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CRS Stack Using Global Simultaneous Multi-parameter Optimization –

A Spatial Velocity Analysis for Near-surface Data.

Z. Heilmann*, G. Satta* and G.P. Deidda***CRS4, Energy and Environment Sector

**University of Cagliari, Department of Civil and Environmental Engineering, and Architecture

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Outline

Part 1: A spatial velocity analysiso Motivation, Concepto Different Implementations

Part 2: Real data exampleo Velocity Analysis & Stacko Tomography & Migration

Conclusions

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PART 1:SPATIAL STACKING

& VELOCITY ANALYSIS

CMP-by-CMP velocity analysis:

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Figure taken from Perroud and Tygel 2005. NMO velocity analysis for a CMP.

𝑡𝐶𝑀𝑃2 (h )=𝑡02+

4h2

𝑣𝑁𝑀𝑂2

Spatial velocity analysis:fitting a reflection surface within an offset and midpoint range

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offset

Time

midpoint

CRS stacking operator:Hyperbolic reflection traveltime:

Figure: Müller 1999, PhD thesis

CRS stacking operator:Hyperbolic reflection traveltime:

CRS velocity analysis:find which parameterize the best fitting operator

Figure: Müller 1999, PhD thesis

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The classical approach is Pragmatic search:

3 x 1 parameter line search in specific gathers (Mann et al. 1999, JAG)

One step search:1 x 3 parameter surface search in prestack data (Garabito et al. 2001)

How is the velocity analysis actually done?

Figure: Mann 2002, PhD thesis

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The straight forward solution isOne step search:

1 x 3 parameter search in the prestack data (e.g. Garabito et al. 2007, SBGf

Meeting)

One step search:1 x 3 parameter surface search in prestack

data (Garabito et al. 2001)

How is the velocity analysis actually done?

α𝑹𝑵𝑰𝑷

𝑹𝑵

Coherence (, ,)

Figure: Mann 2002, PhD thesis

Computational cost -- a rough evaluation

3x1 Pragmatic

1x3 One step

Computational effort

10+10+10 10*10*10 Coherence calculations1 5 CMPs per Coherence

30 5000 Total effort1 166 Relative effort

Assuming: 10 point per dimension grid search without refinement, 5 CMPs per CRS aperture.

Isn’t there anything thing in between?

Sensibility analysis:Hyperbolic reflection traveltime:

Each curve corresponds to the traveltime deviation for a tested parameter value shifted from ±1 to ±10% from the exact value. Blue curves refer to a1, green curves refer to a2, and red curves refer to b2.

a1 is related to the reflector dip, a2 is related to the reflector curvature, while b2 is related to the stacking velocity

Figure: Perroud et al. 2014, NSG

NIP wave theorem:According to the NIP wave theorem (Hubral, 1983), the reflection traveltimes in the CMP gather are up to second order in half-offset h equal to the diffraction traveltimes, which correspond to a diffractor at the normal incidence point (NIP) of the associated normal ray.

Taken from: Seismic True-amplitude Imaging by J. Schleicher, M. Tygel, P. Hubral

Common Diffraction Point operator:Hyperbolic diffraction traveltime:

Figure: Müller 1999, PhD thesis

Hybrid diffraction/reflection search**modified after Garabito et al. 2001, SEG Meeting.

1. Global search with “Common Diffraction Point” operator

2. Local optimization with “Common Reflection Surface” operator

Advantages:● Global search is applied directly to the prestack data using a

spatial operator that extents in offset and midpoint direction● Velocity analysis using the two parameter CDP operator is one

order of magnitude faster compared to the three-parameter CRS operator.

3x1 Pragmatic

1x3 One step

1x2 One step

Computational effort

10+10+10 10*10*10 10*10 Coherence calculations1 5 5 CMPs per Coherence30 5000 500 Total effort1 166 16.6 Relative effort

Computational cost -- a rough evaluation

Assuming: 10 point per dimension grid search without refinement, 5 CMPs per CRS aperture.

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PART 2:DATA EXAMPLE

SHALLOW SH-WAVE SURVEY

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Ultra shallow seismic data:Aim of survey:

1. delineation of overburden-bedrock surface and reflectors within the overburden,

2. estimation of geotechnical properties of overburden from wave velocities

Survey attributes:

type: SH-wave reflection seismics

source: 70 kg steel plate with ground grippers

receiver: 100 Hz horizontal detectors

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Survey geometry:n-receiver = 24rec. spacing = 0.5 m

n-shot = 61shot spacing = 0.5 m

n-cmp = 144cmp spacing = 0.25cmp fold = 12

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CMP gathers 90-94:

offset [cm]

time [s]

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CMP stacking results:

CMP stack after CVS analysis

CMP 90-94

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Stacking results:

CRS stack using global 1x3 reflection search + local 1x3 optimization

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Stacking results:

CRS stack using global 1x3 reflection search + local 1x3 optimization

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Stacking results:

CRS stack using global 1x2 diffraction search + local 1x3 optimization

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Stacking results:

CRS stack using global 3x1reflection search + local 1x3 optimization

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NMO velocities, calculated using and :

CRS stack using global 3x1reflection search + local 1x3 optimization.

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NMO velocities, calculated using and :

CRS stack using global 3x1reflection search + local 1x3 optimization.

Event consisting smoothing

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NMO velocities, calculated using and :

CRS stack using global 3x1reflection search + local 1x3 optimization.

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NMO velocities, calculated using and :

CRS stack using global 1x3 reflection search + local 1x3 optimization

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NMO velocities, calculated using and :

CRS stack using global 1x2 diffraction search + local 1x3 optimization

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NIP-Tomography:

Slide credit: Duveneck, 2003, SBGf Meeting

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NIP-Tomography – Shallow picks

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NIP-Tomo. – Shallow + Intermediate picks

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NIP-Tomo. – Shallow, Interm. & Deep picks

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Velocity model – Shallow picks

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Velocity model – Shallow + Intermediate picks

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Velocity model – Shallow, Interm. & Deep picks

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Prestack depth migration result:

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Poststack depth migration result:

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Conclusions:

• Single-CMP-based velocity analysis has no physical justification dealing with dipping or curved reflectors and diffraction points

• Instead, spatial velocity analysis uses all traces with energy reflected by a common-reflection-surface surrounding the NIP of the central ZO ray

• The many times larger fold (number of traces) makes spatial velocity analysis more stable and reliable

• Using for the global stacking parameter search a 2-parameter diffraction operator instead of the full 3-parameter reflection operator reduces the computational effort drastically without significant drawbacks

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Thank you for your attention!