# Seismic resolution: Vertical and Horizontal

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### Overview

Seismic resolution is the ability to distinguish between two features from one another. There are two types of seismic resolution, being vertical and horizontal. Vertical resolution determines the thickness of the beds, such as two close seismic responds corresponding to different depth levels. Vertical resolution represents the distance between two interfaces as separate reflectors. Horizontal resolution determines the termination of beds by using seismic reflection. Horizontal resolution recognizes two lateral displaced features on the single interface.

### Vertical Resolution

The Rayleigh’s Limit of Resolution states that two events should be separated by half cycle model. To solve for thickness ∆h ≥ λ/4. To resolve for two interfaces that are closely spaced the wavelength is λ/4. For bed thickness that is less than λ/4, amplitude and bed thickness become judgmental values. For bed thickness more than λ/4, the wavelength is used to determine the bed thickness.

Vertical resolution can be calculated from the length of the propagation wave and the layer thickness below 1/4 wavelength for resolving limits of beds. It is possible to detect layers down to 1/32 wavelength. Vertical resolution can vary from shallow to great depth. The shallow depth considers 10-15m and the great depth considers 20-30m.

The Widess model represents the relationship of the wavelength and bed thickness. The thickness of the bed model is resolvable where wavelength is equal or greater until wavelength/4. The beds that wavelength is thinner then wavelength/4, there is no distinct reflection, the vertical resolution is limited. When compared to the bed thickness of 1/8 the reflection from the top and bottom create an amplitude of large value. One of the methods to resolve thin bed is to increase frequency during processing data. Since, wavelength depends on velocity and frequency. The velocity of the thin beds is an independent property that cannot be changed. The only changes that can be applied is to change frequency. The wavelength becomes the indicator for vertical resolution.

The Widess model shows that beds with thickness below λ/8 of wavelength are not affected by frequency significantly. The only changes that are associated with thickness is amplitude of the reflection as thickness of the beds decrease. Thus, the limit of vertical resolution becomes the λ/8. The more recent model of Tirado suggested that peak frequency variation is a function of bed thickness, as bed thickness decreases, peak frequency increases.

### Horizontal Resolution

Horizontal resolution is much poorer when compared to vertical resolution. The poorer resolution is due to a focusing issue. As a result, energy does not return from the single reflection point, it creates finite region of point that influence the reflection. The reflection contains energy from the finite region of points. This region that reflected the energy has a phased difference by half-cycle. This energy creates constructive interference. This region called a Fresnel zone. The reflecting zone in the subsurface is transitive by the first λ/4. If the wavelength is larger than λ/4 from the zone where energy was reflected, then the resolution is lower.

As the propagation wave moves from the source spreading into three dimensions over a large area, the further it gets from the source the larger the radius at a certain depth. The Fresnel zone defines horizontal resolution by the seismic signal at the certain depth. Fresnel zone radius can be calculated by the formula.

Seismic wave that are spread from the source are spherical and when propagated through the interfaces they produce a coherent reflection. Those waves contain a range of frequency that lie on certain interface and creates an individual frequency between areas of contact that cause the reflection.

Horizontal resolution depends not only on the Fresnel zone, but also on the type of the interface. The interface with width less than λ/4 cannot be resolved. Thus, Fresnel zone becomes an indicator for horizontal resolution. The interface characteristics may result in poor imaging quality where waves propagating through faults, erosional unconformities, cracks, salt bodies, folding, concave and convex interfaces produce strong and poor reflections. In structures such as anticlines, there is loss in amplitude because of low reflection, whereas structures such as syncline have a strong amplitude as a strong reflection. Fresnel zone depends on other factors such as seismic wavelength and depth in two-dimension. Fresnel zone is small at a shallow depth but gradually increases at a greater depth. As the goal of horizontal resolution to resolve for small geological features Fresnel zone must be reduced. The migration process reduces the Fresnel zone and improves horizontal and vertical resolution.

Migration is achieved by repositioning the reflector to the true location in the subsurface. This process helps to overcome faults, cracks, erosional unconformities and other complex geological features. Migration processes also collapse diffusion that result in increase of spatial resolution and create a true reflection amplitude. Due to the Fresnel zone before the migration process, a hundreds meter width can be reduced to tens of meter of migrated data.

### Conclusion

Aspects that control seismic resolution are velocity, frequency and wavelength. Seismic waves that travel to great depth will result in decrease in frequency, whereas their velocity and wavelength will increase. As the frequency decreases, seismic resolution will decrease as a result. At the shallow depth there is high frequency, where at the great depth there is low frequency and low resolution. Thus, frequency is controlled by the geology. The greater the depth, the sediment is more compacted and for this reason velocity and wavelength will increase.