logback JSON - print log timestamp in Epoch time format(in seconds)

I have the following in my logback.xml for logging in JSON. I want to print the log_timestamp field below in Epoch time format(in seconds) instead of the date and time.

<appender name="JSON_CONSOLE" class="ch.qos.logback.core.ConsoleAppender">
    <encoder class="net.logstash.logback.encoder.LoggingEventCompositeJsonEncoder">
        <providers>
            <pattern>               
                   <pattern>                       
                        {
                          "appNname": "${appName}",
                          "log_timestamp":"%date",
                          "level": "%level",
                          "method":"%M",
                          "class":"%c",
                          "user_id": "%mdc{user_id}"
                        }    
                   </pattern>
            </pattern>
        </providers>
    </encoder>
</appender>

The question is related to print an epoch timestamp instead of the date and time

I tried the suggestion in the above link by including the following directly under the encoder.But it didn't work.

<encoder class="net.logstash.logback.encoder.LoggingEventCompositeJsonEncoder">
   <layout class="net.logstash.logback.layout.LogstashLayout">    
     <timestampPattern>[UNIX_TIMESTAMP_AS_NUMBER]</timestampPattern>
   </layout>

I appreciate if someone gives me a hint to achieve this.

Since logback's %date conversion word does not support epoch time, you'll need to use logstash-logback-encoder's timestamp provider to add the timestamp field.

<appender name="JSON_CONSOLE" class="ch.qos.logback.core.ConsoleAppender">
    <encoder class="net.logstash.logback.encoder.LoggingEventCompositeJsonEncoder">
        <providers>
            <timestamp>
                <fieldName>log_timestamp</fieldName>
                <pattern>[UNIX_TIMESTAMP_AS_NUMBER]</pattern>
            </timestamp>
            <pattern>               
                   <pattern>                       
                        {
                          "appName": "${appName}",
                          "level": "%level",
                          "method":"%M",
                          "class":"%c",
                          "user_id": "%mdc{user_id}"
                        }    
                   </pattern>
            </pattern>
        </providers>
    </encoder>
</appender>

Note that the timestamp value will be in milliseconds, not seconds.

If you want seconds, then I think the only way would be to implement a custom JsonProvider