are two possibilities to describe shallow velocity anomalies. In this paper, I consider the opposite case – shallow velocity distribution is complicated (shallow velocity anomalies) and we don’t have shallow reflection, but deep geology is gentle. We can say that tomography and prestack depth migration approaches were developed for the situation when the shallow part of the subsurface is simple and complex structures are relatively deep. After that we can use reflection tomography approach to improve this model. That is why, before using any reflection tomography or prestack depth migration velocity analysis or ray-based stacking velocity inversion, we need to develop a method to obtain appropriate initial depth velocity model including the shallow part of the subsurface. To find an initial model, we can try to use Dix type of inversion, which does not require initial model, but in the presence of unresolved shallow anomalies, it will not give reasonable interval velocities. The second and third type of approach (any kind of reflection tomography, prestack depth migration velocity analysis) requires a reasonable initial approximate velocity model. Two descriptions of shallow velocity anomalies. In the presence of unresolved (that is with unknown shallow anomalies) shallow velocity anomalies, any kind of direct inversion will lead to big errors because the difference between NMO velocities for the model with and without shallow velocity anomalies is big (it’s increasing with reflector depth). If we estimate an interval velocity for 2D and 3D models (that is when the 1D local assumption does not work) we have to know the velocity distribution in the overburden. The first type of approach (direct inversion) works on a layers-tripping method except for a 1D model when the Dix formula gives the solution using only two reflections – at the top and at the bottom of the layer. Prestack depth migration velocity analysis.Different types of reflection tomography.Direct inversion of NMO velocities and zero-offset times: Dix type of method, including generalizations of Dix formula.There are three main approaches to build depth velocity model: In these cases we can sometimes use reflections to restore SVAs and to remove their effects on seismic data. In some cases the first break approach does not work because of poor first break determination, a shallow low velocity layer, or permafrost among other possible problems. A conventional approach to deal with SVAs utilizes first breaks to determine shallow velocity structures (Hampson and Russell, 1984, Yilmaz, 1987, Cox, 1999). Non-removed shallow velocity anomalies (SVAs) can reduce the quality of the post-stack image and create time distortions in seismic horizons. As was analytically shown in the first paper (Blias, 2006a) shallow velocity anomalies can cause large lateral variations in stacking velocities.
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