Processing (seismic)

CMP arrangement and runtime differences (normal move out)

The processing is the processing of seismic data in seismic reflection investigations. It is carried out in order to obtain a meaningful geological image of the subsurface from the raw data of a seismic experiment. In a seismic experiment, two- way travel times ( TWT ) are recorded, i.e. the time from the delivery of the pulse at the seismic source down to the reflector and back to the surface of the earth to the geophone . The data must be processed so that from the time measurement information is the depth of the reflectors to successful drilling (e.g., in. Hydrocarbon - Exploration ) or deep-related findings in the geological and geophysical basic research to enable.

Preprocessing

For the subsequent processing, the measured data are first sorted in common midpoint collects .

The subsequent preprocessing includes the analog bandpass filtering of the signal, static corrections and the deconvolution of the signal.

Band pass filtering

The band pass filter consists of a high pass filter and a low pass filter . When digitizing the analog seismic signal, aliasing effects can occur. This happens when the sampling theorem has been violated and the sampling frequency chosen is too low. To prevent this, an analog low-pass filter is used before the signal is sampled. In addition, a high-pass filter is used to suppress noise , mains hum and long-period components of surface waves .

Static correction

The static correction reduces the seismic experiment to a reference level, as the top layer of the subsoil (weathering layer) has height differences and strong velocity inhomogeneities . To calculate the static correction one needs the thickness and the seismic speed of the layer between the reference level and the surface. These can be determined using refraction seismics on the near-surface layers or a seismic source in a borehole . In marine seismics, static corrections are necessary in order to compensate for the influence of the tides and different depths of the receiver and source.

Speed ​​analysis

model	Speed ​​increment
Horizontal reflector	${\displaystyle v}$
n horizontal reflectors	${\displaystyle v_{RMS}}$
Inclined reflector	${\displaystyle {\frac {v}{\cos \zeta }}}$
Any model	${\displaystyle {\sqrt {\frac {1}{t_{0}\cdot {\frac {{\text{d}}^{2}t}{{\text{d}}x^{2}}}}}}}$

The Normal MoveOut (NMO) is the deviation of the running times from the operating time. The speed analysis must be performed before further processing of the seismic data in order to determine and correct the normal MoveOut. The runtime curve of a seismic wave results from . The MoveOut speed includes both the type of wave and the model assumption (see table). ${\displaystyle t^{2}=t_{0}^{2}+{\frac {x^{2}}{v_{NMO}^{2}}}}$ ${\displaystyle v_{NMO}}$

Speed ​​determination

t –Δ t method

The - method is based on the parabolic approximation . The underlying equation is . Now you apply against and can calculate the MoveOut speed from the slope . ${\displaystyle t}$ ${\displaystyle \Delta t}$ ${\displaystyle 2t_{0}\Delta t_{n}\approx {\frac {x^{2}}{v_{NMO}^{2}}}}$ ${\displaystyle 2t_{0}\Delta t_{n}}$ ${\displaystyle x^{2}}$ ${\displaystyle {\frac {1}{v_{NMO}^{2}}}}$

t ² - x ² method

The - method is more accurate than the - method because it is based on the hyperbola approximation. You can enter the runtime curve in a - diagram and determine the speed. As with the - method, the slope of the straight line is . ${\displaystyle t^{2}}$ ${\displaystyle x^{2}}$ ${\displaystyle t}$ ${\displaystyle \Delta t}$ ${\displaystyle t^{2}}$ ${\displaystyle x^{2}}$ ${\displaystyle t}$ ${\displaystyle \Delta t}$ ${\displaystyle {\frac {1}{v_{NMO}^{2}}}}$

Dynamic correction

The dynamic NMO correction reduces the runtime curve to the operating time depending on the offset. An NMO correction is carried out for each CMP gather . This gives a rough estimate of the seismic velocities in the subsurface, but poses problems. The NMO correction is a non-linear stretching of the time axis along the offset. Accordingly, the signal is stretched with increasing offset (NMO stretch) and the frequency is reduced. ${\displaystyle t_{0}}$

The data is corrected for the NMO stretch by applying a linear filter that sets the proportions in the gather to zero. The data is now ready to be stacked .

Average speed

To determine the average speed, geophones are sunk into a borehole and a seismic source is ignited next to the borehole ( vertical seismic profiling ). The average speed describes the geometrically shortest path from the source to the point of reflection.

${\displaystyle v_{a}={\sqrt {\frac {\sum \limits _{k=1}^{n}z_{k}}{\sum \limits _{k=1}^{n}{\frac {z_{k}}{v_{k}}}}}}}$

Effective speed

The root mean square is the root mean square of the speed.

${\displaystyle v_{RMS}={\sqrt {\frac {\sum \limits _{k=1}^{n}z_{k}\cdot v_{k}}{\sum \limits _{k=1}^{n}{\frac {z_{k}}{v_{k}}}}}}}$

Interval speed

The interval speed results from the Dix-Dürbaum-Krey formula:

${\displaystyle v_{n}^{2}={\frac {(v_{RMS}^{n})^{2}\cdot t_{0}^{n}-(v_{RMS}^{n-1})^{2}\cdot t_{0}^{n-1}}{t_{0}^{n}-t_{0}^{n-1}}}}$

${\displaystyle v_{n}}$is the speed of the layer between and . For a homogeneous layer is the layer speed and for a layered area is the effective speed ${\displaystyle t_{0}^{n}}$ ${\displaystyle t_{0}^{n-1}}$ ${\displaystyle v_{n}}$ ${\displaystyle v}$ ${\displaystyle v_{n}}$ ${\displaystyle v_{RMS}}$

Stacking speed

The stacking speed together with the pseudo usage time gives the runtime curve ${\displaystyle t_{0s}}$

${\displaystyle t_{s}={\sqrt {t_{0s}^{2}+{\frac {x^{2}}{v_{s}^{2}}}}}}$.

This hyperbola approaches the true runtime curve in such a way that the surfaces of the positive and negative deviations are balanced. The stacking speed and the pseudo usage time vary with the offset of the runtime curve.

Automatic speed analysis

The - method must be done manually, it cannot be automated, nor is it objective. However, these demands are placed on modern processing algorithms. ${\displaystyle t^{2}}$ ${\displaystyle x^{2}}$

Constant Velocity Scan

Constant speeds from an adequate speed range are used to apply an NMO correction. Then the speed is selected for each reflection, which shifts the MoveOut times to the deployment time. This method has to be evaluated visually and is very subjective , especially if the signal-to-noise ratio is poor .

Constant Velocity Stack

With the Constant Velocity Stack or Brute Stack, constant speeds from a speed range are used again to apply the NMO correction to the CMP-Gather. Then the individual tracks of the CMP are added up. Destructive superimpositions cause runtime curves that are corrected with the wrong NMO speed to be erased during the summation (stacking). If all MoveOut times are in phase with the deployment time, the amplitude of the resulting track is greatest and the selected speed is optimal.

This method still has to be evaluated visually and is subject to a certain subjectivity.

Speed ​​spectrum

Velocity analysis with Seismic Unix

The calculation of speed spectra automates the selection of the speed function . ${\displaystyle v(t_{0})}$

The NMO correction is applied to a speed for each operating time . The semblance coefficient is then calculated for a time window um . ${\displaystyle v}$ ${\displaystyle S}$ ${\displaystyle t_{0}}$

${\displaystyle S={\frac {\sum \limits _{i=1}^{M}\left(\sum \limits _{j=1}^{N}a_{ij}\right)^{2}}{N\sum \limits _{i=1}^{M}\sum \limits _{j=1}^{N}a_{ij}^{2}}}}$

Here, N denotes the number of tracks in the CMP-Gather and M the number of discrete values ​​in the j-th track. The semblance coefficient normalizes the energy of the incoming track to the energy of all tracks, which is why it can only assume values ​​between 1 and 0. This calculation is repeated for all and all and entered in a diagram. The function for the speed spectrum is obtained. The highest semblance coefficient, which characterizes the optimal stacking speed, can now be selected automatically for each reflection. ${\displaystyle t_{0}}$ ${\displaystyle v_{NMO}}$ ${\displaystyle (v,t_{0})}$ ${\displaystyle S(v,t_{0})}$

The semblance coefficient is a measure of the coherence and is used because of the high resolution in time and speed.

Result of the speed analysis

From the speed analysis and NMO correction of the CMP-Gather with subsequent stacking, one obtains a time section from plumbing times, also called zero-offset section or stacking section. These simulate a vertical incident beam from the source to the reflector. The data volume is reduced by the factor of the degree of coverage of the CMP gate.

migration

Non-migrated synthetic zero-offset section with triplication.

Migration (from Latin: migratio , migration, relocation) in seismic refers to the process of creating an underground image from the measured wave field on the surface.

The aim of the migration is to use the reflections in the subsurface to create a geological image of the subsurface with the correct inclinations, lengths and positions of the reflectors.

motivation

CMP gathers can contain triplications and other intersecting layers that do not occur geologically. In addition, these times are migrated to depths in order to enable exact drilling.

Types of migration

Various criteria can be used to distinguish migration.

On the one hand, a distinction is made between time migration into space and deep migration into space. The depth migration reacts more sensitively to errors in the speed model of the subsurface and, in contrast to time migration, provides an authentic image of the subsurface. On the other hand, a distinction can be made between prestack and post-stack migration. Poststack migration is done after speed analysis and stacking. The prestack migration takes place before the speed analysis and the stacking in order to also take into account the amplitudes of the incoming signals. ${\displaystyle (x,t)}$ ${\displaystyle (x,z)}$

Through more specific prestack migrations, statements can be made about the reflection coefficients in the subsurface.

See also

• Runtime diagram
• Refraction seismics

literature

• O. Yilmaz: Seismic data processing. Society of Exploration Geophysicists, Tulsa 2001, ISBN 0-931830-40-0 .
• Dirk Gajewski: Lecture notes: Applied Geophysics II. (PDF; 32.5 MB) Hamburg 2010, accessed on February 26, 2010.
• Claudia Vanelle: Lecture notes: Migration. Hamburg 2009; Chapter 1 (PDF) Chapter 2 (PDF) Chapter 3 (PDF); Retrieved February 26, 2010.