## Statics

Probably the most important aspect of the seismic processing of Onshore data is the near surface statics error calculation and correction. Dayboro has a multitude of methodologies available to calculate near surface static corrections. Most commonly Dayboro uses one of the two of the modern class of refraction statics methodologies “Refraction Inversion” and “Tomostatics”. Figure A

First-arrivals (first breaks) are picked on all traces, Figure A illustrates an example of first breaks picked on a test line. Both methods use the same input information, the first breaks. The methods differ in how they use that information to build a picture of the near surface velocity. Figure B Refraction Inversion Approach and Tomo-statics Approach

The Refraction Inversion method starts with a simple layer-based velocity model, in this case consisting of the surface, a weathering layer (Layer 1) which is defined by the velocity Vo and the depth below the surface Zo, and a sub-weathering layer (Layer 2) defined by just it’s velocity V1 at each point along the line. Figure B.a illustrates the concept. If the near surface is more complicated (as determined during the first-break picking) many more layers can be defined. The program then traces “Refraction” rays through this simple model from same source locations to the same receiver locations at which the first-break information was picked. From this a modelled first-break time is calculated. The modelled first-break time is then compared to the picked first-break time and the error calculated. The model is then perturbed and the process repeated until the error between the modelled first-break and the measured first break is minimized in a least squares sense. The values of Zo, Vo and V1 are allowed to vary spatially along the line (or in 3D). The method is a weighted, constrained least squares solution and produces a robust solution (Woodward, 1991).

Tomography is also a least squares inversion type approach, but the difference here is that rather than starting with a layer based initial velocity model, the subsurface is broken up into a grid of cells with a single parameter in each cell, velocity Vi. The initial model is created with an initial surface velocity and a vertical velocity gradient to produces a smoothly varying model. The tomography program then traces rays through these cells refracting at the cell boundary using Snells Law, to come up with travel times to compare to the measured first-breaks. Because of the way these rays move, they are termed “Turning Rays”, Figure B.b illustrates the concept. The model is then perturbed (velocities in the cells adjusted) and the process iterates until the error between the modelled and measured first-break is suitably small. Tomography doesn’t result in a Zo, Vo and V1 model but rather a continuous grid-based velocity field.

While tomostatics is the “flavour of the month” it is hard to reconcile the fact that it is looking at “Turning Rays” whereas the first-breaks being interpreted are “Refracted” events. Figure C Example Line Refraction Inversion Result and Quality Control Products. Figure D Example Line Tomo-statics Result and Quality Control Products.

Figure C illustrates the result of the Refraction Inversion on a test line. The top box in the image is the statics profile, the source statics being red marks and the receiver statics being blue marks. The middle box in the image is a QC product which shows superimposed lines and points where the lines represent the final modelled travel times for a particular shot and the points represent the picked first breaks. On the computer screen holding the cursor over a shot and clicking will high-light a single shot, enabling examination of how well the modelled and picked first breaks correspond. The bottom panel in the image shows the velocity model and the small box to the right details the RMS error for each iteration of the inversion. Figure D illustrates the Tomo-statics result for the same line. The top panel is the velocity model, the middle panel is the Ray Density and the bottom panel shows the resulting statics profiles, again the shot statics are red marks and the receiver statics are shown in blue. Note that the high values in the Ray Density diagram broadly correspond to the position of the refractor (top of Layer 2) in the Refraction Inversion velocity model shown in Figure C. Figure E Example Line Refraction Inversion and Tomo-Statics Model Comparison. Figure F Example Line Refraction Inversion and Tomo-Statics Statics Comparison.

Figure E compares the velocity models resulting from the two statics methods. In many places the two models are quite similar both in structure and in absolute velocity. There are however some significant differences. Comparing the statics profiles themselves (Figure F) there is generally a good correlation. Both methods resolve similar features and the differences in the long wavelength static are generally small with the two profiles departing in some places by a maximum of 15ms. The Tomo-statics model is a much more sophisticated looking model, perhaps this explains its current popularity amongst exploration company geoscientists. Figure G Example Line Elevation Statics, Refraction Inversion, and Tomo-Statics Stack Comparison.

Applying the statics from the two methods to the data and producing brute stacks (Figure G) reveals that the differences seen in the model and in the statics profile are not necessarily evident. However, close examination of the comparison on this line and many of the others reveals that where the statics profiles and models diverge, a deterioration in the stack quality of the Tomo-statics result can be seen. The effect is subtle and there are situations where the reverse can be observed. Dayboro has conducted numerous tests, on a wide variety of data and determined that the Refraction Inversion result is often superior and this method our preferred option, however we retain the capability to implement the Tomostatics approach if required by our clients.