How We Do It
Introduction  Because shale reservoirs are generally anisotropic and heterogenous, a primary concern in microseismic data processing is velocity model complexity. A reservoir is said to be anisotropic when signal wavelength is much longer than the aligned heterogeneities in the media. This can result from intrinsic properties of the formation (clay platelets orientation) or induced fractures and stress fields. If the reservoir contains heterogeneities whose scale is much larger than signal wavelength, a competent velocity model should not assume homogeneity.
Velocity models can approximate reservoir characteristics by using layered profiles, where each layer is separated by the strong contrast of its elastic properties. An initial velocity model is usually derived from log data, core samples, perforation shots, and surface seismic data. That initial model is input for inversion, but then dynamic ray tracing can model arrival times and polarities of different phases during eventlocation/velocitymodel joint inversion. The velocity profile is general enough to cover the complex structures of a reservoir, where layers are separated by dipped interfaces and the elastic parameters can be anisotropic with rotated symmetric axes.
Upscaling  Standard sonic logs can provide Pwave and Swave velocities along the well direction (approximately vertical) at sonic scale (several kHz). To obtain a reasonable initial velocity model from log data, the scale problem must be considered. The central frequency of a typical microseismic event is often around 150 ~ 200 Hz, while log velocity is measured at several thousand hertz. Such measurements provide great detail for a velocity model. When an elastic wave generated by an event propagates through fine structures, the wave will be scattered by heterogeneities. As mentioned above, if the heterogeneities are of a much smaller scale than the wavelength, the media can be described by an equivalent medium which is homogeneous and anisotropic. This process is called “upscaling,” where the detailed structure is being averaged to a much larger scale.
Logging velocity needs to be “upscaled” to seismic frequency range before being used in modeling – and this process is not trivial. The upscaling method can range from simple arithmetic averaging to a more versatile rock physics modeling method. Generally speaking, a window is defined and then slides throughout the whole depth range of the log data, while the properties within each window are averaged. Finally, a smoothed velocity profile for the seismic frequency range is obtained. Practically, the choice of upscaling method is often determined by the available data. Sonic logs can only provide velocities along the vertical axis and, if that is the only available data, the process can start with an isotropic layered model or layered VTI model. If additional logs or core sample measurements are available (providing information about porosity, mineral composition, shale content, fracture, and water saturation), theoretical rock physics models can predict the full elastic tensor from these data.
Research indicates that the highest symmetry of a fractured rock is orthorhombic. If unfractured rocks are intrinsically anisotropic (e.g., shale), the resulting symmetry will be lower than orthorhombic when the rocks are fractured. An anisotropic initial velocity model can therefore describe true reservoir characteristics more accurately. 

Seismic Data  Various kinds of seismic surveys will provide useful information in building an initial velocity model. The standard practice in building an initial model is to calibrate the interface geometry, or even elastic parameters, with perforation shots. The effectiveness of this method can be limited by the fact that rays generated by perforation shots are likely to cover very limited aperture, and such inadequate information is not enough to calibrate a full velocity model. Borehole Seismic, LLC employs a method in which perforation shot data can be included during inversion with all available events, providing much larger coverage. If interface geometry is known by other methods (reflection or other surface seismic survey), that can also be included in the model.
The Importance of an Accurate Initial Model  Although an initial velocity model will be updated during inversion, there may be local minima in the objective function, and this suggests that it is necessary to start with a decent velocity model and assess bounds on that model’s parameters during inversion. Our inversion method is robust and likely to converge upon a true solution for even noisy data, but an accurate starting model allows inversion to converge faster – greatly reducing processing time and costs.

Determining Complexity of Model for Each Layer  Borehole Seismic™ Reprocessing uses the following guideline for determining anisotropic complexity of layers. Ray coverage and SVD analysis are the primary tools used. To start, we look at the models and their stiffness tensor definitions (in order of complexity):
1. Isotropic Layer
This is the simplest layer. It has two unknown variables and uses the following stiffness tensor: 
2. VTI
This has 5 unknown variables and uses the following stiffness tensor: where,
C66 = (C11 – C12)/2. 
3. ORT
Nine unknown variables and uses the following stiffness tensor: 
4. MNC
Sixteen unknown variables and uses the following stiffness tensor: 
5. TRI
Twentyone unknown variables and is the most complex model, using the following stiffness tensor: 
The first step is to calculate an initial location point first, which can be the location of the perfs or taking the data we have into account. Using the initial location we find the azimuthal ray coverage. Using the azimuthal ray coverage figure, and taking other parameters into consideration, we decide the complexity of each layer:
For, e.g.,
It is evident in the above example that ray coverage for the model is low. We therefore go for a simple model (e.g., the isotropic model) to evaluate this layer.

For, e.g.,
Because the ray coverage in the above example is pretty high, we can consider a more complex model for this layer. Choosing model complexity can involve trialanderror, and can be based upon client instruction (e.g., if the client says ORT, we use ORT).

To decide whether the model chosen is apt, we do SVD analysis:
If the smallest singular values of the SVD analysis plot are very small (< 5), or the condition number during the inversion is greater than 500, this is an indication that some parameter cannot be constrained by the model and a simpler form of anisotropy should be used. (NOTE: For singlemonitorwell jobs, we assume that the PWave polarization is in the same direction as the ray direction. To keep this assumption consistent, we only consider a VTI or ISO model for all layers.)
Would you like to know more? Take a look at our first steps before joint inversion.
¹ Grechka, V. and Yaskevich, S. (2014), Azimuthal anisotropy in microseismic monitoring: A Bakken case study. 79 Geophysics 1, 1115. doi: 10.1190/geo20130211.1
² See Grechka, V. and Yaskevich, S. (2013), Inversion of microseismic data for triclinic velocity models. Geophysical Prospecting 61: 1159–1170. doi: 10.1111/13652478.12042
³ Grechka, V. and Yaskevich, S. (2014), Anisotropic Velocity Model Building in Microseismic Monitoring. GSH Journal 4.5, 1115.
² See Grechka, V. and Yaskevich, S. (2013), Inversion of microseismic data for triclinic velocity models. Geophysical Prospecting 61: 1159–1170. doi: 10.1111/13652478.12042
³ Grechka, V. and Yaskevich, S. (2014), Anisotropic Velocity Model Building in Microseismic Monitoring. GSH Journal 4.5, 1115.