(adjustment_section)=

Adjusting with Depth and Pressure

The dry_rock model can be adjusted according to depth and pressure:

dry_rock:
    model:
        # model type is one of:
        #  * polyfit
        #  * friable_sand
        #  * patchy_cement
        type: polyfit
    porosity:
        # porosity of dry rock gotten from column in csv file
        column: porosity
    # Default polyfit coefficients is used which is:
    # density: [[0.0, 0.0], [1.0, -1.0]]
    # bulk_modulus: [[2900.0, -1300.0]]
    # shear_modulus: [[1700.0, -800.0]]
    # In  dry_rock, effective reference pressure is used:
    # pressure = min(max_pressure, overburden_pressure - reference_pressure)
    adjustments:
       - type: pressure_dependency
         # In pressure dependency effective rock pressure is used:
         # pressure = min(max_pressure, overburden_pressure - rock_pressure)
         # With the exception of the powerfit model which uses rock pore pressure:
         # pressure = rock_pressure
         model:
              # model type is one of:
              # * polyfit
              # * expfit
              # * logfit
              # * powerfit
              # * patchy_cement
              # * friable_sand
             type: powerfit
             coefficients:
                # adjusted_bulk_modulus = original_bulk_modulus +
                #         20.0 * delta_pressure^-40.0
                bulk_modulus: [20.0E+9, -46.0]
                # adjusted_shear_modulus = original_shear_modulus +
                #         12.0 * delta_pressure^-20.0
                vp_over_vs: [12.0, -26.0]
                # adjusted_density = original_density
                density: [1.0, 0.0]
       - type: depth_trend
         depth:
           column: depth
         reference_depth: 0.0
         max_depth: 4000.0
         # delta_depth = min(depth - reference_depth, max_depth)
         # coefficients in a 2d polynomial which
         # adjusts dry rock properties to depth
         coefficients:
           # adjusted_bulk_modulus = c[i][j] * delta_depth^i * original_bulk_modulus^j
           bulk_modulus: [[0.0, 1.5], [1.0, 0.0]]
           # adjusted_shear_modulus = c[i][j] * delta_depth^i * original_shear_modulus^j
           shear_modulus: [[0.0, 1.2], [1.0, 0.0]]
           # adjusted_density = c[i][j] * delta_depth^i * original_density^j
           density: [[0.0, 1.35], [1.0, 0.0]]

In the above example, the dry_rock material changes both with depth and pressure according to the depth_trend and pressure_dependency adjustment. Depth trend simply adjusts the material according to a two dimensional polynomial (see the above example for details).

Pressure Dependency

The models for pressure dependency is one of polyfit, expfit, logfit, powerfit, patchy_cement, and friable_sand. These are used to calculate three factors: f_density, f_1 and f_2.

First the dry rock properties are calculated. Then the pressure depenency at reference pressure and at effective pressure is calculated and the final adjust dry rock properties are as follows, except for powerfit which we will discuss last:

adjusted_density = density * (fd(effective_pressure) / fd(reference_pressure))
adjusted_bulk_modulus = bulk_modulus * (f1(effective_pressure) / f1(reference_pressure))
adjusted_shear_modulus = shear_modulus * (f2(effective_pressure) / f2(reference_pressure))

If velocity coefficients are given to the model then the above calculation is carried out with primary_velocity and secondary_velocity instead of bulk_modulus and shear_modulus. Except for the friable_sand and patchy_cement models which always use moduli.

The models polyfit, friable_sand, and patchy_cement are the same models used in the dry_rock section. The factors calculated from these models are the density, bulk_modulus and shear_modulus for the corresponding dry_rock model, ie.

f_d=density
f_1=bulk_modulus
f_2=shear_modulus

Given that you have the following coefficient section:

 coefficients:
    bulk_modulus: [cb1, cb2, cb3]
    vp_over_vs: [cv1, cv2, cv3]
    density: [cd1, cd2, cd3]

The expfit model is:

f_d = cd1 + cd2*e^(pressure/cd3)
f_1 = cb1 + cb2*e^(pressure/cb3)
f_2 = cv1 + cv2*e^(pressure/cv3)

The logfit model is:

f_d = cd1 + cd2*log_10(pressure)
f_1 = cb1 + cb2*log_10(pressure)
f_2 = cv1 + cv2*log_10(pressure)

Finally, powerfit calculates adjusted dry_rock in a quite different way from the other models. It uses vp_over_vs coefficients:

coefficients:
  bulk_modulus: [cb1, cb2]
  vp_over_vs: [cv1, cv2]
  density: [cd1, cd2]

Which is used to calculate the following factors:

fd = cd1 + pressure ^ cd2
f1 = cb1 + pressure ^ fb2
f2 = cv1 + pressure ^ fv2

Then an adjusted vp_over_vs is calculated:

adjusted_vp_over_vs  = vp_over_vs + f2(effective) - f2(ref)

And the final adjusted values are calculated from that:

adjusted_density = density + fd
adjusted_bulk_modulus = bulk_modulus + f1(eff) - f(reff)
adjusted_shear_modulus = bulk_modulus / ((vp_over_vs + f2(effective) - f2(ref))^2 - 4/3)