Risk-Targeted-Ground-Motion-Calculator-Documentation.md

-## Purpose of this Application
+# Purpose of this Application
 The Risk Targeted Ground Motion Calculator is used to calculate risk-targeted ground motion values in accordance with “Method 2” of 2010 ASCE 7 Standard Section 21.2.1.2. Users can input a hazard curve from a site-specific analysis to obtain a risk-targeted ground motion value.
 
-## Sample input
+# Sample input
 
 Application input can be user-provided or drawn from the [USGS Hazard Curve Data files](http://earthquake.usgs.gov/hazards/products/). The following example incorporates the 2008 USGS Lower 48 “Hazard Curve Data” file for “5Hz (0.2 Second)”. Specifically, the data for the coordinates (34.05, -118.25) in Los Angeles are used:
 
-### Curve Title
+## Curve Title
 This is an optional input. Users can input a string of characters (such as "Office Tower at 123 Main St.") to serve as a reminder of which output values correspond to a particular structure.
 
-### Spectral Response Acceleration Values, in units of 'g' (corresponding to the x-axis on a hazard curve):
+## Spectral Response Acceleration Values, in units of 'g' (corresponding to the x-axis on a hazard curve):
 0.005, 0.0075, 0.0113, 0.0169, 0.0253, 0.038, 0.057, 0.0854, 0.128, 0.192, 0.288, 0.432, 0.649, 0.973, 1.46, 2.190, 3.28, 4.92, 7.38
 
-### Annual Frequency of Exceedance Values (corresponding to the y-axis on a hazard curve):
+## Annual Frequency of Exceedance Values (corresponding to the y-axis on a hazard curve):
 0.5855, 0.5208, 0.4389, 0.3515, 0.2679, 0.1953, 0.1376, 0.09335, 0.06027, 0.03659, 0.02096, 0.01146, 0.005985, 0.002934, 0.001287, 0.0004781, 0.0001411, 0.00003023, 0.000003828
 
 Please note that all numeric input values should be comma separated as in the above example, and all units should be removed. In addition, users must provide an equal number of Spectral Response Acceleration values and Annual Frequency of Exceedance values.
 
-## Sample output
+# Output
 
-### Output summary (yellow box)
-This section provides the risk-targeted ground motion (RTGM) corresponding to a 1% probability of collapse in 50 years. The uniform hazard ground motion (UHGM) used as a starting point for the calculations is provided, as is the Risk Coefficient (RC) representing the ratio of RTGM to UHGM for the site of interest.
+The application uses three iterations to arrive at a ground motion value corresponding to a 1% probability of collapse in 50 years.
 
+## First Iteration
+The application begins by using the ground motion with a 2% probability of being exceeded over a 50 year time period. This value is obtained during Step 1 and is used to arrive at an initial Probability of Collapse in 50 years in Steps 2 through 5. 
 
 Five plots illustrating the step-by-step process of calculating the risk-targeted ground motion are briefly discussed below.
 
-### Hazard Curve
+### Step 1: Hazard Curve
 This is simply a graphical representation of the Spectral Response Acceleration Values (x-axis) and Annual Frequency of Exceedance Values (y-axis) provided by the user. For more information on these values, users are referred to the Documentation for the 2008 Update of the [USGS National Seismic Hazard Model] (http://pubs.usgs.gov/of/2008/1128/).
 
-### Fragility Curves
-These are generic fragility curves…
+### Step 2: Fragility Curves
+These are generic fragility curves defined by a point corresponding to a 10% probability of structural collapse and a Beta (standard deviation) value of 0.8.
 
-### Derivative of Fragility Curves 
+### Step 3: Derivative of Fragility Curves 
 These are simply the derivatives of each respective fragility curve. They are provided as a reference for the next step in the calculation process.
 
-### Hazard Curve x Derivative of Fragility Curves
-Combining the hazard curve for the site with each fragility curve produces a curve illustrating the annual collapse frequency density of a generic structure at the site of interest. This is provided as a reference for the next step in the calculation process.
+### Step 4: Hazard Curve x Derivative of Fragility Curves
+Combining the hazard curve for the site with the derivative of each fragility curve produces a curve illustrating the annual collapse frequency density of a generic structure at the site of interest. This is provided as a reference for the next step in the calculation process.
+
+### Step 5: Cumulative Integral of Hazard Curve x Derivative of Fragility Curves
+Integrating the hazard curve x derivative of each fragility curve produces the cumulative 50-year collapse probability of a generic structure at the site of interest. The "Final Iteration" is used to obtain the ground motion corresponding to a 1% probability of collapse in 50 years. 
 
-### Cumulative Integral of Hazard Curve x Derivative of Fragility Curves
-Integrating the Hazard Curve x Derivatives of Fragility Curves produces the cumulative 50-year collapse probability of a generic structure at the site of interest. 
+## Second Iteration
+If the Conditional Probability of Collapse calculated during Iteration 1 exceeds 1%, the initial ground motion value is increased for Iteration 2. If on the other hand the probability of collapse calculated during Iteration 1 is less than 1%, the initial ground motion value is decreased for Iteration 2. Steps 2 through 5 are then repeated.
 
+## Final Iteration
+With the First and Second Iterations bracketing the target probability of collapse (1%), the ground motion for the Final Iteration can be precisely selected during Step 1 to result in Steps 2 through 5 to correspond to a 1% probability of structural collapse. This ground motion value is referred to as the risk-targeted ground motion, or "RTGM". The Risk Coefficient, or "RC", is simply the ratio of the RTGM divided by the uniform hazard ground motion ("UHGM").
 
-## API Documentation
+## Output summary (yellow box)
+This section provides the risk-targeted ground motion (RTGM) corresponding to a 1% probability of collapse in 50 years. The uniform hazard ground motion (UHGM) used as a starting point for the calculations is provided, as is the Risk Coefficient (RC) representing the ratio of RTGM to UHGM for the site of interest.
+
+# API Documentation
 
 This page describes the process for creating a request and also defines the terms used in the response output. Additionally some examples are provided to help get you started.
 
-### Request API
+## Request API
 
 http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/x0,x1,...xN/y0,y1,...yN[/callback]
 
@@ -57,7 +66,7 @@ callback
 
 Note: All input hazard curve data must be adjusted with max-direction factors by the user before using the data in this application.
 
-### Response API
+## Response API
 
 {
 	status: Response Code,
@@ -120,10 +129,9 @@ originalHCMax
     Number
     The largest input spectral response acceleration value. This is useful for determining if a resulting spectral acceleration value in the upsampled hazard curve is based on extrapolation. 
 
-### Examples
+## Examples
 
     Example 1: JSON request, no callback is specified. Note the content-type header in the response.
     http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/0.01,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.4,1.7,2/0.5696,0.088335,0.02925,0.01229725,0.00564925,0.00275075,0.001385175,0.000733875,0.0003984225,0.0002205625,0.0001235975,6.881825E-5,3.82493775E-5,1.13329875E-5,1.34645E-6,6.4884E-8
     Example 2: JSONP request, a callback is specified. Note the content-type header in the response. The response for this request is wrapped in the specified javascript callback.
     http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/0.01,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.4,1.7,2/0.5739,0.09486,0.032775,0.0143475,0.00689675,0.00349925,0.001878025,0.0010358,0.00059415,0.00034517,0.0002041625,0.00012253,7.213325E-5,2.5567215E-5,4.81976025E-6,7.196E-7/processData
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