The weathering layer may be the most variable of all layers yet in seismic processing it is taken to be either uniform in thickness or velocity. Datuming through an incorrect weathering model can corrupt the stack and can introduce false structure into deep reflectors. It is important to correct for the effect of variable thickness and lateral velocity variation of the weathering layer. The main methods used to correct for these effects are given below.

Uphole Surveys

An uphole survey is used to determine the weathering layer velocity. A borehole is drilled that penetrates below the weathering layer; several geophones are placed at various known depths within the hole. The geophone locations must span the weathering and sub-weathering layers. A shot is fired at the surface near the hole and the direct travel times to the geophones are recorded.

A plot of the direct travel times versus the geophone depths can be used to compute the velocities of the weathering layer and sub-weathering layers along with the thickness of the weathering layer at that point.

This method attempts to construct a model of the weathering layer by estimating the velocity and thickness of the weathering layer at several locations and interpolating between these locations.

Refraction Statics

The purpose of refraction statics is to compute weathering statics corrections during the processing of reflection seismic data by using the travel times of critically refracted seismic energy (first breaks). There are different techniques in the application of refraction statics one of which is the General Linear Inversion method (GLI).

In order to incorporate low velocity layers into the statics solution, accurate uphole information is required. By including the uphole information we have a good estimate of the weathering layer velocity which allows us to build a good initial near-surface geological model.

Spectrum has licences for Hampson-Russell GLI3D, Green Mountain Geophysics Millennium Series and Sigma^{3}’s Seismic Studio^{TM}.

GLI3D relies on user interpretation of layers/velocities (i.e. slope/intercept) at discrete control points which can be used to build the initial depth/velocity model. This is then used as the input to the first run of GLI or Tomography to obtain updates. (This sequence can be iterated as necessary to achieve a stable result).

In contrast, Seismic Studio^{TM} utilizes user picked offset ranges for each refractor to build a velocity/depth model. Delay times are calculated for each defined layer via various methods, or tomography.

GLI3D First Break Picks QC displays

Initial Model (LEFT) Tomographic Model Update (CENTER) GLI Model Update (RIGHT)

Seismic Studio^{TM} is an interactive software package which offers a full geometry build and QC, functions to pick first breaks manually and automatically and can derive full 2D/3D refraction statics.

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For refraction statics the software takes a file of first break picks and derives an earth model which gives the best fit to the measured first breaks. SEGY trace data is loaded into Seismic StudioTM and the first breaks picked. Alternatively the first breaks can be picked externally and loaded, or picks and geometry loaded without trace data. The first break picks can be QC’d in shot, receiver or offset domain, and offset range values assigned.

Earth models can be derived using delay time, or tomographic inversion techniques. Seismic StudioTM has a comprehensive set of interactive tools for QC at every stage, but the main feature of the system is that all the above aspects are fully interconnected. Thus any changes can be made, reviewed, and incorporated without having to repeatedly re-run processing sequences. Both 3D and 2D projects can be loaded, and options are available to load 2D lines into a 3D project. A reliable refraction statics solution is usually an essential prerequisite for a successful land seismic processing sequence. The earth-model can contain numerous layers, within which the velocities are allowed to vary laterally.

The first arrivals do not have to be assigned to any particular refractor – the output effectively replaces a specified number of layers by calculating both the time-delays caused by those layers, and also the surface consistent residual shifts needed to further minimise the discrepancy between measured and calculated travel-times. The many diagnostic features within the package make it very easy to convert first-break data into a static shift file to apply to seismic reflection data, or to a model producing a best fit to seismic refraction data.

Differences in first arrival traveltimes between adjacent records can be used to compute the depth and velocity structure of near surface layers. The traveltime differences as a function of source-receiver offset provide a direct indication of the number of refractors present, with each refractor being defined by an offset range with constant time difference. For each refractor the time difference value at a common receiver from two shotpoints is used to partition the intercept time into the delay time at each shotpoint. This procedure is repeated until the delay times at all shotpoints and for all refractors have been computed. Refractor depths and velocities are evaluated from this suite of delay times.

The Hampson-Russell software, GLI3D, is used for calculating Refraction statics. It is an interactive program designed to interpret first breaks from 2-D and 3-D seismic data. It derives a near-surface geological model from which static corrections are calculated for application to the seismic data. 2-D, 3-D, or crooked lines are all handled with the same algorithm, with no restrictive assumptions concerning the acquisition geometry or ordering of the data.

The first step is to pick the first break times from the unprocessed seismic data. The initial geological model is then specified at selected control points. Once the initial model had been formed, GLI3D uses Generalised Linear Inversion or Tomographic Inversion to iteratively update the model in such a way as to reduce the difference between the observed breaks and those calculated from the model. . This process consists of ray-tracing through the model to predict first break times for each trace.

By analysing the error or misfit between the real first breaks and the predicted values, the model is iteratively updated.

The Linear Inversion method makes a number of assumptions e.g. constant velocity weathering layers. The tomographic inversion method uses a turning-ray model in which first arrivals represent a wave front travelling through a continuous velocity medium with vertical and horizontal velocity gradients. The algorithm uses a finite difference solution for forward modelling of travel times and an inversion procedure that calculates the back propagation of errors and updates the model velocity.

From the final geological model, static corrections are calculated. A series of options, including elevation corrections only, short and/or long period weathering statics, and floating datum statics are available. The calculated statics are then written to the seismic database for later application to the seismic.

It is possible to solve the statics for all lines from a 2D survey in a 3D sense. This is done by importing multiple 2D lines into GLI3D prior to creating the initial model. The model and hence the statics solution are 3D which gives improved ties at intersection points compared to processing each 2D line separately.

Residual Statics

Spectrum has a number of residual static routines, both surface consistent and CDP consistent. Highly flexible iterative techniques are often used to compute static corrections. As well as computing shot and receiver statics the user has options to compute the reflection structure, residual normal moveout (RNMO) and perform a residual phase calculation.

GLI static effect on shot gathers – example from onshore Croatia

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A pilot trace is constructed by summing together a number of stacked inline and crossline traces centred on the CDP. The seismic trace is subtracted from the pilot trace in order to remove the autocorrelation contribution of the trace. The autocorrelation contribution biases the residual statics heavily toward zero, especially when the pilot trace is formed from only a short range of CDPs in a region of poor signal-to-noise ratio.

Each un-stacked, corrected seismic trace is cross-correlated with the pilot trace from the CDP location. All cross-correlation functions from a specific receiver group are summed – the peak time is picked and utilized to form an updated estimate of the static for that group. This operation is repeated for each group and shot to yield new current estimates of residual statics which are available for the next iteration.

Residual statics can also be calculated by cross-correlating traces. There are two steps to this process;

Step 1 – Automatic picking of static shifts using a statistical method and computing the relative static shift by cross-correlating the current trace with a number of traces within a co-ordinate and offset range. The relative static shift is defined by the peak of the cross-correlation function. Three peaks on the cross-correlation function and other information are passed to step 2.

Step 2 – Uses a conjugate gradient method to solve for surface consistent shot and geophone statics, RNMO and dip. Several classes of equations are available. The trace to trace equations are derived from the correlations done in Step1. Taken alone, these consist of an over-determined, under-constrained system of equations which needs some additional information to produce a reasonable solution. This is provided by the constraint and bias equations. Constraint equations try to keep the solution within reasonable bounds.

Straight Ray Datuming

The conventional “statics correction” method to correct for time distortions introduced by the weathering layer has its limitations. It relies on assumed surface consistency, requires a vertical ray path and needs ray theory to be an acceptable approximation of near surface wave propagation.

In the presence of rapid lateral variations of the weathering layer, one or more of these conditions are not met. However, more advanced methods such as Kirchhoff Pre-Stack Re-datuming or finite difference for such corrections can also often be unfeasible. These methods can have a high computational cost and can also require highly rigorous, time consuming processing, and considerable sampling of the sources and receivers, not seen in conventional 3D land acquisition.

Spectrum offers an innovative solution to bridge the gap between these methods. Straight Ray Datuming (SRD) is an advance in statics modelling developed for commercial use by Tariq Ali Alhalifah.

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SRD kinematics are derived using geometrical optics. The figure above schematizes the rays involved in the SRD impulse response. SRD rays are selected to satisfy Snell’s law at the datum, so the impulse response depends on the velocity below the datum which can initially be set to an expected average value.

The application of Snell’s law at the interface allows the reduction of the surface integral, needed in Kirchhoff datuming, to a surface integral applied once (a stationary phase approximation). The trajectory of the summation operator depends on offset, elevation of the source and receiver, and the velocity of the weathering layer under each source and receiver.

The technique has been proven to work on both 3D and 2D acquisition.

As well as having provided an intermediate statics process, straight ray gives some additional advantages:

**• More flexibility in acquisition –** Can be applied to common shot gathers and common receiver gathers.

**• Less input – **SRD does not require detailed near surface velocity models, refraction static information or other common near surface time shift input.

**• Irregular Sampling – **SRD can also be used to spatially map irregularly sampled data into regularly sampled data at the datum

**• Noise Reduction – **As the process is a partial migration, it helps suppress diffractions generated from above datum in-homogeneities.

Marine – Water Column Statics

The variation in water velocity due to temperature and salinity changes can be compensated for by applying an appropriate static to the shot records. The way this static is calculated is to accurately measure the velocity of the seabed reflection using near offset data from one of the inner cables. The difference in the picked velocity from a reference velocity of 1480 ms-1 is mapped for each sail line and a static is worked out using the following formula:

Static = Twb{(Vwater/1480)-1}

Where Twb and Vwater are the picked times and velocity of the water bottom.

The raw static values are applied to near trace crossline stacks to check for sail line to sail line continuity and adjusted by manual editing. The final statics are then applied to the data